Assuming that the debt financing costs do not change, what effect would a shift to a more highly leveraged capital structure consisting of 50% longterm debt, 0% preferred stock, and 50% common stock have on the risk premium for Eco's common stock? What would be Eco's new cost of common equity?
Assuming that the debt financing costs do not change, what effect would a shift to a more highly leveraged capital structure consisting of 50% longterm debt, 0% preferred stock, and 50% common stock have on the risk premium for Eco’s common stock? What would be Eco’s new cost of common equity?
This is the Team Assignement. This Portion of the assignment is mine. Please do in Excel and must be complete by Sunday 11.00PM (Due in 45 hours. I will also post what other member of the team has done… Tomorrow I will be on a flight all day. So cannot respond to email till Sunday morning(24hours from now)
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Resource: Principles of Managerial Finance, Ch. 9
Complete the Spreadsheet Exercise on p. 390, and The Interactive Case 4 Eco Plastics in Ch 9.
Create a spreadsheet with two tabs. Use one tab for the Spreadsheet Exercise on p. 390, and the other tab for The Interactive Case 4 Eco Plastics.
MY PORTION OF THE ASSIGNMENT:
f.
 (1) Assuming that the debt financing costs do not change, what effect would a shift to a more highly leveraged capital structure consisting of 50% longterm debt, 0% preferred stock, and 50% common stock have on the risk premium for Eco’s common stock? What would be Eco’s new cost of common equity?
 (2) What would be Eco’s new weighted average cost of capital?
 (3) Which capital structure–the original one or this one–seems better? Why
CHAPTER 9
9 The Cost of Capital
Learning Goals
 LG 1 Understand the basic concept and sources of capital associated with the cost of capital.
 LG 2 Explain what is meant by the marginal cost of capital.
 LG 3 Determine the cost of longterm debt, and explain why the aftertax cost of debt is the relevant cost of debt.
 LG 4 Determine the cost of preferred stock.
 LG 5 Calculate the cost of common stock equity, and convert it into the cost of retained earnings and the cost of new issues of common stock.
 LG 6 Calculate the weighted average cost of capital (WACC), and discuss alternative weighting schemes.
Why This Chapter Matters to You
In your professional life
ACCOUNTING You need to understand the various sources of capital and how their costs are calculated to provide the data necessary to determine the firm’s overall cost of capital.
INFORMATION SYSTEMS You need to understand the various sources of capital and how their costs are calculated to develop systems that will estimate the costs of those sources of capital as well as the overall cost of capital.
MANAGEMENT You need to understand the cost of capital to select longterm investments after assessing their acceptability and relative rankings.
MARKETING You need to understand the firm’s cost of capital because proposed projects must earn returns in excess of it to be acceptable.
OPERATIONS You need to understand the firm’s cost of capital to assess the economic viability of investments in plant and equipment needed to improve or grow the firm’s capacity.
In your personal life
Knowing your personal cost of capital will allow you to make informed decisions about your personal consuming, borrowing, and investing. Managing your personal wealth is a lot like managing the wealth of a business in that you need to understand the tradeoffs between consuming wealth and growing wealth and how growing wealth can be accomplished by investing your own monies or borrowed monies. Understanding the cost of capital concepts will allow you to make better longterm decisions and maximize the value of your personal wealth.
Alcoa Falling Short of Expectations
Often listed among America’s most admired corporations, Alcoa, Inc., is the world’s largest producer of aluminum, with more than 61,000 employees in 30 countries. A quick glance at its financial statements might suggest that the company has been doing very well in recent years. Alcoa increased its total sales from $18.4 billion in 2009 to $23.7 billion in 2012, an annual growth rate of almost 9 percent, far exceeding overall economic growth over the same period. In each of those years, Alcoa spent more than $1 billion on capital expenditures, expanding and upgrading its manufacturing facilities, entering new joint ventures, and making strategic acquisitions.
During that span, however, Alcoa’s stock underperformed. During the 5year period ending in May 2013, Alcoa common stock lost almost 80 percent of its value, while the broader stock market (as measured by the Standard & Poor’s 500 Stock Composite Index) rose by about 20 percent. Why did Alcoa perform so poorly? A simple answer is that its business investments failed to earn a return sufficient to meet the expectations of investors. Despite Alcoa’s continued growth, the rate of return that it earned on the assets that it had invested was not sufficient to satisfy investors. When a firm’s operating results disappoint investors, its stock price will fall as investors sell their shares and move to a more attractive investment. According to some estimates, Alcoa’s cost of capital exceeded 12 percent, but its investments were consistently earning returns below 5 percent. That is a recipe for a declining stock price, which is precisely what Alcoa had been experiencing for several years.
For companies to succeed, their investments have to earn a rate of return that exceeds investors’ expectations. How, though, do companies know what investors expect? The answer is that companies have to measure their cost of capital. Read on to learn how firms do that.
9.1 Overview of the Cost of Capital
LG 1
LG 2
My Finance Lab Video
Chapter 1 established that the goal of the firm is to maximize shareholder wealth. To do so, managers must make investments that are worth more than they cost. In this chapter, you will learn about the cost of capital, which is the rate of return that financial managers use to evaluate all possible investment opportunities to determine which ones add value to the firm. The cost of capital represents the firm’s cost of financing and is the minimum rate of return that a project must earn to increase firm value. In particular, the cost of capital refers to the cost of the next dollar of financing necessary to finance a new investment opportunity. Investments with a rate of return above the cost of capital will increase the value of the firm, because these investments are worth more than they cost. In contrast, projects with a rate of return below the cost of capital will decrease firm value.
Represents the firm’s cost of financing and is the minimum rate of return that a project must earn to increase firm value.
The cost of capital is an extremely important financial concept. It acts as a major link between the firm’s longterm investment decisions and the wealth of the firm’s owners as determined by the market value of their shares. Financial managers are ethically bound to invest only in projects that they expect to exceed the cost of capital; see the Focus on Ethics box for more discussion of this responsibility.
in practice focus on ETHICS: The Ethics of Profit
Business Week once referred to Peter Drucker as “The Man Who Invented Management.” In his role as writer and management consultant, Drucker stressed the importance of ethics to business leaders. He believed that it was the ethical responsibility of a business to earn a profit. In his mind, profitable businesses create opportunities, whereas unprofitable ones waste society’s resources. Drucker once said, “Profit is not the explanation, cause, or rationale of business behavior and business decisions, but rather the test of their validity. If archangels instead of businessmen sat in directors’ chairs, they would still have to be concerned with profitability, despite their total lack of personal interest in making profits.”
But what happens when businesses abandon ethics for profits? Consider Merck’s experience with the drug, Vioxx. Introduced in 1999, Vioxx was an immediate success, quickly reaching $2.5 billion in annual sales. However, a Merck study launched in 1999 eventually found that patients who took Vioxx suffered from an increased risk of heart attacks and strokes. Despite the risks, Merck continued to market and sell Vioxx. By the time Vioxx was withdrawn from the market, an estimated 20 million Americans had taken the drug, 88,000 had suffered Vioxxrelated heart attacks, and 38,000 had died.
News of the 2004 Vioxx withdrawal hit Merck’s stock hard. The company’s shares fell 27 percent on the day of the announcement, slashing $27 billion off the firm’s market capitalization. Moody’s, Standard & Poor’s, and Fitch cut Merck’s credit ratings, costing the firm its coveted AAA rating. The company’s bottom line also suffered as its net income fell 21 percent in the final three months of 2004.
The recall dealt a major blow to Merck’s reputation. The company was criticized for aggressively marketing Vioxx despite the drug’s serious side effects. Questions were also raised about the research reports Merck had submitted in support of the drug. Lawsuits followed. In 2008, Merck agreed to fund a $4.85 billion settlement to resolve approximately 50,000 Vioxxrelated lawsuits. The company had also incurred $1.53 billion in legal costs by the time of the settlement.
The Vioxx recall increased Merck’s cost of capital. What effect would an increased cost of capital have on a firm’s future investments?
THE BASIC CONCEPT
A firm’s cost of capital reflects the expected average future cost of funds over the long run, and it reflects the entirety of the firm’s financing activities. For example, a firm may raise the money it needs to build a new manufacturing facility by borrowing money (debt), by selling common stock (equity), or by doing both. Managers must take into account respective costs of both forms of capital when they estimate a firm’s cost of capital. In fact, most firms do finance their activities with a blend of equity and debt. In Chapter 13, we will explore the factors that determine what mix of debt and equity is optimal for any particular firm. For now, we will simply say that most firms have a desired mix of financing, and the cost of capital must reflect the cost of each type of financing that a firm uses. To capture all the relevant financing costs, assuming some desired mix of financing, we need to look at the overall cost of capital rather than just the cost of any single source of financing.
Example 9.1
My Finance Lab Solution Video
A firm is currently considering two investment opportunities. Two financial analysts, working independently of each other, are evaluating these opportunities. Assume the following information about investments A and B.
Investment A
The analyst studying this investment recalls that the company recently issued bonds paying a 6% rate of return. He reasons that because the investment project earns 7% while the firm can issue debt at 6%, the project must be worth doing, so he recommends that the company undertake this investment.
Investment B
Least costly financing source available
Equity = 14%
The analyst assigned to this project knows that the firm has common stock outstanding and that investors who hold the company’s stock expect a 14% return on their investment. The analyst decides that the firm should not undertake this investment because it only produces a 12% return while the company’s shareholders expect a 14% return.
In this example, each analyst is making a mistake by focusing on one source of financing rather than on the overall financing mix. What if instead the analysts used a combined cost of financing? By weighting the cost of each source of financing by its relative proportion in the firm’s target capital structure, the firm can obtain a weighted average cost of capital. Assuming that this firm desires a 50–50 mix of debt and equity, the weighted average cost here would be 10%[(0.50 × 6% debt) + (0.50 × 14% equity)]. With this average cost of financing, the firm should reject the first opportunity (7% expected return < 10% weighted average cost) and accept the second (12% expected return > 10% weighted average cost).
SOURCES OF LONGTERM CAPITAL
In this chapter, our concern is only with the longterm sources of capital available to a firm because they are the sources that supply the financing necessary to support the firm’s capital budgeting activities. Capital budgeting is the process of evaluating and selecting longterm investments. This process is intended to achieve the firm’s goal of maximizing shareholders’ wealth. Although the entire capital budgeting process is discussed throughout Part 5, at this point it is sufficient to say that capital budgeting activities are chief among the responsibilities of financial managers and that they cannot be carried out without knowing the appropriate cost of capital with which to judge the firm’s investment opportunities.
There are four basic sources of longterm capital for firms: longterm debt, preferred stock, common stock, and retained earnings. All entries on the righthand side of the balance sheet, other than current liabilities, represent these sources:
Not every firm will use all of these sources of financing. In particular, preferred stock is relatively uncommon. Even so, most firms will have some mix of funds from these sources in their capital structures. Although a firm’s existing mix of financing sources may reflect its target capital structure, it is ultimately the marginal cost of capital necessary to raise the next marginal dollar of financing that is relevant for evaluating the firm’s future investment opportunities.
REVIEW QUESTIONS
9.2 Cost of LongTerm Debt
LG 3
The cost of longterm debt is the financing cost associated with new funds raised through longterm borrowing. Typically, the funds are raised through the sale of corporate bonds.
The financing cost associated with new funds raised through longterm borrowing.
NET PROCEEDS
The net proceeds from the sale of a bond, or any security, are the funds that the firm receives from the sale. The total proceeds are reduced by the flotation costs, which represent the total costs of issuing and selling securities. These costs apply to all public offerings of securities: debt, preferred stock, and common stock. They include two components: (1) underwriting costs, or compensation earned by investment bankers for selling the security; and (2) administrative costs, or issuer expenses such as legal and accounting costs.
Funds actually received by the firm from the sale of a security.
The total costs of issuing and selling a security.
Example 9.2
Duchess Corporation, a major hardware manufacturer, is contemplating selling $10 million worth of 20year, 9% coupon (stated annual interest rate) bonds, each with a par value of $1,000. Because bonds with similar risk earn returns greater than 9%, the firm must sell the bonds for $980 to compensate for the lower coupon interest rate. The flotation costs are 2% of the par value of the bond (0.02 × $1,000), or $20. The net proceeds to the firm from the sale of each bond are therefore $960 ($980 minus $20).
BEFORETAX COST OF DEBT
The beforetax cost of debt, r_{d}, is simply the rate of return the firm must pay on new borrowing. A firm’s beforetax cost of debt for bonds can be found in any of three ways: quotation, calculation, or approximation.
Using Market Quotations
A relatively quick method for finding the beforetax cost of debt is to observe the yield to maturity (YTM) on the firm’s existing bonds or bonds of similar risk issued by other companies. The YTM of existing bonds reflects the rate of return required by the market. For example, if the market requires a YTM of 9.7 percent for a similarrisk bond, this value can be used as the beforetax cost of debt, r_{d}, for new bonds. Bond yields are widely reported by sources such as the Wall Street Journal.
Calculating the Cost
This approach finds the beforetax cost of debt by calculating the YTM generated by the bond’s cash flows, given the net proceeds that the firm receives when it issues the bonds. From the issuer’s point of view, this value is the cost to maturity of the cash flows associated with the debt. The YTM can be calculated by using a financial calculator or an electronic spreadsheet. It represents the annual beforetax percentage cost of the debt.
Example 9.3
In the preceding example, $960 were the net proceeds of a 20year bond with a $1,000 par value and 9% coupon interest rate. The calculation of the annual cost is quite simple. The cash flow pattern associated with this bond’s sales consists of an initial inflow (the net proceeds) followed by a series of annual outlays (the interest payments). In the final year, when the debt is retired, an outlay representing the repayment of the principal also occurs. The cash flows associated with Duchess Corporation’s bond issue are as follows:
End of year(s)  Cash flow 

0  $ 960 
1–20  −$ 90 
20  − $1,000 
The initial $960 inflow is followed by annual interest outflows of $90 (9% coupon interest rate × $1,000 par value) over the 20year life of the bond. In year 20, an outflow of $1,000 (the repayment of the principal) occurs. We can determine the cost of debt by finding the YTM, which is the discount rate that equates the present value of the bond outflows to the initial inflow.
My Finance Lab Financial Calculator
Calculator use (Note: Most calculators require either the present value [net proceeds] or the future value [annual interest payments and repayment of principal] to be input as negative numbers when we calculate yield to maturity. That approach is used here.) Using the calculator and the inputs shown at the left, you should find the beforetax cost of debt (yield to maturity) to be 9.452%.
Spreadsheet use The beforetax cost of debt on the Duchess Corporation bond can be calculated using an Excel spreadsheet. The following Excel spreadsheet shows that by referencing the cells containing the bond’s net proceeds, coupon payment, years to maturity, and par value as part of Excel’s RATE function, you can quickly determine that the appropriate beforetax cost of debt for Duchess Corporation’s bond is 9.452%.
Although you may not recognize it, both the calculator and the Excel function are using trialanderror to find the bond’s YTM, they just do it faster than you can.
Approximating the Cost
Although not as precise as using a calculator, there is a method for quickly approximating the beforetax cost of debt. The beforetax cost of debt, r_{d}, for a bond with a $1,000 par value can be approximated by
(9.1) 
Where
Example 9.4
Substituting the appropriate values from the Duchess Corporation example into the approximation formula given in Equation 9.1, we get
This approximate value of beforetax cost of debt is close to the 9.452%, but it lacks the precision of the value derived using the calculator or spreadsheet.
AFTERTAX COST OF DEBT
Unlike the dividends paid to equityholders, the interest payments paid to bondholders are tax deductable for the firm, so the interest expense on debt reduces the firm’s taxable income and, therefore, the firm’s tax liability. To find the firm’s net cost of debt, we must account for the tax savings created by debt and solve for the cost of longterm debt on an aftertax basis. The aftertax cost of debt, r_{i}, can be found by multiplying the beforetax cost, r_{d}, by 1 minus the tax rate, T:
r_{i} = r_{d} × (1 − T)  (9.2) 
Example 9.5
My Finance Lab Solution Video
Duchess Corporation has a 40% tax rate. Using the 9.452% beforetax debt cost calculated above and applying Equation 9.2, we find an aftertax cost of debt of 5.67%[9.452% × (1 − 0.40)]. Typically, the cost of longterm debt for a given firm is less than the cost of preferred or common stock, partly because of the tax deductibility of interest.
Personal Finance Example 9.6
My Finance Lab Solution Video
Kait and Kasim Sullivan, a married couple in the 28% federal incometax bracket, wish to borrow $60,000 to pay for a new luxury car. To finance the purchase, they can either borrow the $60,000 through the auto dealer at an annual interest rate of 6.0%, or they can take a $60,000 second mortgage on their home. The best annual rate they can get on the second mortgage is 7.2%. They already have qualified for both of the loans being considered.
If they borrow from the auto dealer, the interest on this “consumer loan” will not be deductible for federal tax purposes. However, the interest on the second mortgage would be tax deductible because the tax law allows individuals to deduct interest paid on a home mortgage. To choose the leastcost financing, the Sullivans calculated the aftertax cost of both sources of longterm debt. Because interest on the auto loan is not tax deductible, its aftertax cost equals its stated cost of 6.0%. Because the interest on the second mortgage is tax deductible, its aftertax cost can be found using Equation 9.2:
Because the 5.2% aftertax cost of the second mortgage is less than the 6.0% cost of the auto loan, the Sullivans may decide to use the second mortgage to finance the auto purchase.
REVIEW QUESTIONS
EXCEL REVIEW QUESTION
My Finance Lab
9.3 Cost of Preferred Stock
LG 4
Preferred stock represents a special type of ownership interest in the firm. It gives preferred stockholders the right to receive their stated dividends before the firm can distribute any earnings to common stockholders. The key characteristics of preferred stock were described in Chapter 7. However, the one aspect of preferred stock that requires review is dividends.
PREFERRED STOCK DIVIDENDS
When dividends are stated as “preferred stock dividends,” the stock is often referred to as “xdollar preferred stock.” Thus, a “$4 preferred stock” is expected to pay preferred stockholders $4 in dividends each year on each share of preferred stock owned.
Sometimes preferred stock dividends are stated as an annual percentage rate. This rate represents the percentage of the stock’s par, or face, value that equals the annual dividend. For instance, an 8 percent preferred stock with a $50 par value would be expected to pay an annual dividend of $4 per share (0.08 × $50 par = $4). Before the cost of preferred stock is calculated, any dividends stated as percentages should be converted to annual dollar dividends.
CALCULATING THE COST OF PREFERRED STOCK
The cost of preferred stock, r_{p}, is the ratio of the preferred stock dividend to the firm’s net proceeds from the sale of the preferred stock. The net proceeds represent the amount of money to be received minus any flotation costs. The following equation gives the cost of preferred stock, r_{p}, in terms of the annual dollar dividend, D_{p}, and the net proceeds from the sale of the stock, N_{p}:
The ratio of the preferred stock dividend to the firm’s net proceeds from the sale of preferred stock.
(9.3) 
Example 9.7
Duchess Corporation is contemplating issuance of a 10% preferred stock that they expect to sell for $87 per share. The cost of issuing and selling the stock will be $5 per share. The first step in finding the cost of the stock is to calculate the dollar amount of the annual preferred dividend, which is $8.70 (0.10 × $87). The net proceeds per share from the proposed sale of stock equals the sale price minus the flotation costs ($87 − $5 = $82). Substituting the annual dividend, D_{p}, of $8.70 and the net proceeds, N_{p}, of $82 into Equation 9.3 gives the cost of preferred stock, 10.6% ($8.70 ÷ $82).
The cost of Duchess’s preferred stock (10.6%) is much greater than the cost of its longterm debt (5.67%). This difference exists both because the cost of longterm debt (the interest) is tax deductible and because preferred stock is riskier than longterm debt.
REVIEW QUESTION
9.4 Cost of Common Stock
LG 5
The cost of common stock is the return required on the stock by investors in the marketplace. There are two forms of common stock financing: (1) retained earnings and (2) new issues of common stock. As a first step in finding each of these costs, we must estimate the cost of common stock equity.
FINDING THE COST OF COMMON STOCK EQUITY
The cost of common stock equity, r_{s}, is the rate at which investors discount the expected common stock dividends of the firm to determine its share value. Two techniques are used to measure the cost of common stock equity. One relies on the constantgrowth valuation model, the other on the capital asset pricing model (CAPM).
The rate at which investors discount the expected dividends of the firm to determine its share value.
Using the ConstantGrowth Valuation (Gordon Growth) Model
In Chapter 7, we found the value of a share of stock to be equal to the present value of all future dividends, which in one model are assumed to grow at a constant annual rate over an infinite time horizon. This model, the constantgrowth valuation model, is also known as the Gordon growth model. The key expression derived for this model, first presented as Equation 7.4, is
Assumes that the value of a share of stock equals the present value of all future dividends (assumed to grow at a constant rate) that it is expected to provide over an infinite time horizon.
(9.4) 
where
Solving Equation 9.4 for r_{s} results in the following expression for the cost of common stock equity:
(9.5) 
Equation 9.5 indicates that the cost of common stock equity can be found by dividing the dividend expected at the end of year 1 by the current market price of the stock (the “dividend yield”) and adding the expected growth rate (the “capital gains yield”).
Example 9.8
Duchess Corporation wishes to determine its cost of common stock equity, r_{s}. The market price, P_{0}, of its common stock is $50 per share. The firm expects to pay a dividend, D_{1}, of $4 at the end of the coming year, 2016. The dividends paid on the outstanding stock over the past 6 years (2010 through 2015) were as follows:
Year  Dividend 

2015  $3.80 
2014  3.62 
2013  3.47 
2012  3.33 
2011  3.12 
2010  2.97 
Using a financial calculator or electronic spreadsheet, in conjunction with the technique described for finding growth rates in Chapter 5, we can calculate the annual rate at which dividends have grown, g, from 2010 to 2015. It turns out to be approximately 5% (more precisely, it is 5.05%). Substituting D_{1} = $4, P_{0} = $50, and g = 5% into Equation 9.5 yields the cost of common stock equity:
The 13.0% cost of common stock equity represents the return required by existing shareholders on their investment. If the actual return is less than that, shareholders are likely to begin selling their stock.
Using the Capital Asset Pricing Model (CAPM)
Recall from Chapter 8 that the capital asset pricing model (CAPM) describes the relationship between the required return, r_{s}, and the nondiversifiable risk of the firm as measured by the beta coefficient, β. The basic CAPM is
Describes the relationship between the required return, r_{s}, and the nondiversifiable risk of the firm as measured by the beta coefficient, β.
r_{s} = R_{F} + [β × (r_{m} − R_{F})]  (9.6) 
where
Using the CAPM indicates that the cost of common stock equity is the return required by investors as compensation for the firm’s nondiversifiable risk, measured by beta.
Example 9.9
Duchess Corporation now wishes to calculate its cost of common stock equity, r_{s}, by using the CAPM. The firm’s investment advisors and its own analysts indicate that the riskfree rate, R_{F}, equals 7%; the firm’s beta, β, equals 1.5; and the market return, r_{m}, equals 11%. Substituting these values into Equation 9.6, the company estimates the cost of common stock equity, r_{s}, to be
r_{s} = 7.0% + [1.5 × (11.0% − 7.0%)] = 7.0% + 6.0% = 13.0%
The 13.0% cost of common stock equity represents the required return of investors in Duchess Corporation common stock. It is the same as that found by using the constantgrowth valuation model.
Comparing ConstantGrowth and CAPM Techniques
The CAPM technique differs from the constantgrowth valuation model in that it directly considers the firm’s risk, as reflected by beta, in determining the required return or cost of common stock equity. The constantgrowth model does not look at risk; it uses the market price, P_{0}, as a reflection of the expected risk–return preference of investors in the marketplace. The constantgrowth valuation and CAPM techniques for finding r_{s} are theoretically equivalent, although in practice estimates from the two methods do not always agree. The two methods can produce different estimates because they require (as inputs) estimates of other quantities, such as the expected dividend growth rate or the firm’s beta.
Another difference is that when the constantgrowth valuation model is used to find the cost of common stock equity, it can easily be adjusted for flotation costs to find the cost of new common stock; the CAPM does not provide a simple adjustment mechanism. The difficulty in adjusting the cost of common stock equity calculated by using the CAPM occurs because in its common form the model does not include the market price, P_{0}, a variable needed to make such an adjustment. Although the CAPM has a stronger theoretical foundation, the computational appeal of the traditional constantgrowth valuation model justifies its use throughout this text to measure financing costs of common stock. As a practical matter, analysts might want to estimate the cost of equity using both approaches and then take an average of the results to arrive at a final estimate of the cost of equity.
COST OF RETAINED EARNINGS
As you know, dividends are paid out of a firm’s earnings. Their payment, made in cash to common stockholders, reduces the firm’s retained earnings. Suppose that a firm needs common stock equity financing of a certain amount. It has two choices relative to retained earnings: It can issue additional common stock in that amount and still pay dividends to stockholders out of retained earnings, or it can increase common stock equity by retaining the earnings (not paying the cash dividends) in the needed amount. In a strict accounting sense, the retention of earnings increases common stock equity in the same way that the sale of additional shares of common stock does. Thus, the cost of retained earnings, r_{r}, to the firm is the same as the cost of an equivalent fully subscribed issue of additional common stock. Stockholders find the firm’s retention of earnings acceptable only if they expect that it will earn at least their required return on the reinvested funds.
The same as the cost of an equivalent fully subscribed issue of additional common stock, which is equal to the cost of common stock equity, r_{s}.
Viewing retained earnings as a fully subscribed issue of additional common stock, we can set the firm’s cost of retained earnings, r_{r}, equal to the cost of common stock equity as given by Equations 9.5 and 9.6.
r_{r} = r_{s}  (9.7) 
Thus, it is not necessary to adjust the cost of retained earnings for flotation costs because by retaining earnings the firm “raises” equity capital without incurring these costs.
Example 9.10
The cost of retained earnings for Duchess Corporation was actually calculated in the preceding examples: It is equal to the cost of common stock equity. Thus, r_{r} equals 13.0%. As we will show in the next section, the cost of retained earnings is always lower than the cost of a new issue of common stock because it entails no flotation costs.
Matter of fact
Retained Earnings, the Preferred Source of Financing
In the United States and most other countries, firms rely more heavily on retained earnings than any other financing source. For example, a 2013 survey of Chinese firms found that 64% of the companies surveyed listed retained earnings as one of their primary sources of funds. Bank loans were a distant second choice, mentioned as a primary source of funds by just 44% of the companies.^{1}
COST OF NEW ISSUES OF COMMON STOCK
Our purpose in finding the firm’s overall cost of capital is to determine the aftertax cost of new funds required for financing projects. The cost of a new issue of common stock, r_{n}, is determined by calculating the cost of common stock, net of underpricing and associated flotation costs. Normally, when new shares are issued, they are underpriced, meaning that they are sold at a discount relative to the current market price, P_{0}. Underpricing is the difference between the market price and the issue price, which is the price paid by the primary market investors discussed in Chapter 2.
The cost of common stock, net of underpricing and associated flotation costs.
Stock sold at a price below its current market price, P_{0}.
1. Business in China Survey 2013, China Europe International Business School.
We can use the constantgrowth valuation model expression for the cost of existing common stock, r_{s}, as a starting point. If we let N_{n} represent the net proceeds from the sale of new common stock after subtracting underpricing and flotation costs, the cost of the new issue, r_{n}, can be expressed as^{2}
(9.8) 
The net proceeds from sale of new common stock, N_{n}, will be less than the current market price, P_{0}. Therefore, the cost of new issues, r_{n}, will always be greater than the cost of existing issues, r_{s}, which is equal to the cost of retained earnings, r_{r}. The cost of new common stock is normally greater than any other longterm financing cost.
Example 9.11
In the constantgrowth valuation example, we found Duchess Corporation’s cost of common stock equity, r_{s}, to be 13%, using the following values: an expected dividend, D_{1}, of $4; a current market price, P_{0}, of $50; and an expected growth rate of dividends, g, of 5%.
To determine its cost of new common stock, r_{n}, Duchess Corporation has estimated that on average, new shares can be sold for $47. The $3pershare underpricing is due to the competitive nature of the market. A second cost associated with a new issue is flotation costs of $2.50 per share that would be paid to issue and sell the new shares. The total underpricing and flotation costs per share are therefore $5.50.
Subtracting the $5.50pershare underpricing and flotation cost from the current $50 share price results in expected net proceeds of $44.50 per share ($50.00 minus $5.50). Substituting D_{1} = $4, N_{n} = $44.50, and g = 5% into Equation 9.8 results in a cost of new common stock, r_{n}:
Duchess Corporation’s cost of new common stock is therefore 14.0%. That is the value to be used in subsequent calculations of the firm’s overall cost of capital.
REVIEW QUESTIONS
2. An alternative, but computationally less straightforward, form of this equation is
(9.8a) 
where f represents the percentage reduction in current market price expected as a result of underpricing and flotation costs. Simply stated, N_{n} in Equation 9.8 is equivalent to p_{0} × (1 − f) in Equation 9.8a. For convenience, Equation 9.8 is used to define the cost of a new issue of common stock, r_{n}.
9.5 Weighted Average Cost of Capital
LG 6
As noted earlier, the weighted average cost of capital (WACC), r_{a}, reflects the expected average future cost of capital over the long run. It is found by weighting the cost of each specific type of capital by its proportion in the firm’s capital structure.
Reflects the expected average future cost of capital over the long run; found by weighting the cost of each specific type of capital by its proportion in the firm’s capital structure.
CALCULATING WEIGHTED AVERAGE COST OF CAPITAL (WACC)
Calculating the weighted average cost of capital (WACC) is straightforward: Multiply the individual cost of each form of financing by its proportion in the firm’s capital structure and sum the weighted values. As an equation, the weighted average cost of capital, r_{a}, can be specified as
r_{a} = (w_{i} × r_{i}) + (w_{p} × r_{p}) + (w_{s} × r_{r or n})  (9.9) 
where
Three important points should be noted in Equation 9.9:
 1. For computational convenience, it is best to convert the weights into decimal form and leave the individual costs in percentage terms.
 2. The weights must be nonnegative and sum to 1.0. Simply stated, WACC must account for all financing costs within the firm’s capital structure.
 3. The firm’s common stock equity weight, w_{s}, is multiplied by either the cost of retained earnings, r_{r}, or the cost of new common stock, r_{n}. Which cost is used depends on whether the firm’s common stock equity will be financed using retained earnings, r_{r}, or new common stock, r_{n}.
Example 9.12
In earlier examples, we found the costs of the various types of capital for Duchess Corporation to be as follows:
The company uses the following weights in calculating its weighted average cost of capital:
Source of capital  Weight 

Longterm debt  40% 
Preferred stock  10 
Common stock equity  50 
Total  100% 
TABLE 9.1 Calculation of the Weighted Average Cost of Capital for Duchess Corporation
Source of capital  Weight (1)  Cost (2)  Weighted cost [(1) × (2)] (3) 

Longterm debt  0.40  5.6%  2.2% 
Preferred stock  0.10  10.6  1.1 
Common stock equity  0.50  13.0  6.5 
Totals  1.00  WACC = 9.8% 
Because the firm expects to have a sizable amount of retained earnings available ($300,000), it plans to use its cost of retained earnings, r_{r}, as the cost of common stock equity. Duchess Corporation’s weighted average cost of capital is calculated in Table 9.1. The resulting weighted average cost of capital for Duchess is 9.8%. Assuming an unchanged risk level, the firm should accept all projects that will earn a return greater than 9.8%.
in practice focus on PRACTICE: Uncertain Times Make for an Uncertain Weighted Average Cost of Capital
As U.S. financial markets experienced and recovered from the 2008 financial crisis and 2009 “great recession,” firms struggled to keep track of their weighted average cost of capital. The individual component costs were moving rapidly in response to the financial market turmoil. Volatile financial markets can make otherwise manageable costofcapital calculations exceedingly complex and inherently error prone, possibly wreaking havoc with investment decisions. If a firm underestimates its cost of capital, it risks making investments that are not economically justified, and if a firm overestimates its financing costs, it risks foregoing valuemaximizing investments.
Although the WACC computation does not change when markets become unstable, the uncertainty surrounding the components that comprise the WACC increases dramatically. The financial crisis pushed credit costs to a point where longterm debt was largely inaccessible, and the great recession saw Treasury bond yields fall to historic lows, making cost of equity projections appear unreasonably low. With these key components in flux, it is exceedingly difficult, if not impossible, for firms to get a handle on a cost of longterm capital.
According to CFO Magazine, at least one firm resorted to a twopronged approach for determining its cost of capital during the uncertain times. Ron Domanico is the chief financial officer (CFO) at Caraustar Industries, Inc., and he reported that his company dealt with the costofcapital uncertainty by abandoning the conventional onesizefitsall approach. “In the past, we had one cost of capital that we applied to all our investment decisions … today that’s not the case. We have a shortterm cost of capital we apply to shortterm opportunities, and a longerterm cost of capital we apply to longerterm opportunities … and the reality is that the longerterm cost is so high that it has forced us to focus only on those projects that have immediate returns,” Mr. Domanico is quoted saying.^{a}
Part of Caraustar’s motivation for implementing this twopronged approach was to account for the excessively large spread between short and longterm debt rates that emerged during the financial market crisis. Mr. Domanico reported that during the crisis Caraustar could borrow shortterm funds at the lower of Prime plus 4 percent or LIBOR plus 5 percent, where either rate was reasonable for making shortterm investment decisions. Alternatively, longterm investment decisions were being required to clear Caraustar’s longterm costofcapital calculation accounting for borrowing rates in excess of 12 percent.
Why don’t firms generally use both short and longrun weighted average costs of capital?
WEIGHTING SCHEMES
Firms can calculate weights on the basis of either book value or market value using either historical or target proportions.
Book Value versus Market Value
Book value weights use accounting values to measure the proportion of each type of capital in the firm’s financial structure. Market value weights measure the proportion of each type of capital at its market value. Market value weights are appealing because the market values of securities closely approximate the actual dollars to be received from their sale. Moreover, because firms calculate the costs of the various types of capital by using prevailing market prices, it seems reasonable to use market value weights. In addition, the longterm investment cash flows to which the cost of capital is applied are estimated in terms of current as well as future market values. Market value weights are clearly preferred over book value weights.
Weights that use accounting values to measure the proportion of each type of capital in the firm’s financial structure.
Weights that use market values to measure the proportion of each type of capital in the firm’s financial structure.
Historical versus Target Weights
Historical weights can be either book or market value weights based on actual capital structure proportions. For example, past or current book value proportions would constitute a form of historical weighting, as would past or current market value proportions. Such a weighting scheme would therefore be based on real—rather than desired—proportions.
Either book or market value weights based on actual capital structure proportions.
Target weights, which can also be based on either book or market values, reflect the firm’s desired capital structure proportions. Firms using target weights establish such proportions on the basis of the “optimal” capital structure they wish to achieve. (The development of these proportions and the optimal structure are discussed in detail in Chapter 13.)
Either book or market value weights based on desired capital structure proportions.
When one considers the somewhat approximate nature of the calculation of weighted average cost of capital, the choice of weights may not be critical. However, from a strictly theoretical point of view, the preferred weighting scheme is target market value proportions, and we assume this scheme throughout this chapter.
Personal Finance Example 9.13
Chuck Solis currently has three loans outstanding, all of which mature in exactly 6 years and can be repaid without penalty any time prior to maturity. The outstanding balances and annual interest rates on these loans are as follows:
Loan  Outstanding balance  Annual interest rate 

1  $26,000  9.6% 
2  9,000  10.6 
3  45,000  7.4 
After a thorough search, Chuck found a lender who would loan him $80,000 for 6 years at an annual interest rate of 9.2% on the condition that the loan proceeds be used to fully repay the three outstanding loans, which combined have an outstanding balance of $80,000 ($26,000 + $9,000 + $45,000).
Chuck wishes to choose the least costly alternative: (1) to do nothing or (2) to borrow the $80,000 and pay off all three loans. He calculates the weighted average cost of his current debt by weighting each debt’s annual interest cost by the proportion of the $80,000 total it represents and then summing the three weighted values as follows:
Given that the weighted average cost of the $80,000 of current debt of 8.5% is below the 9.2% cost of the new $80,000 loan, Chuck should do nothing and just continue to pay off the three loans as originally scheduled.
REVIEW QUESTIONS
Summary
FOCUS ON VALUE
The cost of capital is an extremely important rate of return, particularly in capital budgeting decisions. It is the expected average future cost to the firm of funds over the long run. Because the cost of capital is the pivotal rate of return used in the investment decision process, its accuracy can significantly affect the quality of these decisions.
Underestimation of the cost of capital can make poor projects look attractive; overestimation can make good projects look unattractive. By applying the techniques presented in this chapter to estimate the firm’s cost of capital, the financial manager will improve the likelihood that the firm’s longterm decisions will be consistent with the firm’s overall goal of maximizing stock price (owner wealth).
REVIEW OF LEARNING GOALS
LG 1 Understand the basic concept and sources of capital associated with the cost of capital. The cost of capital is the minimum rate of return that a firm must earn on its investments to grow firm value. A weighted average cost of capital should be used to find the expected average future cost of funds over the long run. The individual costs of the basic sources of capital (longterm debt, preferred stock, retained earnings, and common stock) can be calculated separately.
LG 2 Explain what is meant by the marginal cost of capital. The relevant cost of capital for a firm is the marginal cost of capital necessary to raise the next marginal dollar of financing to fund the firm’s future investment opportunities. A firm’s future investment opportunities in expectation will be required to exceed the firm’s cost of capital.
LG 3 Determine the cost of longterm debt, and explain why the aftertax cost of debt is the relevant cost of debt. The beforetax cost of longterm debt can be found by using cost quotations, calculations (either by calculator or spreadsheet), or an approximation. The aftertax cost of debt is calculated by multiplying the beforetax cost of debt by 1 minus the tax rate. The aftertax cost of debt is the relevant cost of debt because it is the lowest possible cost of debt for the firm due to the deductibility of interest expenses.
LG 4 Determine the cost of preferred stock. The cost of preferred stock is the ratio of the preferred stock dividend to the firm’s net proceeds from the sale of preferred stock.
LG 5 Calculate the cost of common stock equity, and convert it into the cost of retained earnings and the cost of new issues of common stock. The cost of common stock equity can be calculated by using the constantgrowth valuation (Gordon growth) model or the CAPM. The cost of retained earnings is equal to the cost of common stock equity. An adjustment in the cost of common stock equity to reflect underpricing and flotation costs is necessary to find the cost of new issues of common stock.
LG 6 Calculate the weighted average cost of capital (WACC), and discuss alternative weighting schemes. The firm’s WACC reflects the expected average future cost of funds over the long run. It combines the costs of specific types of capital after weighting each of them by its proportion. The theoretically preferred approach uses target weights based on market values.
OpenerinReview
In the chapter opener you learned that Alcoa’s weighted average cost of capital was around 12 percent, but its investments were earning returns closer to 5 percent. From 2010 to 2012, Alcoa invested roughly $1 billion in capital expenditures. Suppose Alcoa spends $1 billion expanding its manufacturing facilities today, and that investment produces a net cash flow of $50 million (5 percent of $1 billion) every year in perpetuity. Calculate the NPV of that investment using a 12 percent discount rate. How much value does the $1 billion investment create or destroy? Does it seem that Alcoa should be pursuing growth in this market?
SelfTest Problem
(Solutions in Appendix)
LG 3
LG 4
LG 5
LG 6
 Debt The firm can raise debt by selling $1,000parvalue, 10% coupon interest rate, 10year bonds on which annual interest payments will be made. To sell the issue, an average discount of $30 per bond must be given. The firm must also pay flotation costs of $20 per bond.
 Preferred stock The firm can sell 11% (annual dividend) preferred stock at its $100pershare par value. The cost of issuing and selling the preferred stock is expected to be $4 per share.
 Common stock The firm’s common stock is currently selling for $80 per share. The firm expects to pay cash dividends of $6 per share next year. The firm’s dividends have been growing at an annual rate of 6%, and this rate is expected to continue in the future. The stock will have to be underpriced by $4 per share, and flotation costs are expected to amount to $4 per share.
 Retained earnings The firm expects to have $225,000 of retained earnings available in the coming year. Once these retained earnings are exhausted, the firm will use new common stock as the form of common stock equity financing.
 a. Calculate the individual cost of each source of financing. (Round to the nearest 0.1%.)
 b. Calculate the firm’s weighted average cost of capital using the weights shown in the following table, which are based on the firm’s target capital structure proportions. (Round to the nearest 0.1%.)
Source of capital Weight Longterm debt 40% Preferred stock 15 Common stock equity 45 Total 100%  c. In which, if any, of the investments shown in the following table do you recommend that the firm invest? Explain your answer. How much new financing is required?
Investment opportunity Expected rate of return Initial investment A 11.2% $100,000 B 9.7 500,000 C 12.9 150,000 D 16.5 200,000 E 11.8 450,000 F 10.1 600,000 G 10.5 300,000
WarmUp Exercises
All problems are available in MyFinanceLab.
LG 4
LG 5
LG 6
LG 6
Problems
All problems are available in MyFinanceLab.
LG 1
Basic variables  North  South 

Cost  $6 million  $5 million 
Life  15 years  15 years 
Expected return  8%  15% 
Leastcost financing  
Source  Debt  Equity 
Cost (aftertax)  7%  16% 
Decision  
Action  Invest  Don’t invest 
Reason  8% > 7% cost  15% < 16% cost 
 a. An analyst evaluting the North facility expects that the project will be financed by debt that costs the firm 7%. What recommendation do you think this analyst will make regarding the investment opportunity?
 b. Another analyst assigned to study the South facility believes that funding for that project will come from the firm’s retained earnings at a cost of 16%. What recommendation do you expect this analyst to make regarding the investment?
 c. Explain why the decisions in parts a and b may not be in the best interests of the firm’s investors.
 d. If the firm maintains a capital structure containing 40% debt and 60% equity, find its weighted average cost using the data in the table.
 e. If both analysts had used the weighted average cost calculated in part d, what recommendations would they have made regarding the North and South facilities?
 f. Compare and contrast the analyst’s initial recommendations with your findings in part e. Which decision method seems more appropriate? Explain why.
LG 3
 a. Find the net proceeds from sale of the bond, N_{d}.
 b. Show the cash flows from the firm’s point of view over the maturity of the bond.
 c. Calculate the beforetax and aftertax costs of debt.
 d. Use the approximation formula to estimate the beforetax and aftertax costs of debt.
 e. Compare and contrast the costs of debt calculated in parts c and d. Which approach do you prefer? Why?
Personal Finance Problem
LG 3
Sony bond  

Par value  $1,000  Coupon interest rate 6%  Corporate tax rate 20% 
Cost  $ 930  Years to maturity 10 
 a. Calculate the beforetax cost of the Sony bond.
 b. Calculate the aftertax cost of the Sony bond given the corporate tax rate.
LG 3
Bond  Life (years)  Underwriting fee  Discount (−) or premium (+)  Coupon interest rate 

A  20  $25  −$20  9% 
B  16  40  +10  10 
C  15  30  −15  12 
D  25  15  Par  9 
E  22  20  −60  11 
LG 3
Alternative  Coupon rate  Time to maturity (years)  Premium or discount 

A  9%  16  $250 
B  7  5  50 
C  6  7  par 
D  5  10  − 75 
Personal Finance Problem
 a. Calculate the aftertax cost of borrowing from the motorcycle dealership.
 b. Calculate the aftertax cost of borrowing through a second mortgage on Bella’s home.
 c. Which source of borrowing is less costly for Bella?
 d. Is there any other consideration that Bella ought to think about when deciding which loan to take out to pay for the motorcycle?
LG 4
 a. Calculate the cost of the preferred stock.
 b. If the firm sells the preferred stock with a 10% annual dividend and nets $90.00 after flotation costs, what is its cost?
LG 4
Preferred stock  Par value  Sale price  Flotation cost  Annual dividend 

A  $100  $101  $9.00  11% 
B  40  38  $3.50  8% 
C  35  37  $4.00  $5.00 
D  30  26  5% of par  $3.00 
E  20  20  $2.50  9% 
LG 5
 a. Determine the risk premium on J&M common stock.
 b. Determine the required return that J&M common stock should provide.
 c. Determine J&M’s cost of common stock equity using the CAPM.
LG 5
Year  Dividend 

2015  $3.10 
2014  2.92 
2013  2.60 
2012  2.30 
2011  2.12 
After underpricing and flotation costs, the firm expects to net $52 per share on a new issue.
 a. Determine the growth rate of dividends from 2011 to 2015.
 b. Determine the net proceeds, N_{n}, that the firm will actually receive.
 c. Using the constantgrowth valuation model, determine the cost of retained earnings, r_{r}.
 d. Using the constantgrowth valuation model, determine the cost of new common stock, r_{n}.
LG 5
Firm  Current market price per share  Dividend growth rate  Projected dividend per share next year  Underpricing per share  Flotation cost per share 

A  $50.00  8%  $2.25  $2.00  $1.00 
B  20.00  4  1.00  0.50  1.50 
C  42.50  6  2.00  1.00  2.00 
D  19.00  2  2.10  1.30  1.70 
LG 3
LG 4
LG 5
LG 6
 a. Tax rate = 40%
 b. Tax rate = 35%
 c. Tax rate = 25%
 d. Describe the relationship between changes in the rate of taxation and the weighted average cost of capital.
LG 6
Source of capital  Book value  Individual cost 

Longterm debt  $700,000  5.3% 
Preferred stock  50,000  12.0 
Common stock equity  650,000  16.0 
 a. Calculate the firm’s weighted average cost of capital using book value weights.
 b. Explain how the firm can use this cost in the investment decisionmaking process.
LG 6
Source of capital  Book value  Market value  Aftertax cost 

Longterm debt  $4,000,000  $3,840,000  6.0% 
Preferred stock  40,000  60,000  13.0 
Common stock equity  1,060,000  3,000,000  17.0 
Totals  $5,100,000  $6,900,000 
 a. Calculate the weighted average cost of capital using book value weights.
 b. Calculate the weighted average cost of capital using market value weights.
 c. Compare the answers obtained in parts a and b. Explain the differences.
LG 6
Source of capital  Target market value weight 

Longterm debt  30% 
Preferred stock  15 
Common stock equity  55 
Total  100% 
The cost of debt is estimated to be 7.2%, the cost of preferred stock is estimated to be 13.5%, the cost of retained earnings is estimated to be 16.0%, and the cost of new common stock is estimated to be 18.0%. All are aftertax rates. The company’s debt represents 25%, the preferred stock represents 10%, and the common stock equity represents 65% of total capital on the basis of the market values of the three components. The company expects to have a significant amount of retained earnings available and does not expect to sell any new common stock.
 a. Calculate the weighted average cost of capital on the basis of historical market value weights.
 b. Calculate the weighted average cost of capital on the basis of target market value weights.
 c. Compare the answers obtained in parts a and b. Explain the differences.
LG 3
LG 4
LG 5
LG 6
 a. If the market price of the common stock is $40 and dividends are expected to grow at a rate of 6% per year for the foreseeable future, what is the company’s cost of retained earnings financing?
 b. If underpricing and flotation costs on new shares of common stock amount to $7.00 per share, what is the company’s cost of new common stock financing?
 c. The company can issue $2.00 dividend preferred stock for a market price of $25.00 per share. Flotation costs would amount to $3.00 per share. What is the cost of preferred stock financing?
 d. The company can issue $1,000parvalue, 10% coupon, 5year bonds that can be sold for $1,200 each. Flotation costs would amount to $25.00 per bond. Use the estimation formula to figure the approximate cost of debt financing.
 e. What is the WACC?
LG 3
LG 4
LG 5
LG 6
 Debt The firm can sell for $980 a 10year, $1,000parvalue bond paying annual interest at a 10% coupon rate. A flotation cost of 3% of the par value is required in addition to the discount of $20 per bond.
 Preferred stock Eight percent (annual dividend) preferred stock having a par value of $100 can be sold for $65. An additional fee of $2 per share must be paid to the underwriters.
 Common stock The firm’s common stock is currently selling for $50 per share. The dividend expected to be paid at the end of the coming year (2016) is $4. Its dividend payments, which have been approximately 60% of earnings per share in each of the past 5 years, were as shown in the following table.
Year Dividend 2015 $3.75 2014 3.50 2013 3.30 2012 3.15 2011 2.85
It is expected that to attract buyers, new common stock must be underpriced $5 per share, and the firm must also pay $3 per share in flotation costs. Dividend payments are expected to continue at 60% of earnings. (Assume that r_{r} = r_{s}.)
 a. Calculate the aftertax cost of debt.
 b. Calculate the cost of preferred stock.
 c. Calculate the cost of common stock.
 d. Calculate the WACC for Dillon Labs.
Personal Finance Problem
LG 6
Loan  Balance due  Annual interest rate 

1  $20,000  6% 
2  12,000  9 
3  32,000  5 
John can also combine the total of his three debts (that is, $64,000) and create a consolidated loan from his bank. His bank will charge a 7.2% annual interest rate for a period of 5 years.
Should John do nothing (leave the three individual loans as is) or create a consolidated loan (the $64,000 question)?
LG 3
LG 4
LG 5
LG 6
 Debt The firm can raise debt by selling $1,000parvalue, 8% coupon interest rate, 20year bonds on which annual interest payments will be made. To sell the issue, an average discount of $30 per bond would have to be given. The firm also must pay flotation costs of $30 per bond.
 Preferred stock The firm can sell 8% preferred stock at its $95pershare par value. The cost of issuing and selling the preferred stock is expected to be $5 per share. Preferred stock can be sold under these terms.
 Common stock The firm’s common stock is currently selling for $90 per share. The firm expects to pay cash dividends of $7 per share next year. The firm’s dividends have been growing at an annual rate of 6%, and this growth is expected to continue into the future. The stock must be underpriced by $7 per share, and flotation costs are expected to amount to $5 per share. The firm can sell new common stock under these terms.
 Retained earnings When measuring this cost, the firm does not concern itself with the tax bracket or brokerage fees of owners. It expects to have available $100,000 of retained earnings in the coming year; once these retained earnings are exhausted, the firm will use new common stock as the form of common stock equity financing.
 a. Calculate the aftertax cost of debt.
 b. Calculate the cost of preferred stock.
 c. Calculate the cost of common stock.
 d. Calculate the firm’s weighted average cost of capital using the capital structure weights shown in the following table. (Round answer to the nearest 0.1%.)
Source of capital Weight Longterm debt 30% Preferred stock 20 Common stock equity 50 Total 100%
LG 6
 a. What is American Exploration’s current WACC?
 b. Assuming that its cost of debt and equity remain unchanged, what will be American Exploration’s WACC under the revised target capital structure?
 c. Do you think that shareholders are affected by the increase in debt to 70%? If so, how are they affected? Are their common stock claims riskier now?
 d. Suppose that in response to the increase in debt, American Exploration’s shareholders increase their required return so that cost of common equity is 16%. What will its new WACC be in this case?
 e. What does your answer in part b suggest about the tradeoff between financing with debt versus equity?
LG 1
Spreadsheet Exercise
Nova Corporation is interested in measuring the cost of each specific type of capital as well as the weighted average cost of capital. Historically, the firm has raised capital in the following manner:
Source of capital  Weight 

Longterm debt  35% 
Preferred stock  12 
Common stock equity  53 
The tax rate of the firm is currently 40%. The needed financial information and data are as follows:
 Debt Nova can raise debt by selling $1,000parvalue, 6.5% coupon interest rate, 10year bonds on which annual interest payments will be made. To sell the issue, an average discount of $20 per bond needs to be given. There is an associated flotation cost of 2% of par value.
 Preferred stock Preferred stock can be sold under the following terms: The security has a par value of $100 per share, the annual dividend rate is 6% of the par value, and the flotation cost is expected to be $4 per share. The preferred stock is expected to sell for $102 before cost considerations.
 Common stock The current price of Nova’s common stock is $35 per share. The cash dividend is expected to be $3.25 per share next year. The firm’s dividends have grown at an annual rate of 5%, and it is expected that the dividend will continue at this rate for the foreseeable future. The flotation costs are expected to be approximately $2 per share. Nova can sell new common stock under these terms.
 Retained earnings The firm expects to have available $100,000 of retained earnings in the coming year. Once these retained earnings are exhausted, the firm will use new common stock as the form of common stock equity financing. (Note: When measuring this cost, the firm does not concern itself with the tax bracket or brokerage fees of owners.)
TO DO
Create a spreadsheet to answer the following questions:
 a. Calculate the aftertax cost of debt.
 b. Calculate the cost of preferred stock.
 c. Calculate the cost of retained earnings.
 d. Calculate the cost of new common stock.
 e. Calculate the firm’s weighted average cost of capital using retained earnings and the capital structure weights shown in the table above.
 f. Calculate the firm’s weighted average cost of capital using new common stock and the capital structure weights shown in the table above.
Visit www.myfinancelab.com for Chapter Case: Making Star Products’ Financing/Investment Decision, Group Exercises, and numerous online resources.
Integrative Case 4 Eco Plastics Company
Since its inception, Eco Plastics Company has been revolutionizing plastic and trying to do its part to save the environment. Eco’s founder, Marion Cosby, developed a biodegradable plastic that her company is marketing to manufacturing companies throughout the southeastern United States. After operating as a private company for 6 years, Eco went public in 2012 and is listed on the Nasdaq stock exchange.
As the chief financial officer of a young company with lots of investment opportunities, Eco’s CFO closely monitors the firm’s cost of capital. The CFO keeps tabs on each of the individual costs of Eco’s three main financing sources: longterm debt, preferred stock, and common stock. The target capital structure for Eco is given by the weights in the following table:
Source of capital  Weight 

Longterm debt  30% 
Preferred stock  20 
Common stock equity  50 
Total  100% 
At the present time, Eco can raise debt by selling 20year bonds with a $1,000 par value and a 10.5% annual coupon interest rate. Eco’s corporate tax rate is 40%, and its bonds generally require an average discount of $45 per bond and flotation costs of $32 per bond when being sold. Eco’s outstanding preferred stock pays a 9% dividend and has a $95pershare par value. The cost of issuing and selling additional preferred stock is expected to be $7 per share. Because Eco is a young firm that requires lots of cash to grow it does not currently pay a dividend to common stockholders. To track the cost of common stock the CFO uses the capital asset pricing model (CAPM). The CFO and the firm’s investment advisors believe that the appropriate riskfree rate is 4% and that the market’s expected return equals 13%. Using data from 2012 through 2015, Eco’s CFO estimates the firm’s beta to be 1.3.
Although Eco’s current target capital structure includes 20% preferred stock, the company is considering using debt financing to retire the outstanding preferred stock, thus shifting their target capital structure to 50% longterm debt and 50% common stock. If Eco shifts its capital mix from preferred stock to debt, its financial advisors expect its beta to increase to 1.5.
TO DO
 a. Calculate Eco’s current aftertax cost of longterm debt.
 b. Calculate Eco’s current cost of preferred stock.
 c. Calculate Eco’s current cost of common stock.
 d. Calculate Eco’s current weighted average cost capital.
 e.
 (1) Assuming that the debt financing costs do not change, what effect would a shift to a more highly leveraged capital structure consisting of 50% longterm debt, 0% preferred stock, and 50% common stock have on the risk premium for Eco’s common stock? What would be Eco’s new cost of common equity?
 (2) What would be Eco’s new weighted average cost of capital?
 (3) Which capital structure—the original one or this one—seems better? Why?
_____________________________________________________________________________________________________________________________
THIS IS THE INDIVIDUAL ASSIGNMENT AND IS DUE MONDAY 6.00PM (52 HOURS). PLEASE USE EXCEL
THIS HAS 2 PART WITH 2 CHAPTERS 10 AND 11 I WILL CUT AND PASTE THE CHAPTERS UNDER THE ASSINMENT.
Complete the following problems in Ch 10:
 P102
 P107
 P1010
 P1014
 P1021
Complete the following problems in Chapter 11:
 P111
 P114
 P117
 P118
 P119
CHAPTER 10
10 Capital Budgeting Techniques
Learning Goals
 LG 1 Understand the key elements of the capital budgeting process.
 LG 2 Calculate, interpret, and evaluate the payback period.
 LG 3 Calculate, interpret, and evaluate the net present value (NPV) and economic value added (EVA).
 LG 4 Calculate, interpret, and evaluate the internal rate of return (IRR).
 LG 5 Use net present value profiles to compare NPV and IRR techniques.
 LG 6 Discuss NPV and IRR in terms of conflicting rankings and the theoretical and practical strengths of each approach.
Why This Chapter Matters to You
In your professional life
ACCOUNTING You need to understand capital budgeting techniques to help determine the relevant cash flows associated with proposed capital expenditures.
INFORMATION SYSTEMS You need to understand capital budgeting techniques to design decision modules that help reduce the amount of work required to analyze proposed capital expenditures.
MANAGEMENT You need to understand capital budgeting techniques to correctly analyze the relevant cash flows of proposed projects and decide whether to accept or reject them.
MARKETING You need to understand capital budgeting techniques to grasp how proposals for new marketing programs, for new products, and for the expansion of existing product lines will be evaluated by the firm’s decision makers.
OPERATIONS You need to understand capital budgeting techniques to know how proposals for the acquisition of new equipment and plants will be evaluated by the firm’s decision makers.
In your personal life You can use the capital budgeting techniques used by financial managers to measure either the value of a given asset purchase or its compound rate of return. The IRR technique is widely applied in personal finance to measure both actual and forecast rate of returns on investment securities, real estate, credit card debt, consumer loans, and leases.
Seafield Resources The Gold Standard for Evaluating Gold Mines
On June 19, 2013, Seafield Resources, a Canadian mining firm, announced the results of a preliminary economic assessment of a property it had purchased in Colombia. Seafield’s plan was to exploit gold deposits on the property. Before investing the initial $83.6 million that would be required to begin extracting gold from the area, however, the company wanted to be sure that the investment would benefit its shareholders. The economic assessment indicated that Seafield could expect to extract more than 42,000 ounces of gold annually over the mine’s 12year life. The costs of running the mine would run about $725 per ounce of gold extracted. Assuming a market price of gold of $1,500 per ounce, the assessment suggested that the mining project would pay back its upfront costs within 4 years, and it would produce an aftertax internal rate of return of 20% and a net present value of $66 million. The assessment went on to confirm that even if gold prices fell, the project would still be desirable. For example, if gold prices fell to $1,300 per ounce, the mine would still pay back its upfront costs in about 6 years, and it would deliver an internal rate of return of 13% and a net present value of $27 million.
Payback, internal rate of return, and net present value are all methods that companies use to evaluate potential investment projects. Each of these techniques has advantages and disadvantages, but the net present value method has become the gold standard for analyzing investments. This chapter explains why.
10.1 Overview of Capital Budgeting
LG 1
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Longterm investments represent sizable outlays of funds that commit a firm to some course of action. Consequently, the firm needs procedures to analyze and select its longterm investments. Capital budgeting is the process of evaluating and selecting longterm investments that are consistent with the firm’s goal of maximizing owners’ wealth. Firms typically make a variety of longterm investments, but the most common is in fixed assets, which include property (land), plant, and equipment. These assets, often referred to as earning assets, generally provide the basis for the firm’s earning power and value.
The process of evaluating and selecting longterm investments that are consistent with the firm’s goal of maximizing owners’ wealth.
Because firms treat capital budgeting (investment) and financing decisions separately, Chapters 10 through 12 concentrate on fixedasset acquisition without regard to the specific method of financing used. We begin by discussing the motives for capital expenditure.
MOTIVES FOR CAPITAL EXPENDITURE
A capital expenditure is an outlay of funds by the firm that is expected to produce benefits over a period of time greater than 1 year. An operating expenditure is an outlay resulting in benefits received within 1 year. Fixedasset outlays are capital expenditures, but not all capital expenditures are classified as fixed assets. A $60,000 outlay for a new machine with a usable life of 15 years is a capital expenditure that would appear as a fixed asset on the firm’s balance sheet. A $60,000 outlay for an advertising campaign that is expected to produce benefits over a long period is also a capital expenditure, but it would rarely be shown as a fixed asset.
An outlay of funds by the firm that is expected to produce benefits over a period of time greater than 1 year.
An outlay of funds by the firm resulting in benefits received within 1 year.
Companies make capital expenditures for many reasons. The primary motives for capital expenditures are to expand operations, to replace or renew fixed assets, and to obtain some other, less tangible benefit over a long period.
STEPS IN THE PROCESS
The capital budgeting process consists of five distinct but interrelated steps:
Five distinct but interrelated steps: proposal generation, review and analysis, decision making, implementation, and followup.
 1. Proposal generation. Proposals for new investment projects are made at all levels within a business organization and are reviewed by finance personnel. Proposals that require large outlays are more carefully scrutinized than less costly ones.
 2. Review and analysis. Financial managers perform formal review and analysis to assess the merits of investment proposals.
 3. Decision making. Firms typically delegate capital expenditure decision making on the basis of dollar limits. Generally, the board of directors must authorize expenditures beyond a certain amount. Often, plant managers are given authority to make decisions necessary to keep the production line moving.
 4. Implementation. Following approval, expenditures are made and projects implemented. Expenditures for a large project often occur in phases.
 5. Followup. Results are monitored, and actual costs and benefits are compared with those that were expected. Action may be required if actual outcomes differ from projected ones.
Each step in the process is important. Review and analysis and decision making (Steps 2 and 3) consume the majority of time and effort, however. Followup (Step 5) is an important but often ignored step aimed at allowing the firm to improve the accuracy of its cash flow estimates continuously. Because of their fundamental importance, this and the following chapters give primary consideration to review and analysis and to decision making.
BASIC TERMINOLOGY
Before we develop the concepts, techniques, and practices related to the capital budgeting process, we need to explain some basic terminology. In addition, we will present some key assumptions that are used to simplify the discussion in the remainder of this chapter and in Chapters 11 and 12.
Independent versus Mutually Exclusive Projects
Most investments can be placed into one of two categories: (1) independent projects or (2) mutually exclusive projects. Independent projects are those with cash flows that are unrelated to (or independent of) one another; the acceptance of one project does not eliminate the others from further consideration. Mutually exclusive projects are those that have the same function and therefore compete with one another. The acceptance of one eliminates from further consideration all other projects that serve a similar function. For example, a firm in need of increased production capacity could obtain it by (1) expanding its plant, (2) acquiring another company, or (3) contracting with another company for production. Clearly, accepting any one option eliminates the immediate need for either of the others.
Projects whose cash flows are unrelated to (or independent of) one another; the acceptance of one does not eliminate the others from further consideration.
Projects that compete with one another so that the acceptance of one eliminates from further consideration all other projects that serve a similar function.
Unlimited Funds versus Capital Rationing
The availability of funds for capital expenditures affects the firm’s decisions. If a firm has unlimited funds for investment (or if it can raise as much money as it needs by borrowing or issuing stock), making capital budgeting decisions is quite simple: All independent projects that will provide an acceptable return can be accepted. Often, though, firms operate under capital rationing instead, which means that they have a fixed budget available for capital expenditures and that numerous projects will compete for these dollars. Procedures for dealing with capital rationing are presented in Chapter 12. The discussions here and in Chapter 12 assume unlimited funds.
The financial situation in which a firm is able to accept all independent projects that provide an acceptable return.
The financial situation in which a firm has only a fixed number of dollars available for capital expenditures and numerous projects compete for these dollars.
Accept–Reject versus Ranking Approaches
Two standard approaches to capital budgeting decisions are available. The accept–reject approach involves evaluating capital expenditure proposals to determine whether they meet the firm’s minimum acceptance criterion. This approach can be used when the firm has unlimited funds, as a preliminary step when evaluating mutually exclusive projects, or in a situation in which capital must be rationed. In these cases, only acceptable projects should be considered.
The evaluation of capital expenditure proposals to determine whether they meet the firm’s minimum acceptance criterion.
The second method, the ranking approach, involves ranking projects on the basis of some predetermined measure, such as the rate of return. The project with the highest return is ranked first, and the project with the lowest return is ranked last. Only acceptable projects should be ranked. Ranking is useful in selecting the “best” of a group of mutually exclusive projects and in evaluating projects with a view of capital rationing.
The ranking of capital expenditure projects on the basis of some predetermined measure, such as the rate of return.
TABLE 10.1 Capital Expenditure Data for Bennett Company
Project A  Project B  

Initial investment  $42,000  $45,000 
Year  Operating cash inflows  
1  $14,000  $28,000 
2  14,000  12,000 
3  14,000  10,000 
4  14,000  10,000 
5  14,000  10,000 
CAPITAL BUDGETING TECHNIQUES
Large firms evaluate dozens, perhaps even hundreds, of different ideas for new investments each year. To ensure that the investment projects selected have the best chance of increasing the value of the firm, financial managers need tools to help them evaluate the merits of individual projects and to rank competing investments. A number of techniques are available for performing such analyses. The preferred approaches integrate time value procedures, risk and return considerations, and valuation concepts to select capital expenditures that are consistent with the firm’s goal of maximizing owners’ wealth. This chapter focuses on the use of these techniques in an environment of certainty.
FIGURE 10.1 Bennett Company’s Projects A and B
1. A conventional cash flow pattern is one in which the upfront cash flow is negative and all subsequent cash flows are positive. A nonconventional pattern occurs if the upfront cash flow is positive and subsequent cash flows are negative (for example, when a firm sells extended warranties and pays benefits later) or when the cash flows oscillate between positive and negative (as might occur when firms have to reinvest in a project to extend its life).
Bennett Company’s Relevant Cash Flows
We will use one basic problem to illustrate all the techniques described in this chapter. The problem concerns Bennett Company, a mediumsized metal fabricator that is currently contemplating two projects with conventional cash flow patterns:^{1} Project A requires an initial investment of $42,000, and project B requires an initial investment of $45,000. The projected relevant cash flows for the two projects are presented in Table 10.1 and depicted on the time lines in Figure 10.1. Both projects involve one initial cash outlay followed by annual cash inflows, a fairly typical pattern for new investments. We begin with a look at the three most popular capital budgeting techniques: payback period, net present value, and internal rate of return.
REVIEW QUESTION
10.2 Payback Period
LG 2
Small and mediumsized firms often use the payback period approach to evaluate proposed investments. The payback period is the time it takes the firm to recover its initial investment in a project, as calculated from cash inflows. In the case of an annuity (such as the Bennett Company’s project A), the payback period can be found by dividing the initial investment by the annual cash inflow. For a mixed stream of cash inflows (such as project B), the yearly cash inflows must be accumulated until the initial investment is recovered. Although popular, the payback period is generally viewed as an unsophisticated capital budgeting technique because it does not explicitly consider the time value of money.
The amount of time required for a firm to recover its initial investment in a project as calculated from cash inflows.
DECISION CRITERIA
When the payback period is used to make accept–reject decisions, the following decision criteria apply:
 • If the payback period is less than the maximum acceptable payback period, accept the project.
 • If the payback period is greater than the maximum acceptable payback period, reject the project.
The length of the maximum acceptable payback period is determined by management. This value is set subjectively on the basis of a number of factors, including the type of project (expansion, replacement or renewal, other), the product life cycle, the perceived risk of the project, and the perceived relationship between the payback period and the share value. It is simply a value that management feels, on average, will result in valuecreating investment decisions.
Example 10.1
We can calculate the payback period for Bennett Company’s projects A and B using the data in Table 10.1. For project A, which is an annuity, the payback period is 3.0 years ($42,000 initial investment ÷ $14,000 annual cash inflow). Because project B generates a mixed stream of cash inflows, the calculation of its payback period is not as clearcut. In year 1, the firm will recover $28,000 of its $45,000 initial investment. By the end of year 2, $40,000 ($28,000 from year 1 + $12,000 from year 2) will have been recovered. At the end of year 3, $50,000 will have been recovered. Only 50% of the year3 cash inflow of $10,000 is needed to complete the payback of the initial $45,000. The payback period for project B is therefore 2.5 years (2 years + 50% of year 3).
If Bennett’s maximum acceptable payback period were 2.75 years, project A would be rejected and project B would be accepted. If the maximum acceptable payback period were 2.25 years, both projects would be rejected. If the projects were being ranked, B would be preferred over A because it has a shorter payback period.
PROS AND CONS OF PAYBACK ANALYSIS
Large firms sometimes use the payback approach to evaluate small projects, and small firms use it to evaluate most projects. Its popularity results from its computational simplicity and intuitive appeal. By measuring how quickly the firm recovers its initial investment, the payback period also gives implicit consideration to the timing of cash flows and therefore to the time value of money. Because it can be viewed as a measure of risk exposure, many firms use the payback period as a decision criterion or as a supplement to other decision techniques. The longer the firm must wait to recover its invested funds, the greater the possibility of a calamity. Hence, the shorter the payback period, the lower the firm’s risk exposure.
The major weakness of the payback period is that the appropriate payback period is merely a subjectively determined number. It cannot be specified in light of the wealth maximization goal because it is not based on discounting cash flows to determine whether they add to the firm’s value. Instead, the appropriate payback period is simply the maximum acceptable period of time over which management decides that a project’s cash flows must break even (that is, just equal to the initial investment). The Focus on Practice box offers more information about these time limits in actual practice.
Matter of fact
Payback in Europe
A 2011 survey of firms in ten Central and Eastern European countries found that twothirds of those firms always or almost always conducted payback analysis when they made major investment decisions. In contrast to what has been observed in the United States, large firms in Eastern Europe were more likely than small firms to use the payback approach. For all its flaws, the payback approach still sees widespread use around the world.
Personal Finance Example 10.2
Seema Mehdi is considering investing $20,000 to obtain a 5% interest in a rental property. Her good friend and real estate agent, Akbar Ahmed, put the deal together and he conservatively estimates that Seema should receive between $4,000 and $6,000 per year in cash from her 5% interest in the property. The deal is structured in a way that forces all investors to maintain their investment in the property for at least 10 years. Seema expects to remain in the 25% incometax bracket for quite a while. To be acceptable, Seema requires the investment to pay itself back in terms of aftertax cash flows in less than 7 years.
Seema’s calculation of the payback period on this deal begins with calculation of the range of annual aftertax cash flow:
The aftertax cash flow ranges from $3,000 to $4,500. Dividing the $20,000 initial investment by each of the estimated aftertax cash flows, we get the payback period:
Because Seema’s proposed rental property investment will pay itself back between 4.44 and 6.67 years, which is a range below her maximum payback of 7 years, the investment is acceptable.
in practice focus on PRACTICE: Limits on Payback Analysis
In tough economic times, the standard for a payback period is often reduced. Chief information officers (CIOs) are apt to reject projects with payback periods of more than 2 years. “We start with payback period,” says Ron Fijalkowski, CIO at Strategic Distribution, Inc., in Bensalem, Pennsylvania. “For sure, if the payback period is over 36 months, it’s not going to get approved. But our rule of thumb is we’d like to see 24 months. And if it’s close to 12, it’s probably a nobrainer.”
Although easy to compute and easy to understand, the payback period’s simplicity brings with it some drawbacks. “Payback gives you an answer that tells you a bit about the beginning stage of a project, but it doesn’t tell you much about the full lifetime of the project,” says Chris Gardner, a cofounder of iValue LLC, an IT valuation consultancy in Barrington, Illinois. “The simplicity of computing payback may encourage sloppiness, especially the failure to include all costs associated with an investment, such as training, maintenance, and hardware upgrade costs,” says Douglas Emond, senior vice president and chief technology officer at Eastern Bank in Lynn, Massachusetts. For example, he says, “you may be bringing in a hot new technology, but uhoh, after implementation you realize that you need a .Net guru inhouse, and you don’t have one.”
But the payback method’s emphasis on the short term has a special appeal for IT managers. “That’s because the history of IT projects that take longer than 3 years is disastrous,” says Gardner. Indeed, Ian Campbell, chief research officer at Nucleus Research, Inc., in Wellesley, Massachusetts, says payback period is an absolutely essential metric for evaluating IT projects—even more important than discounted cash flow (NPV and IRR)—because it spotlights the risks inherent in lengthy IT projects. “It should be a hardandfast rule to never take an IT project with a payback period greater than 3 years, unless it’s an infrastructure project you can’t do without,” Campbell says.
Whatever the weaknesses of the payback period method of evaluating capital projects, the simplicity of the method does allow it to be used in conjunction with other, more sophisticated measures. It can be used to screen potential projects and winnow them down to the few that merit more careful scrutiny with, for example, net present value (NPV).
In your view, if the payback period method is used in conjunction with the NPV method, should it be used before or after the NPV evaluation?
www.computerworld.com/s/article/78529/ROI_Guide_Payback_Period?taxono.
A second weakness is that this approach fails to take fully into account the time factor in the value of money.^{2} This weakness can be illustrated by an example.
2. To consider differences in timing explicitly in applying the payback method, the discounted payback period is sometimes used. It is found by first calculating the present value of the cash inflows at the appropriate discount rate and then finding the payback period by using the present value of the cash inflows.
Example 10.3
DeYarman Enterprises, a small medical appliance manufacturer, is considering two mutually exclusive projects named Gold and Silver. The firm uses only the payback period to choose projects. The cash flows and payback period for each project are given in Table 10.2. Both projects have 3year payback periods, which would suggest that they are equally desirable. But comparison of the pattern of cash inflows over the first 3 years shows that more of the $50,000 initial investment in project Silver is recovered sooner than is recovered for project Gold. For example, in year 1, $40,000 of the $50,000 invested in project Silver is recovered, whereas only $5,000 of the $50,000 investment in project Gold is recovered. Given the time value of money, project Silver would clearly be preferred over project Gold, even though both have identical 3year payback periods. The payback approach does not fully account for the time value of money, which, if recognized, would cause project Silver to be preferred over project Gold.
TABLE 10.2 Relevant Cash Flows and Payback Periods for DeYarman Enterprises’ Projects
Project gold  Project silver  

Initial investment  $50,000  $50,000 
Year  Operating cash inflows  
1  $ 5,000  $40,000 
2  5,000  2,000 
3  40,000  8,000 
4  10,000  10,000 
5  10,000  10,000 
Payback period  3 years  3 years 
A third weakness of payback is its failure to recognize cash flows that occur after the payback period.
Example 10.4
Rashid Company, a software developer, has two investment opportunities, X and Y. Data for X and Y are given in Table 10.3. The payback period for project X is 2 years; for project Y, it is 3 years. Strict adherence to the payback approach suggests that project X is preferable to project Y. However, if we look beyond the payback period, we see that project X returns only an additional $1,200 ($1,000 in year 3 + $100 in year 4 + $100 in year 5), whereas project Y returns an additional $7,000 ($4,000 in year 4 + $3,000 in year 5). On the basis of this information, project Y appears preferable to X. The payback approach ignored the cash inflows occurring after the end of the payback period.
TABLE 10.3 Calculation of the Payback Period for Rashid Company’s Two Alternative Investment Projects
Project X  Project Y  

Initial investment  $10,000  $10,000 
Year  Operating cash inflows  
1  $5,000  $3,000 
2  5,000  4,000 
3  1,000  3,000 
4  100  4,000 
5  100  3,000 
Payback period  2 years  3 years 
REVIEW QUESTIONS
10.3 Net Present Value (NPV)
LG 3
The method used by most large companies to evaluate investment projects is called net present value (NPV). The intuition behind the NPV method is simple. When firms make investments, they are spending money that they obtained, in one form or another, from investors. Investors expect a return on the money that they give to firms, so a firm should undertake an investment only if the present value of the cash flow that the investment generates is greater than the cost of making the investment in the first place. Because the NPV method takes into account the time value of investors’ money, it is a more sophisticated capital budgeting technique than the payback rule. The NPV method discounts the firm’s cash flows at the firm’s cost of capital. This rate—as discussed in Chapter 9—represents the firm’s cost of financing and is the minimum return that must be earned on a project to satisfy the firm’s investors. Projects with lower returns fail to meet investors’ expectations and therefore decrease firm value, and projects with higher returns increase firm value.
The net present value (NPV) is found by subtracting a project’s initial investment (CF_{0}) from the present value of its cash inflows (CF_{t}) discounted at a rate equal to the firm’s cost of capital (r):
A sophisticated capital budgeting technique; found by subtracting a project’s initial investment from the present value of its cash inflows discounted at a rate equal to the firm’s cost of capital.
NPV = Present value of cash inflows − Initial investment
(10.1) 
When NPV is used, both inflows and outflows are measured in terms of present dollars. For a project that has cash outflows beyond the initial investment, the net present value of a project would be found by subtracting the present value of outflows from the present value of inflows.
DECISION CRITERIA
When NPV is used to make accept–reject decisions, the decision criteria are as follows:
 • If the NPV is greater than $0, accept the project.
 • If the NPV is less than $0, reject the project.
If the NPV is greater than $0, the firm will earn a return greater than its cost of capital. Such action should increase the market value of the firm, and therefore the wealth of its owners, by an amount equal to the NPV.
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Example 10.5
We can illustrate the net present value (NPV) approach by using the Bennett Company data presented in Table 10.1. If the firm has a 10% cost of capital, the net present values for projects A (an annuity) and B (a mixed stream) can be calculated as shown on the time lines in Figure 10.2. These calculations result in net present values for projects A and B of $11,071 and $10,924, respectively. Both projects are acceptable because the net present value of each is greater than $0. If the projects were being ranked, however, project A would be considered superior to B because it has a higher net present value than that of B ($11,071 versus $10,924).
FIGURE 10.2 Calculation of NPVs for Bennett Company’s Capital Expenditure Alternatives
Calculator use The preprogrammed NPV function in a financial calculator can be used to simplify the NPV calculation. The keystrokes for project A—the annuity—typically are as shown at left. Note that because project A is an annuity, only its first cash inflow, CF_{1} = 14000, is input, followed by its frequency, N = 5.
The keystrokes for project B—the mixed stream—are as also shown. Because the last three cash inflows for project B are the same (CF_{3} = CF_{4} = CF_{5} = 10,000), after inputting the first of these cash inflows, CF_{3}, we merely input its frequency, N = 3.
The calculated NPVs for projects A and B of $11,071 and $10,924, respectively, agree with the NPVs already cited.
Spreadsheet use The NPVs can be calculated as shown on the following Excel spreadsheet.
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NPV AND THE PROFITABILITY INDEX
A variation of the NPV rule is called the profitability index (PI). For a project that has an initial cash outflow followed by cash inflows, the profitability index (PI) is simply equal to the present value of cash inflows divided by the initial cash outflow:^{3}
(10.2) 
When companies evaluate investment opportunities using the PI, the decision rule they follow is to invest in the project when the index is greater than 1.0. A PI greater than 1.0 implies that the present value of cash inflows is greater than the (absolute value of the) initial cash outflow, so a profitability index greater than 1.0 corresponds to a net present value greater than 0. In other words, the NPV and PI methods will always come to the same conclusion regarding whether a particular investment is worth doing or not.
3. To be a bit more precise, the denominator in Equation 10.2 should be a positive number, so we are taking the absolute value of the initial cash outflow.
Example 10.6
We can refer back to Figure 10.2, which shows the present value of cash inflows for projects A and B, to calculate the PI for each of Bennett’s investment options:
According to the profitability index, both projects are acceptable (because PI > 1.0 for both), which shouldn’t be surprising because we already know that both projects have positive NPVs. Furthermore, in this particular case, the NPV rule and the PI both indicate that project A is preferred over project B. It is not always true that the NPV and PI methods will rank projects in exactly the same order. Different rankings can occur when alternative projects require initial outlays that have very different magnitudes.
NPV AND ECONOMIC VALUE ADDED
Economic Value Added (EVA), a registered trademark of the consulting firm Stern Stewart & Co., is another close cousin of the NPV method. Whereas the NPV approach calculates the value of an investment over its entire life, the EVA approach is typically used to measure an investment’s performance on a yearbyyear basis. The EVA method begins the same way that NPV does: by calculating a project’s net cash flows. However, the EVA approach subtracts from those cash flows a charge that is designed to capture the return that the firm’s investors demand on the project. That is, the EVA calculation asks whether a project generates positive cash flows above and beyond what investors demand. If so, the project is worth undertaking.
The EVA method determines whether a project earns a pure economic profit. When accountants say that a firm has earned a profit, they mean that revenues are greater than expenses. But the term pure economic profit refers to a profit that is higher than expected given the competitive rate of return on a particular line of business. A firm that shows a positive profit on its income statement may or may not earn a pure economic profit, depending on how large the profit is relative to the capital invested in the business. For instance, in the four quarters ending on March 30, 2013, Alcoa Inc., the aluminum producing giant, reported that it had earned a net profit of $264 million. Does that seem like a large profit? Perhaps it doesn’t when you consider that Alcoa’s balance sheet showed total assets of more than $40 billion. In other words, Alcoa’s profit represented a return of 0.6% on the firm’s assets. That return was not far from the rate offered on riskfree government securities in 2013, so it clearly fell below the expectations of Alcoa’s investors (who would have expected a higher return as compensation for the risks they were taking). Thus, the company earned a pure economic loss over those four quarters. Stated differently, Alcoa’s EVA during that period was negative.
A profit above and beyond the normal competitive rate of return in a line of business.
4. We are using Equation 5.7 to calculate the present value of the perpetual stream of $120,000 cash flows.
Example 10.7
Suppose that a certain project costs $1,000,000 up front, but after that it will generate net cash inflows each year (in perpetuity) of $120,000. To calculate the NPV of this project, we would simply discount the cash flows and add them up. If the firm’s cost of capital is 10%, the project’s NPV is:^{4}
NPV = −$1,000,000 + ($120,000 ÷ 0.10) = $200,000
To calculate the investment’s economic value added in any particular year, we start with the annual $120,000 cash flow. Next, we assign a charge that accounts for the return that investors demand on the capital that the firm has invested in the project. In this case, the firm invested $1,000,000, and investors expect a 10% return. That means that the project’s annual capital charge is $100,000 ($1,000,000 × 10%), and its EVA is $20,000 per year:
In other words, this project earns more than its cost of capital each year, so the project is clearly worth doing. To calculate the EVA for the project over its entire life, we would simply discount the annual EVA figures using the firm’s cost of capital. In this case, the project produces an annual EVA of $20,000 in perpetuity. Discounting at 10% gives a project EVA of $200,000 ($20,000 ÷ 0.10), identical to the NPV. In this example, both the NPV and EVA methods reach the same conclusion, namely that the project creates $200,000 in value for shareholders. If the cash flows in our example had fluctuated through time rather than remaining fixed at $120,000 per year, an analyst would calculate the investment’s EVA every year and then discount those figures to the present using the firm’s cost of capital. If the resulting figure is positive, the project generates a positive EVA and is worth doing.
REVIEW QUESTIONS
EXCEL REVIEW QUESTION
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10.4 Internal Rate of Return (IRR)
LG 4
The internal rate of return (IRR) is the discount rate that equates the NPV of an investment opportunity with $0 (because the present value of cash inflows equals the initial investment). It is the rate of return that the firm will earn if it invests in the project and receives the given cash inflows. Mathematically, the IRR is the value of r in Equation 10.1 that causes NPV to equal $0, or
The discount rate that equates the NPV of an investment opportunity with $0 (because the present value of cash inflows equals the initial investment); it is the rate of return that the firm will earn if it invests in the project and receives the given cash inflows.
(10.3)  
(10.3a) 
DECISION CRITERIA
When IRR is used to make accept–reject decisions, the decision criteria are as follows:
 • If the IRR is greater than the cost of capital, accept the project.
 • If the IRR is less than the cost of capital, reject the project.
These criteria guarantee that the firm will earn at least its required return. Such an outcome should increase the market value of the firm and therefore the wealth of its owners.
CALCULATING THE IRR
With these calculators, you merely punch in all cash flows just as if to calculate NPV and then depress IRR to find the internal rate of return. Computer software, including spreadsheets, is also available for simplifying these calculations. All NPV and IRR values presented in this and subsequent chapters are obtained by using these functions on a financial calculator.
Example 10.8
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We can demonstrate the internal rate of return (IRR) approach by using the Bennett Company data presented in Table 10.1. Figure 10.3 uses time lines to depict the framework for finding the IRRs for Bennett’s projects A and B. We can see in the figure that the IRR is the unknown discount rate that causes the NPV to equal $0.
Calculator use To find the IRR using the preprogrammed function in a financial calculator, the keystrokes for each project are the same as those shown on pages 404 and 405 for the NPV calculation, except that the last two NPV keystrokes (punching I and then NPV) are replaced by a single IRR keystroke.
FIGURE 10.3 Calculation of IRRs for Bennett Company’s Capital Expenditure Alternatives
Comparing the IRRs of projects A and B given in Figure 10.3 to Bennett Company’s 10% cost of capital, we can see that both projects are acceptable because
Comparing the two projects’ IRRs, we prefer project B over project A because project B delivers a higher IRR (IRR_{B} = 21.7% > IRR_{A} = 19.9%). If these projects are mutually exclusive, meaning that we can choose one project or the other but not both, the IRR decision technique would recommend project B.
Spreadsheet use The internal rate of return also can be calculated as shown on the following Excel spreadsheet.
In the preceding example, note that the IRR suggests that project B, which has an IRR of 21.7%, is preferable to project A, which has an IRR of 19.9%. This suggestion conflicts with the NPV rankings obtained in an earlier example. Such conflicts are not unusual. There is no guarantee that NPV and IRR will rank projects in the same order. However, both methods usually reach the same conclusion about whether a single project, considered in isolation, is acceptable or not.
Personal Finance Example 10.9
Tony DiLorenzo is evaluating an investment opportunity. He is comfortable with the investment’s level of risk. Based on competing investment opportunities, he believes that this investment must earn a minimum compound annual aftertax return of 9% to be acceptable. Tony’s initial investment would be $7,500, and he expects to receive annual aftertax cash flows of $500 per year in each of the first 4 years, followed by $700 per year at the end of years 5 through 8. He plans to sell the investment at the end of year 8 and net $9,000, after taxes.
To calculate the investment’s IRR (compound annual return), Tony first summarizes the aftertax cash flows as shown in the following table:
Year  Cash flow (− or +) 

0  −$7,500 (Initial investment) 
1  500 
2  500 
3  500 
4  500 
5  700 
6  700 
7  700 
8  9,700 ($700 + $9,000) 
Substituting the aftertax cash flows for years 0 through 8 into a financial calculator or spreadsheet, he finds the investment’s IRR of 9.54%. Given that the expected IRR of 9.54% exceeds Tony’s required minimum IRR of 9%, the investment is acceptable.
REVIEW QUESTIONS
EXCEL REVIEW QUESTION
My Finance Lab
10.5 Comparing NPV and IRR Techniques
LG 5
LG 6
To understand the differences between the NPV and IRR techniques and decision makers’ preferences in their use, we need to look at net present value profiles, conflicting rankings, and the question of which approach is better.
NET PRESENT VALUE PROFILES
Projects can be compared graphically by constructing net present value profiles that depict the project’s NPVs for various discount rates. These profiles are useful in evaluating and comparing projects, especially when conflicting rankings exist. They are best demonstrated via an example.
Graph that depicts a project’s NPVs for various discount rates.
Example 10.10
To prepare net present value profiles for Bennett Company’s two projects, A and B, the first step is to develop a number of “discount rate–net present value” coordinates. Three coordinates can be easily obtained for each project; they are at a discount rate of 0%, at a discount rate of 10% (the cost of capital, r), and the IRR. The net present value at a 0% discount rate is found by merely adding all the cash inflows and subtracting the initial investment. Using the data in Table 10.1 and Figure 10.1, we get
For project A:
($14,000 + $14,000 + $14,000 + $14,000 + $14,000) − $42,000 = $28,000
For project B:
($28,000 + $12,000 + $10,000 + $10,000 + $10,000) − $45,000 = $25,000
The net present values for projects A and B at the 10% cost of capital are $11,071 and $10,924, respectively (from Figure 10.2). Because the IRR is the discount rate for which net present value equals zero, the IRRs (from Figure 10.3) of 19.9% for project A and 21.7% for project B result in $0 NPVs. The three sets of coordinates for each of the projects are summarized in Table 10.4.
Plotting the data from Table 10.4 on the next page results in the net present value profiles for projects A and B shown in Figure 10.4. The figure reveals three important facts:
 1. The IRR of project B is greater than the IRR of project A, so managers using the IRR method to rank projects will always choose B over A if both projects are acceptable.
 2. The NPV of project A is sometimes higher and sometimes lower than the NPV of project B; thus, the NPV method will not consistently rank A above B or vice versa. The NPV ranking will depend on the firm’s cost of capital.
 3. When the cost of capital is approximately 10.7%, projects A and B have identical NPVs.
The cost of capital for Bennett Company is 10%; at that rate, project A has a higher NPV than project B (the red line is above the blue line in Figure 10.4 when the discount rate is 10%). Therefore, the NPV and IRR methods rank the two projects differently. If Bennett’s cost of capital were a little higher, say 12%, the NPV method would rank project B over project A and there would be no conflict in the rankings provided by the NPV and IRR approaches.
TABLE 10.4 Discount Rate–NPV Coordinates for Projects A and B
Net present value  



Discount rate  Project A  Project B 
0%  $28,000  $25,000 
10  11,071  10,924 
19.9  0  — 
21.7  —  0 
FIGURE 10.4 NPV Profiles
CONFLICTING RANKINGS
Ranking different investment opportunities is an important consideration when projects are mutually exclusive or when capital rationing is necessary. When projects are mutually exclusive, ranking enables the firm to determine which project is best from a financial standpoint. When capital rationing is necessary, ranking projects will provide a logical starting point for determining which group of projects to accept. As we’ll see, conflicting rankings using NPV and IRR result from differences in the reinvestment rate assumption, the timing of each project’s cash flows, and the magnitude of the initial investment.
Conflicts in the ranking given a project by NPV and IRR, resulting from differences in the magnitude and timing of cash flows.
Reinvestment Assumption
One underlying cause of conflicting rankings is different implicit assumptions about the reinvestment of intermediate cash inflows, cash inflows received prior to the termination of a project. NPV assumes that intermediate cash inflows are reinvested at the cost of capital, whereas IRR assumes that intermediate cash inflows are reinvested at a rate equal to the project’s IRR.^{5} These differing assumptions can be demonstrated with an example.
Cash inflows received prior to the termination of a project.
5. To eliminate the reinvestment rate assumption of the IRR, some practitioners calculate the modified internal rate of return (MIRR). The MIRR is found by converting each operating cash inflow to its future value measured at the end of the project’s life and then summing the future values of all inflows to get the project’s terminal value. Each future value is found by using the cost of capital, thereby eliminating the reinvestment rate criticism of the traditional IRR. The MIRR represents the discount rate that causes the terminal value just to equal the initial investment. Because it uses the cost of capital as the reinvestment rate, the MIRR is generally viewed as a better measure of a project’s true profitability than the IRR. Although this technique is frequently used in commercial real estate valuation and is a preprogrammed function on some financial calculators, its failure to resolve the issue of conflicting rankings and its theoretical inferiority to NPV have resulted in the MIRR receiving only limited attention and acceptance in the financial literature.
Example 10.11
A project requiring a $170,000 initial investment is expected to provide operating cash inflows of $52,000, $78,000, and $100,000 at the end of each of the next 3 years. The NPV of the project (at the firm’s 10% cost of capital) is $16,867, and its IRR is 15%. Clearly, the project is acceptable (NPV = $16,867 > $0 and IRR = 15% > 10% cost of capital). Table 10.5 demonstrates calculation of the project’s future value at the end of its 3year life, assuming both a 10% (its cost of capital) and a 15% (its IRR) rate of return. A future value of $248,720 results from reinvestment at the 10% cost of capital, and a future value of $258,470 results from reinvestment at the 15% IRR.
TABLE 10.5 Reinvestment Rate Comparisons for a Project
Year  Operating cash inflows  Number of years earnings interest (t)  Reinvestment rate



10%  15%  
Future value  Future value  
1  $ 52,000  2  $ 62,920  $ 68,770 
2  78,000  1  85,800  89,700 
3  100,000  0  100,000  100,000 
Future value end of year 3  $248,720  $258,470  
NPV @ 10% = $16,867  
IRR = 15% 
If the future value in each case in Table 10.5 were viewed as the return received 3 years from today from the $170,000 initial investment, the cash flows would be those given in Table 10.6. The NPVs and IRRs in each case are shown below the cash flows in Table 10.6. You can see that at the 10% reinvestment rate, the NPV remains at $16,867; reinvestment at the 15% IRR produces an NPV of $24,192.
From this result, it should be clear that the NPV technique assumes reinvestment at the cost of capital (10% in this example). (Note that with reinvestment at 10%, the IRR would be 13.5%.) On the other hand, the IRR technique assumes an ability to reinvest intermediate cash inflows at the IRR. If reinvestment does not occur at this rate, the IRR will differ from 15%. Reinvestment at a rate lower than the IRR would result in an IRR lower than that calculated (at 13.5%, for example, if the reinvestment rate were only 10%). Reinvestment at a rate higher than the IRR would result in an IRR higher than that calculated.
TABLE 10.6 Project Cash Flows after Reinvestment
Timing of the Cash Flow
Another reason the IRR and NPV methods may provide different rankings for investment options has to do with differences in the timing of cash flows. Go back to the timelines for investments A and B in Figure 10.1 on page 398. The upfront investment required by each investment is similar, but after that, the timing of each project’s cash flows is quite different. Project B has a large cash inflow almost immediately (in year 1), whereas Project A provides cash flows that are distributed evenly across time. Because so much of Project B’s cash flows arrive early in its life (especially compared to the timing for Project A), the NPV of Project B will not be particularly sensitive to changes in the discount rate. Project A’s NPV, on the other hand, will fluctuate more as the discount rate changes. In essence, Project B is somewhat akin to a shortterm bond, whose price doesn’t change much when interest rates move, and Project A is more like a longterm bond whose price fluctuates a great deal when rates change.
You can see this pattern if you review the NPV profiles for projects A and B in Figure 10.4 on page 412. The red line representing project A is considerably steeper than the blue line representing project B. At very low discount rates, project A has a higher NPV, but as the discount rate increases, the NPV of project A declines rapidly. When the discount rate is high enough, the NPV of project B overtakes that of project A.
We can summarize this discussion as follows. Because project A’s cash flows arrive later than project B’s cash flows do, when the firm’s cost of capital is relatively low (to be specific, below about 10.7 percent), the NPV method will rank project A ahead of project B. At a higher cost of capital, the early arrival of project B’s cash flows becomes more advantageous, and the NPV method will rank project B over project A. The differences in the timing of cash flows between the two projects does not affect the ranking provided by the IRR method, which always puts project B ahead of project A. Table 10.7 illustrates how the conflict in rankings between the NPV and IRR approaches depends on the firm’s cost of capital.
TABLE 10.7 Ranking Projects A and B Using IRR and NPV Methods
Method  Project A  Project B 

IRR  ✓  
NPV  
if r < 10.7%  ✓  
if r > 10.7%  ✓ 
Magnitude of the Initial Investment
Suppose that someone offered you the following two investment options. You could invest $2 today and receive $3 tomorrow, or you could invest $1,000 today and receive $1,100 tomorrow. The first investment provides a return (an IRR) of 50 percent in just 1 day, a return that surely would surpass any reasonable hurdle rate. But after making this investment, you’re only better off by $1. On the other hand, the second choice offers a return of 10 percent in a single day. That’s far less than the first opportunity, but earning 10 percent in a single day is still a very high return. In addition, if you accept this investment, you will be $100 better off tomorrow than you were today.
Most people would choose the second option presented above, even though the rate of return on that option (10 percent) is far less than the rate offered by the first option (50 percent). They reason (correctly) that it is sometimes better to accept a lower return on a larger investment than to accept a very high return on a small investment. Said differently, most people know that they are better off taking the investment that pays them a $100 profit in just 1 day rather than the investment that generates just a $1 profit.^{6}
The preceding example illustrates what is known as the scale (or magnitude) problem. The scale problem occurs when two projects are very different in terms of how much money is required to invest in each project. In these cases, the IRR and NPV methods may rank projects differently. The IRR approach (and the PI method) may favor small projects with high returns (like the $2 loan that turns into $3), whereas the NPV approach favors the investment that makes the investor the most money (like the $1,000 investment that yields $1,100 in 1 day). In the case of the Bennett Company’s projects, the scale problem is not likely to be the cause of the conflict in project rankings because the initial investment required to fund each project is quite similar.
To summarize, it is important for financial managers to keep an eye out for conflicts in project rankings provided by the NPV and IRR methods, but differences in the magnitude and timing of cash inflows do not guarantee conflicts in ranking. In general, the greater the difference between the magnitude and timing of cash inflows, the greater the likelihood of conflicting rankings. Conflicts based on NPV and IRR can be reconciled computationally; to do so, one creates and analyzes an incremental project reflecting the difference in cash flows between the two mutually exclusive projects.
WHICH APPROACH IS BETTER?
Many companies use both the NPV and IRR techniques because current technology makes them easy to calculate. But it is difficult to choose one approach over the other because the theoretical and practical strengths of the approaches differ. Clearly, it is wise to evaluate NPV and IRR techniques from both theoretical and practical points of view.
Theoretical View
On a purely theoretical basis, NPV is the better approach to capital budgeting as a result of several factors. Most important, the NPV measures how much wealth a project creates (or destroys if the NPV is negative) for shareholders. Given that the financial manager’s objective is to maximize shareholder wealth, the NPV approach has the clearest link to this objective and therefore is the “gold standard” for evaluating investment opportunities.
6. Note that the profitability index also provides an incorrect ranking in this example. The first option has a PI of 1.5 ($3 ÷ $2), and the second option’s PI equals 1.1 ($1,100 ÷ $1,000). Just like the IRR, the PI suggests that the first option is better, but we know that the second option makes more money.
In addition, certain mathematical properties may cause a project with a nonconventional cash flow pattern to have multiple IRRs, or more than one IRR. Mathematically, the maximum number of real roots to an equation is equal to its number of sign changes. Take an equation like x^{2} − 5x + 6 = 0, which has two sign changes in its coefficients—from positive (+x^{2}) to negative (−5x) and then from negative (−5x) to positive (+6). If we factor the equation (remember factoring from high school math?), we get (x − 2) × (x − 3), which means that x can equal either 2 or 3; there are two correct values for x. Substitute them back into the equation, and you’ll see that both values work.
More than one IRR resulting from a capital budgeting project with a nonconventional cash flow pattern; the maximum number of IRRs for a project is equal to the number of sign changes in its cash flows.
This same outcome can occur when finding the IRR for projects with nonconventional cash flows because they have more than one sign change in the stream of cash flows. Clearly, when multiple IRRs occur for nonconventional cash flows, the analyst faces the timeconsuming need to interpret their meanings so as to evaluate the project. That such a challenge does not exist when using NPV enhances its theoretical superiority.
Practical View
Evidence suggests that despite the theoretical superiority of NPV, financial managers use the IRR approach just as often as the NPV method. The appeal of the IRR technique is due to the general disposition of business people to think in terms of rates of return rather than actual dollar returns. Because interest rates, profitability, and so on are most often expressed as annual rates of return, the use of IRR makes sense to financial decision makers. They tend to find NPV less intuitive because it does not measure benefits relative to the amount invested. Because a variety of techniques are available for avoiding the pitfalls of the IRR, its widespread use does not imply a lack of sophistication on the part of financial decision makers. Clearly, corporate financial analysts are responsible for identifying and resolving problems with the IRR before the decision makers use it as a decision technique.
Matter of fact
Which Methods Do Companies Actually Use?
Researchers surveyed chief financial officers (CFOs) about what methods the CFOs used to evaluate capital investment projects. One interesting finding was that many companies use more than one of the approaches we’ve covered in this chapter. The most popular approaches by far were IRR and NPV, used by 76 percent and 75 percent (respectively) of the CFOs responding to the survey. These techniques enjoy wider use in larger firms, with the payback approach being more common in smaller firms.^{7}
7. John R. Graham and Campbell R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics 60 (2001), pp. 187–243.
in practice focus on ETHICS: Nonfinancial Considerations in Project Selection
Corporate ethics codes are often faulted for being “window dressing,” for having little or no effect on actual behavior. Financial ethics expert John Dobson says daytoday behavior in the workplace “acculturates” employees, teaching them that the behavior they see is rational and acceptable in that environment. The good news is that professional ethics codes, such as those developed for chartered financial analysts, corporate treasury professionals, and certified financial planners, actually provide sound guidelines for behavior. These codes, notes Dobson, are based on economically rational concepts such as integrity and trustworthiness, which guide the decision maker in attempting to increase shareholder wealth. Financial executives insist that there should be no separation between an individual’s personal ethics and his or her business ethics. “It’s a jungle out there” and “Business is business” should not be excuses for engaging in unethical behavior.
How do ethics codes apply to project selection and capital budgeting? For most companies, ethical considerations are primarily concerned with the reduction of potential risks associated with a project. For example, Gateway Computers clearly outlines in its corporate code of ethics the increased regulatory and procurement laws with which an employee must be familiar so as to sell to the government. The company points out that knowingly submitting a false claim or statement to a governmental agency could subject Gateway and its employees to significant monetary civil damages, penalties, and even criminal sanctions.
Another way to incorporate nonfinancial considerations into capital project evaluation is to take into account the likely effect of decisions on nonshareholder parties or stakeholders: employees, customers, the local community, and suppliers. Chipotle Mexican Grill’s “Food with Integrity” mission is one example. Chipotle’s philosophy is that the company “can always do better in terms of the food we buy. And when we say better, we mean better in every sense of the word—better tasting, coming from better sources, better for the environment, better for the animals, and better for the farmers who raise the animals and grow the produce.”^{a}
In support of their mission, Chipotle sources meat from animals that are raised humanely, fed a vegetarian diet, and never given antibiotics or hormones. The company favors locally grown produce, organically grown beans, and dairy products made from milk from cows raised in pastures and free of growth hormones. Chipotle’s efforts have been rewarded, as sales increased by nearly 50 percent from 2007 to 2009 and by nearly 80 percent from 2009 to 2012. Investors have also profited, as shares that sold for $44 at the company’s 2006 initial public offering were priced at over $400 in mid2013.
What are the potential risks to a company of unethical behaviors by employees? What are potential risks to the public and to stakeholders?
In addition, decision makers should keep in mind that nonfinancial considerations may be important elements in project selection, as discussed in the Focus on Ethics box.
REVIEW QUESTIONS
Summary
FOCUS ON VALUE
The financial manager must apply appropriate decision techniques to assess whether proposed investment projects create value. Net present value (NPV) and internal rate of return (IRR) are the generally preferred capital budgeting techniques. Both use the cost of capital as the required return. The appeal of NPV and IRR stems from both indicating whether a proposed investment creates or destroys shareholder value.
NPV clearly indicates the expected dollar amount of wealth creation from a proposed project, whereas IRR only provides the same acceptorreject decision as NPV. As a consequence of some fundamental differences, NPV and IRR do not necessarily rank projects in the same way. NPV is the theoretically preferred approach. In practice, however, IRR enjoys widespread use because of its intuitive appeal. Regardless, the application of NPV and IRR to good estimates of relevant cash flows should enable the financial manager to recommend projects that are consistent with the firm’s goal of maximizing shareholder wealth.
REVIEW OF LEARNING GOALS
LG 1 Understand the key elements of the capital budgeting process. Capital budgeting techniques are the tools used to assess project acceptability and ranking. Applied to each project’s relevant cash flows, they indicate which capital expenditures are consistent with the firm’s goal of maximizing owners’ wealth.
LG 2 Calculate, interpret, and evaluate the payback period. The payback period is the amount of time required for the firm to recover its initial investment, as calculated from cash inflows. Shorter payback periods are preferred. The payback period is relatively easy to calculate, has simple intuitive appeal, considers cash flows, and measures risk exposure. Its weaknesses include lack of linkage to the wealth maximization goal, failure to consider time value explicitly, and that it ignores cash flows that occur after the payback period.
LG 3 Calculate, interpret, and evaluate the net present value (NPV) and economic value added (EVA). Because it gives explicit consideration to the time value of money, NPV is considered a sophisticated capital budgeting technique. NPV measures the amount of value created by a given project; only positive NPV projects are acceptable. The rate at which cash flows are discounted in calculating NPV is called the discount rate, required return, cost of capital, or opportunity cost. By whatever name, this rate represents the minimum return that must be earned on a project to leave the firm’s market value unchanged. The EVA method begins the same way that NPV does: by calculating a project’s net cash flows. However, the EVA approach subtracts from those cash flows a charge that is designed to capture the return that the firm’s investors demand on the project. That is, the EVA calculation asks whether a project generates positive cash flows above and beyond what investors demand. If so, the project is worth undertaking.
LG 4 Calculate, interpret, and evaluate the internal rate of return (IRR). Like NPV, IRR is a sophisticated capital budgeting technique. IRR is the compound annual rate of return that the firm will earn by investing in a project and receiving the given cash inflows. By accepting only those projects with IRRs in excess of the firm’s cost of capital, the firm should enhance its market value and the wealth of its owners. Both NPV and IRR yield the same accept–reject decisions, but they often provide conflicting rankings.
LG 5 Use net present value profiles to compare NPV and IRR techniques. A net present value profile is a graph that depicts projects’ NPVs for various discount rates. The NPV profile is prepared by developing a number of “discount rate–net present value” coordinates (including discount rates of 0 percent, the cost of capital, and the IRR for each project) and then plotting them on the same set of discount rate–NPV axes.
LG 6 Discuss NPV and IRR in terms of conflicting rankings and the theoretical and practical strengths of each approach. Conflicting rankings of projects frequently emerge from NPV and IRR as a result of differences in the reinvestment rate assumption as well as the magnitude and timing of cash flows. NPV assumes reinvestment of intermediate cash inflows at the more conservative cost of capital; IRR assumes reinvestment at the project’s IRR. On a purely theoretical basis, NPV is preferred over IRR because NPV assumes the more conservative reinvestment rate and does not exhibit the mathematical problem of multiple IRRs that often occurs when IRRs are calculated for nonconventional cash flows. In practice, the IRR is more commonly used because it is consistent with the general preference of business professionals for rates of return, and corporate financial analysts can identify and resolve problems with the IRR before decision makers use it.
OpenerinReview
The following is some additional information regarding the Seafield Resources’ mining opportunity mentioned in the chapter opener.
Seafield’s cost of capital  10% 
Initial cost  $83.6 million 
Project life  12 years 
Cash flow in years 1–12  $18.8 million 
 a. The chapter opener reported that the project had an NPV of $66 million and an internal rate of return of 20%. From those two facts alone, what can you conclude about Seafield’s cost of capital? (Hint: Is it more than or less than 20%?)
 b. Given the information above about the project’s initial cost and subsequent cash flows as well as the information from part a, can you estimate Seagate’s cost of capital?
SelfTest Problem
(Solutions in Appendix)
LG 2
LG 3
LG 4
LG 5
LG 6
Project M  Project N  



Initial investment (CF_{0})  $28,500  $27,000 
Year (t)  Cash inflows (CF_{t})  
1  $10,000  $11,000 
2  10,000  10,000 
3  10,000  9,000 
4  10,000  8,000 
 a. Calculate each project’s payback period.
 b. Calculate the net present value (NPV) for each project.
 c. Calculate the internal rate of return (IRR) for each project.
 d. Summarize the preferences dictated by each measure you calculated, and indicate which project you would recommend. Explain why.
 e. Draw the net present value profiles for these projects on the same set of axes, and explain the circumstances under which a conflict in rankings might exist.
Warmup Exercises
All problems are available in MyFinanceLab.
LG 2
Expected cash inflows  



Year  Hydrogen  Helium 
1  $6,000  $7,000 
2  6,000  7,000 
3  8,000  8,000 
4  4,000  5,000 
5  3,500  5,000 
6  2,000  4,000 
LG 3
Year  Cash inflow 

1  $400,000 
2  375,000 
3  300,000 
4  350,000 
5  200,000 
LG 3
LG 4
LG 4
LG 5
Terra  Firma  



Initial investment  $30,000  $25,000 
Year  Operating cash inflows  
1  $ 7,000  $6,000 
2  10,000  9,000 
3  12,000  9,000 
4  10,000  8,000 
Problems
All problems are available in MyFinanceLab.
LG 2
 a. Determine the payback period for this project.
 b. Should the company accept the project? Why or why not?
 a. Determine the payback period for each machine.
 b. Comment on the acceptability of the machines, assuming that they are independent projects.
 c. Which machine should the firm accept? Why?
 d. Do the machines in this problem illustrate any of the weaknesses of using payback? Discuss.
LG 2
Cash inflows (CF_{t})  



Year  Project A  Project B 
1  $10,000  $40,000 
2  20,000  30,000 
3  30,000  20,000 
4  40,000  10,000 
5  20,000  20,000 
 a. Determine the payback period of each project.
 b. Because they are mutually exclusive, Shell must choose one. Which should the company invest in?
 c. Explain why one of the projects is a better choice than the other.
Personal Finance Problem
LG 2
 a. How long will it take for Bill to recoup his initial investment in project A?
 b. How long will it take for Bill to recoup his initial investment in project B?
 c. Using the payback period, which project should Bill choose?
 d. Do you see any problems with his choice?
LG 3
 a. Initial investment is $1,000,000; cash inflows are $150,000 per year.
 b. Initial investment is $2,500,000; cash inflows are $320,000 per year.
 c. Initial investment is $3,000,000; cash inflows are $365,000 per year.
LG 3
 a. The cost of capital is 10%.
 b. The cost of capital is 12%.
 c. The cost of capital is 14%.
LG 3
Project A  Project B  Project C  Project D  Project E  



Initial investment (CF_{0})  $26,000  $500,000  $170,000  $950,000  $80,000 
Year (t)  Cash inflows (CF_{t})  
1  $4,000  $100,000  $20,000  $230,000  $ 0 
2  4,000  120,000  19,000  230,000  0 
3  4,000  140,000  18,000  230,000  0 
4  4,000  160,000  17,000  230,000  20,000 
5  4,000  180,000  16,000  230,000  30,000 
6  4,000  200,000  15,000  230,000  0 
7  4,000  14,000  230,000  50,000  
8  4,000  13,000  230,000  60,000  
9  4,000  12,000  70,000  
10  4,000  11,000 
LG 3
 a. If Simes has a cost of capital of 9%, which form of payment should it choose?
 b. What yearly payment would make the two offers identical in value at a cost of capital of 9%?
 c. Would your answer to part a of this problem be different if the yearly payments were made at the beginning of each year? Show what difference, if any, that change in timing would make to the present value calculation.
 d. The aftertax cash inflows associated with this purchase are projected to amount to $250,000 per year for 15 years. Will this factor change the firm’s decision about how to fund the initial investment?
LG 3
 a. Determine the net present value (NPV) of the equipment, assuming that the firm has a 10% cost of capital. Is the project acceptable?
 b. If the firm’s cost of capital is lower than 10%, does the investment in equipment become more or less desirable? What is the highest cost of capital (closest wholepercentage rate) that the firm can have and still find that purchasing the equipment is worthwhile? Discuss this finding in light of your response in part a.
LG 3
Press A  Press B  Press C  



Initial investment (CF_{0})  $85,000  $60,000  $130,000 
Year (t)  Cash inflows (CF_{t})  
1  $18,000  $12,000  $50,000 
2  18,000  14,000  30,000 
3  18,000  16,000  20,000 
4  18,000  18,000  20,000 
5  18,000  20,000  20,000 
6  18,000  25,000  30,000 
7  18,000  —  40,000 
8  18,000  —  50,000 
 a. Calculate the net present value (NPV) of each press.
 b. Using NPV, evaluate the acceptability of each press.
 c. Rank the presses from best to worst using NPV.
 d. Calculate the profitability index (PI) for each press.
 e. Rank the presses from best to worst using PI.
Personal Finance Problem
LG 3
LG 2
LG 3
Project A  Project B  Project C  



Initial investment (CF_{0})  $40,000  $40,000  $40,000 
Year (t)  Cash inflows (CF_{t})  
1  $13,000  $ 7,000  $19,000 
2  13,000  10,000  16,000 
3  13,000  13,000  13,000 
4  13,000  16,000  10,000 
5  13,000  19,000  7,000 
 a. Calculate each project’s payback period. Which project is preferred according to this method?
 b. Calculate each project’s net present value (NPV). Which project is preferred according to this method?
 c. Comment on your findings in parts a and b, and recommend the best project. Explain your recommendation.
LG 3
 a. Calculate the project’s NPV.
 b. Calculate the annual EVA in a typical year.
 c. Calculate the overall project EVA and compare to your answer in part a.
Project A  Project B  Project C  Project D  



Initial investment (CF_{0})  $90,000  $490,000  $20,000  $240,000 
Year (t)  Cash inflows (CF_{t})  
1  $20,000  $150,000  $7,500  $120,000 
2  25,000  150,000  7,500  100,000 
3  30,000  150,000  7,500  80,000 
4  35,000  150,000  7,500  60,000 
5  40,000  —  7,500  — 
LG 4
LG 4
Project X  Project Y  



Initial investment (CF_{0})  $500,000  $325,000 
Year (t)  Cash inflows (CF_{t)}  
1  $100,000  $140,000 
2  120,000  120,000 
3  150,000  95,000 
4  190,000  70,000 
5  250,000  50,000 
 a. Calculate the IRR to the nearest whole percent for each of the projects.
 b. Assess the acceptability of each project on the basis of the IRRs found in part a.
 c. Which project, on this basis, is preferred?
Personal Finance Problem
LG 4
 a. Determine the IRR of this project. Is it acceptable?
 b. Assuming that the cash inflows continue to be $10,000 per year, how many additional years would the flows have to continue to make the project acceptable (that is, to make it have an IRR of 15%)?
 c. With the given life, initial investment, and cost of capital, what is the minimum annual cash inflow that the firm should accept?
LG 3
LG 4
 a. Determine the net present value (NPV) for the project.
 b. Determine the internal rate of return (IRR) for the project.
 c. Would you recommend that the firm accept or reject the project? Explain your answer.
LG 3
LG 4
Project A  Project B  Project C  Project D  



Initial investment (CF_{0})  $50,000  $100,000  $80,000  $180,000 
Year (t)  Cash inflows (CF_{t})  
1  $20,000  $35,000  $20,000  $100,000 
2  20,000  50,000  40,000  80,000 
3  20,000  50,000  60,000  60,000 
 a. Calculate the NPV of each project, using a cost of capital of 15%.
 b. Rank acceptable projects by NPV.
 c. Calculate the IRR of each project, and use it to determine the highest cost of capital at which all the projects would be acceptable.
LG 2
LG 3
LG 4
Cash inflows (CF_{t})  



Year  Project A  Project B 
1  $45,000  $75,000 
2  45,000  60,000 
3  45,000  30,000 
4  45,000  30,000 
5  45,000  30,000 
6  45,000  30,000 
 a. Calculate the payback period for each project.
 b. Calculate the NPV of each project at 0%.
 c. Calculate the NPV of each project at 9%.
 d. Derive the IRR of each project.
 e. Rank the projects by each of the techniques used. Make and justify a recommendation.
 f. Go back one more time and calculate the NPV of each project using a cost of capital of 12%. Does the ranking of the two projects change compared to your answer in part e? Why?
LG 2
LG 3
LG 4
Year (t)  Cash inflows (CF_{t}) 

1  $20,000 
2  25,000 
3  30,000 
4  35,000 
5  40,000 
 a. Calculate the payback period for the proposed investment.
 b. Calculate the net present value (NPV) for the proposed investment.
 c. Calculate the internal rate of return (IRR), rounded to the nearest whole percent, for the proposed investment.
 d. Evaluate the acceptability of the proposed investment using NPV and IRR. What recommendation would you make relative to implementation of the project? Why?
LG 3
LG 4
LG 5
Project A  Project B  



Initial investment (CF_{0})  $130,000  $85,000 
Year (t)  Cash inflows (CF_{t})  
1  $25,000  $40,000 
2  35,000  35,000 
3  45,000  30,000 
4  50,000  10,000 
5  55,000  5,000 
 a. Calculate the NPV of each project, and assess its acceptability.
 b. Calculate the IRR for each project, and assess its acceptability.
 c. Draw the NPV profiles for both projects on the same set of axes.
 d. Evaluate and discuss the rankings of the two projects on the basis of your findings in parts a, b, and c.
 e. Explain your findings in part d in light of the pattern of cash inflows associated with each project.
LG 2
LG 3
LG 4
LG 5
LG 6
Cash flows  Project A  Project B  Project C 

Initial investment (CF_{0})  $60,000  $100,000  $110,000 
Cash inflows (CF_{t}), t = 1 to 5  20,000  31,500  32,500 
 a. Calculate the payback period for each project.
 b. Calculate the net present value (NPV) of each project, assuming that the firm has a cost of capital equal to 13%.
 c. Calculate the internal rate of return (IRR) for each project.
 d. Draw the net present value profiles for both projects on the same set of axes, and discuss any conflict in ranking that may exist between NPV and IRR.
 e. Summarize the preferences dictated by each measure, and indicate which project you would recommend. Explain why.
LG 2
LG 3
LG 4
LG 5
LG 6
 a. Calculate each project’s payback period.
 b. Calculate the net present value (NPV) for each project.
 c. Calculate the internal rate of return (IRR) for each project.
 d. Draw the net present value profiles for both projects on the same set of axes, and discuss any conflict in ranking that may exist between NPV and IRR.
 e. Summarize the preferences dictated by each measure, and indicate which project you would recommend. Explain why.
Project A  Project B  



Initial investment (CF_{0})  $80,000  $50,000 
Year (t)  Cash inflows (CF_{t})  
1  $15,000  $15,000 
2  20,000  15,000 
3  25,000  15,000 
4  30,000  15,000 
5  35,000  15,000 
LG 6
Year  Cash flow 

0  $ 200,000 
1  −920,000 
2  1,582,000 
3  −1,205,200 
4  343,200 
 a. Why is it difficult to calculate the payback period for this project?
 b. Calculate the investment’s net present value at each of the following discount rates: 0%, 5%, 10%, 15%, 20%, 25%, 30%, 35%.
 c. What does your answer to part b tell you about this project’s IRR?
 d. Should Froogle invest in this project if its cost of capital is 5%? What if the cost of capital is 15%?
 e. In general, when faced with a project like this one, how should a firm decide whether to invest in the project or reject it?
LG 3
LG 4
LG 5
 a. Calculate the NPV, IRR, and PI for both projects.
 b. Rank the projects based on their NPVs, IRRs, and PIs.
 c. Do the rankings in part b agree or not? If not, why not?
 d. The firm can only afford to undertake one of these investments, and the CEO favors the product introduction because it offers a higher rate of return (that is, a higher IRR) than the plant expansion. What do you think the firm should do? Why?
Year  Plant expansion  Product introduction 

0  −$3,500,000  −$500,000 
1  1,500,000  250,000 
2  2,000,000  350,000 
3  2,500,000  375,000 
4  2,750,000  425,000 
LG 1
LG 6
Diane’s friend and coworker, David, has analyzed another energysaving investment opportunity that involves replacing outdoor lighting with solarpowered fixtures in a few of the company’s stores. David also used a 10year horizon to conduct his analysis. Cash flow forecasts for each project appear below. The company uses a 10% discount rate to analyze capital budgeting proposals.
Year  LED project  Solar project 

0  −$4,200,000  −$500,000 
1  700,000  60,000 
2  700,000  60,000 
3  700,000  60,000 
4  700,000  60,000 
5  1,000,000  60,000 
6  700,000  60,000 
7  700,000  60,000 
8  700,000  60,000 
9  700,000  60,000 
10  700,000  60,000 
 a. What is the NPV of each investment? Which investment (if either) should the company undertake?
 b. David approaches Diane for a favor. David says that the solar lighting project is a pet project of his boss, and David really wants to get the project approved to curry favor with his boss. He suggests to Diane that they roll their two projects into a single proposal. The cash flows for this combined project would simply equal the sum of the two individual projects. Calculate the NPV of the combined project? Does it appear to be worth doing? Would you recommend investing in the combined project?
 c. What is the ethical issue that Diane faces? Is any harm done if she does the favor for David as he asks?
Spreadsheet Exercise
The Drillago Company is involved in searching for locations in which to drill for oil. The firm’s current project requires an initial investment of $15 million and has an estimated life of 10 years. The expected future cash inflows for the project are as shown in the following table.
Year  Cash inflows 

1  $ 600,000 
2  1,000,000 
3  1,000,000 
4  2,000,000 
5  3,000,000 
6  3,500,000 
7  4,000,000 
8  6,000,000 
9  8,000,000 
10  12,000,000 
The firm’s current cost of capital is 13%.
TO DO
Create a spreadsheet to answer the following questions.
 a. Calculate the project’s net present value (NPV). Is the project acceptable under the NPV technique? Explain.
 b. Calculate the project’s internal rate of return (IRR). Is the project acceptable under the IRR technique? Explain.
 c. In this case, did the two methods produce the same results? Generally, is there a preference between the NPV and IRR techniques? Explain.
 d. Calculate the payback period for the project. If the firm usually accepts projects that have payback periods between 1 and 7 years, is this project acceptable?
Visit www.myfinancelab.com for Chapter Case: Making Norwich Tool’s Lathe Investment Decision, Group Exercises, and numerous online resources.
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CHAPTER 11
11 Capital Budgeting Cash Flows
Learning Goals
 LG 1 Discuss the three major cash flow components.
 LG 2 Discuss relevant cash flows, expansion versus replacement decisions, sunk costs and opportunity costs, and international capital budgeting.
 LG 3 Calculate the initial investment associated with a proposed capital expenditure.
 LG 4 Discuss the tax implications associated with the sale of an old asset.
 LG 5 Find the relevant operating cash flows associated with a proposed capital expenditure.
 LG 6 Determine the terminal cash flow associated with a proposed capital expenditure.
Why This Chapter Matters to You
In your professional life
ACCOUNTING You need to understand capital budgeting cash flows to provide revenue, cost, depreciation, and tax data for use both in monitoring existing projects and in developing cash flows for proposed projects.
INFORMATION SYSTEMS You need to understand capital budgeting cash flows to maintain and facilitate the retrieval of cash flow data for both completed and existing projects.
MANAGEMENT You need to understand capital budgeting cash flows so that you will understand which cash flows are relevant in making decisions about proposals for acquiring additional production facilities, for new marketing programs, for new products, and for the expansion of existing product lines.
MARKETING You need to understand capital budgeting cash flows so that you can make revenue and cost estimates for proposals for new marketing programs, for new products, and for the expansion of existing product lines.
OPERATIONS You need to understand capital budgeting cash flows so that you can make revenue and cost estimates for proposals for the acquisition of new equipment and production facilities.
In your personal life
You are not mandated to provide financial statements prepared using generally accepted accounting principles, so you naturally focus on cash flows. When considering a major outflow of funds (for example, purchase of a house, funding of a college education), you can project the associated cash flows and use these estimates to assess the value and affordability of the assets and any associated future outlays.
Diamond Comic Distributors A Superhero for Retailers
Diamond Comic Distributors is the world’s largest distributor of Englishlanguage comics and graphic novels. As a distributor, Diamond has a strong incentive to see the retail segment of the comic book market thrive. In the summer of 2013, Diamond announced a new plan to help retail comic book stores expand. Under the new plan, Diamond would offer significant discounts on comic books and related merchandise to retailers who were opening new stores. The cost of opening a new, fully stocked comic book store can run as much as $400,000, and most of that investment is the cost of filling a store’s shelves with new merchandise inventory.
In announcing its new program, Diamond recognized that comic book retailers could only expand if they could earn a sufficient return on their investment and that for some businesses the initial cost of inventory was at least as important as the costs associated with fixed assets. By lowering the upfront costs required to open a new comic book store, Diamond was hoping to raise the rate of return (and the NPV) that retailers could earn by expanding their operations.
Every firm must evaluate the costs and returns of projects for expansion, asset replacement or renewal, research and development, advertising, and other areas that require a longterm commitment of funds in expectation of future returns. This chapter explains how to identify the relevant cash outflows and inflows that must be considered in making major investment decisions.
11.1 Relevant Cash Flows
LG 1
LG 2
Chapter 10 introduced the capital budgeting process and the techniques financial managers use for evaluating and selecting longterm investments. To evaluate investment opportunities, financial managers must determine the relevant cash flows associated with the project: the incremental cash outflows (investment) and inflows (return). The incremental cash flows represent the additional cash flows—outflows or inflows—expected to result from a proposed capital expenditure. As noted in Chapter 4, we focus on cash flows rather than accounting figures because cash flows directly affect the firm’s ability to pay bills and purchase assets. The Focus on Ethics box discusses the accuracy of cash flow estimates and cites one reason even wellestimated deals may not work out as planned.
The incremental cash outflow (investment) and resulting subsequent inflows associated with a proposed capital expenditure.
The additional cash flows—outflows or inflows—expected to result from a proposed capital expenditure.
The remainder of this chapter is devoted to the procedures for measuring the relevant cash flows associated with proposed capital expenditures.
in practice focus on ETHICS: A Question of Accuracy
The process of capital budgeting based on projected cash flows has been a part of the investment decision process for many years. This procedure for evaluating investment opportunities works well when cash flows can be estimated with certainty, but in realworld corporate practice, many investment decisions involve a high degree of uncertainty. The decision is even more complicated when the project under consideration is the acquisition of another company or part of another company.
Because estimates of the cash flows from an investment project involve making assumptions about the future, they may be subject to considerable error. The problem becomes more complicated as the period of time under consideration becomes longer as well as when the project is unique and there are no historical precedents to use in forming cash flow forecasts. Other complications may arise involving accounting for additional (extraordinary) cash flows, such as the cost of litigation, compliance with tougher environmental standards, or the costs of disposal or recycling of an asset at the completion of the project.
For managers of a firm, undertaking a new, major investment can be exhilarating. All too often, however, the initial champagne celebration gives way once the final cost of a deal is tallied. A large body of research suggests that, on average, mergers and acquisitions do not create much value for the acquiring firms, and, in fact, these deals may harm acquiring shareholders more often than not. Although the financial data necessary to generate discounted cash flow estimates are ever more readily available, more attention is being paid to the accuracy of the numbers. Inspired in part by increased scrutiny from government and the threat of shareholder lawsuits, board members have been pushing corporate managers to make a stronger case for the deals they propose. Says Glenn Gurtcheff, managing director and cohead of middle market M&A for Piper Jaffray & Co., “They’re not just taking the company’s audited and unaudited financial statements at face value; they are really diving into the numbers and trying to understand not just their accuracy, but what they mean in terms of trends.”
If valuation has improved so much, why do analyses show that the shareholders of acquiring companies often do not benefit from mergers and acquisitions? The answer may be found in the CEO’s office. Improvements in valuation techniques can be negated when the process deteriorates into a game of tweaking the numbers to justify a deal the CEO wants to do, regardless of price. This “make it work” form of capital budgeting may result in building the empire under the CEO’s control at the expense of the firm’s shareholders.
What would your options be when faced with the demands of an assertive CEO who expects you to “make it work”? Brainstorm several options.
MAJOR CASH FLOW COMPONENTS
The cash flows of any project may include three basic components: (1) an initial investment, (2) operating cash flows (which may be inflows or outflows), and (3) terminal cash flow. All projects—whether for expansion, replacement or renewal, or some other purpose—have the first two components. Some, however, lack the final component, terminal cash flow.
FIGURE 11.1 Cash Flow Components
Figure 11.1 depicts on a time line the cash flows for a project. The initial investment for the proposed project is $50,000, the relevant cash outflow at time zero. The operating cash flows, which are the net incremental aftertax cash inflows and outflows resulting from implementation of the project during its life, gradually increase from $4,000 in its first year to $10,000 in its tenth and final year. For the project depicted in Figure 11.1, the net operating cash flows are all positive, but that is not necessarily the case for every investment opportunity. The terminal cash flow is the aftertax nonoperating cash flow occurring in the final year of the project. It is usually attributable to liquidation of the project. In this case, it is $25,000, received at the end of the project’s 10year life. Note that the terminal cash flow does not include the $10,000 operating cash inflow for year 10.
The relevant cash outflow for a proposed project at time zero.
The incremental aftertax cash inflows resulting from implementation of a project during its life.
The aftertax nonoperating cash flow occurring in the final year of a project. It is usually attributable to liquidation of the project.
EXPANSION VERSUS REPLACEMENT DECISIONS
Developing relevant cash flow estimates is most straightforward in the case of expansion decisions. In this case, the initial investment, operating cash flows, and terminal cash flow are merely the aftertax cash flows associated with the proposed expansion.
Identifying relevant cash flows for replacement decisions is more complicated because the firm must identify the incremental cash flows that would result from the proposed replacement. The initial investment in the case of replacement is the difference between the initial investment needed to acquire the new asset and any aftertax cash inflows or outflows expected from liquidation of the old asset. The operating cash flows are the difference between the operating cash flows from the new asset and those from the old asset. The terminal cash flow is the difference between the aftertax cash flows expected upon termination of the new and the old assets. These relationships are shown in Figure 11.2.
Actually, all capital budgeting decisions can be viewed as replacement decisions. Expansion decisions are merely replacement decisions in which all cash flows from the old asset are zero. In light of this fact, this chapter focuses primarily on replacement decisions.
FIGURE 11.2 Relevant Cash Flows for Replacement Decisions
SUNK COSTS AND OPPORTUNITY COSTS
When estimating the relevant cash flows associated with a proposed capital expenditure, the firm must recognize any sunk costs and opportunity costs. These costs are easy to mishandle or ignore, particularly when determining a project’s incremental cash flows. Sunk costs are cash outlays that have already been made (past outlays) and cannot be recovered. Sunk costs have no effect on the cash flows relevant to the current decision. As a result, sunk costs should not be included in a project’s incremental cash flows.
Cash outlays that have already been made (past outlays) and therefore have no effect on the cash flows relevant to a current decision.
Opportunity costs are cash flows that could be realized from the best alternative use of an asset that is already in place. They therefore represent cash flows that will not be realized as a result of employing that asset in the proposed project. Thus, any opportunity costs should be included as cash outflows when one is determining a project’s incremental cash flows.
Cash flows that could be realized from the best alternative use of an owned asset.
Example 11.1
My Finance Lab Solution Video
Jankow Equipment is considering renewing its drill press X12, which it purchased 3 years earlier for $237,000, by retrofitting it with the computerized control system from an obsolete piece of equipment it owns. The obsolete equipment could be sold today for a $42,000, but without its computerized control system, it would be worth nothing. Jankow is in the process of estimating the labor and materials costs of retrofitting the system to drill press X12 and the benefits expected from the retrofit. The $237,000 cost of drill press X12 is a sunk cost because it represents an earlier cash outlay. It would not be included as a cash outflow when determining the cash flows relevant to the retrofit decision. On the other hand, if Jankow uses the computerized control system of the obsolete machine, there is an opportunity cost of $42,000, which is the cash that Jankow could have received by selling the obsolete equipment in its current condition. By retrofitting the drill press, Jankow gives up the opportunity to sell the old equipment for $42,000. This opportunity cost would be included as a cash outflow associated with using the computerized control system.
INTERNATIONAL CAPITAL BUDGETING AND LONGTERM INVESTMENTS
Although the same basic capital budgeting principles are used for domestic as well as international projects, several additional factors must be addressed in evaluating foreign investment opportunities. International capital budgeting differs from the domestic version because (1) cash outflows and inflows occur in a foreign currency and (2) foreign investments entail potentially significant political risk. Both of these risks can be minimized through careful planning.
Companies face both longterm and shortterm currency risks related to both the invested capital and the cash flows resulting from it. Longterm currency risk can be minimized by financing the foreign investment at least partly in the local capital markets. This step ensures that the project’s revenues, operating costs, and financing costs will be in the local currency. Likewise, the dollar value of shortterm, localcurrency cash flows can be protected by using special securities and strategies such as futures, forwards, and options market instruments.
Political risks can be minimized by using both operating and financial strategies. For example, by structuring the investment as a joint venture and selecting a wellconnected local partner, the U.S. company can minimize the risk of its operations being seized or harassed. Companies also can protect themselves from having their investment returns blocked by local governments by structuring the financing of such investments as debt rather than as equity. Debtservice payments are legally enforceable claims, whereas equity returns (such as dividends) are not. Even if local courts do not support the claims of the U.S. company, the company can threaten to pursue its case in U.S. courts.
Despite the preceding difficulties, foreign direct investment (FDI), which involves the transfer of capital, managerial, and technical assets to a foreign country, has surged in recent years. Such investment is evident in the growing market values of foreign assets owned by U.S.–based companies and of foreign direct investment in the United States, particularly by British, Canadian, Chinese, Dutch, German, and Japanese companies. Furthermore, foreign direct investment by U.S. companies seems to be accelerating. See the Global Focus box for a discussion of recent foreign direct investment in China.
The transfer of capital, managerial, and technical assets to a foreign country.
Matter of fact
Who Receives the Most FDI?
According to the U.S. Department of Commerce’s Bureau of Economic Analysis (BEA), FDI plays an important role in the U.S. economy. BEA divides FDI into two categories: (1) Greenfield Investment and (2) Mergers and Acquisitions. Greenfield Investments creates new enterprises and develops or expands production facilities. Mergers and Acquisitions involves the purchase of an existing enterprise.
In 2012, the United States was the world’s largest recipient of FDI, receiving $174.7 billion in FDI. However, that figure represented a decrease from the record $234 billion in FDI received in 2011. Perhaps not surprisingly, China is not far behind the United States. In fact, for the first half of 2012, more FDI flowed into China than into any other country.
REVIEW QUESTIONS
in practice GLOBAL focus: Changes May Influence Future Investments in China
Foreign direct investment in China has been growing rapidly for many years. From 2001 to 2011, FDI in China grew from $46.9 billion to $116 billion, a compound annual growth rate of roughly 9.5%. China allows three types of foreign investments: a wholly foreignowned enterprise (WFOE), in which the firm is entirely funded with foreign capital; a joint venture, in which the foreign partner must provide at least 25 percent of initial capital; and a representative office (RO), the most common and easily established entity, which cannot perform business activities that directly result in profits. Generally, an RO is the first step in establishing a China presence and includes mechanisms for upgrading to a WFOE or joint venture. More than threefourths of the dollar value of Chinese FDI takes the form of whollyowned foreign enterprises operating in China, and most of the rest consists of joint ventures.
China has run a trade surplus for many years, although recently the surplus has been shrinking, and some outsiders believe that the surplus figures are artificially inflated by the Chinese government. With the trade surplus, China is no longer desperate for capital from overseas, but is now primarily interested in foreign skills and technologies. Prime Minister Li Keqiang wants to steer investments toward science and technology. Li is giving tax breaks and promising speedy approvals for investments in the country’s western and central regions.
Typical of foreign investors in China is Intel Capital, a subsidiary of Intel Corporation. From 1998 to 2013, Intel Capital invested more than $670 million in more than 110 companies in China. Intel Capital focuses its investments in projects such as data centers and cloud computing, smartphones and tablets, and semiconductor design and manufacturing. Intel Capital is no beginner at foreign investment; it has invested more than $10.8 billion in almost 1,300 companies around the world.
As with any foreign investment, investing in China is not without risk. One potential risk facing foreign investors in China is that the government could decide to nationalize private companies. Many public companies in China are firms that were once owned by the communist government, such as China Life Insurance Company, and it is always possible that the government may decide that it wishes to own and control these companies again. The list of governments similar to China’s that have nationalized private companies is fairly long. Although there is no evidence that it will happen in China, it should be considered one of the risks.
Although China has been actively campaigning for foreign investment, how do you think that having a communist government affects its foreign investment?
11.2 Finding the Initial Investment
LG 3
LG 4
The term initial investment as used here refers to the relevant cash outflows to be considered when evaluating a prospective capital expenditure. Our discussion of capital budgeting will focus on projects with initial investments that occur at time zero, the time at which the expenditure is made. The initial investment is calculated by subtracting all cash inflows occurring at time zero from all cash outflows occurring at time zero.
The basic format for determining the initial investment is given in Table 11.1. The cash flows that must be considered when determining the initial investment associated with a capital expenditure are the installed cost of the new asset, the aftertax proceeds (if any) from the sale of an old asset, and the change (if any) in net working capital. Note that if there are no installation costs and the firm is not replacing an existing asset, the cost (purchase price) of the new asset, adjusted for any change in net working capital, is equal to the initial investment.
TABLE 11.1 The Basic Format for Determining Initial Investment
INSTALLED COST OF NEW ASSET
As shown in Table 11.1, the installed cost of the new asset is found by adding the cost of the new asset to its installation costs. The cost of new asset is the net outflow that its acquisition requires. Usually, we are concerned with the acquisition of a fixed asset for which a definite purchase price is paid. Installation costs are any added costs that are necessary to place an asset into operation. The Internal Revenue Service requires the firm to add installation costs to the purchase price of an asset to determine its depreciable value, which is expensed over a period of years. The installed cost of new asset, calculated by adding the cost of new asset to its installation costs, equals its depreciable value.
The net outflow necessary to acquire a new asset.
Any added costs that are necessary to place an asset into operation.
The cost of new asset plus its installation costs; equals the asset’s depreciable value.
AFTERTAX PROCEEDS FROM SALE OF OLD ASSET
Table 11.1 shows that the aftertax proceeds from sale of old asset decrease the firm’s initial investment in the new asset. These proceeds are the difference between the old asset’s sale proceeds and any applicable taxes or tax refunds related to its sale. The proceeds from sale of old asset are the net cash inflows it provides. This amount is net of any costs incurred in the process of removing the asset. Included in these removal costs are cleanup costs, such as those related to removal and disposal of chemical and nuclear wastes. These costs may not be trivial, and in some cases they may outweigh any sale proceeds received from the old asset. In other words, the net proceeds from selling or disposing of the old asset may be positive or negative.
The difference between the old asset’s sale proceeds and any applicable taxes or tax refunds related to its sale.
The cash inflows, net of any removal or cleanup costs, resulting from the sale of an existing asset.
The proceeds from the sale of an old asset are normally subject to some type of tax. This tax on sale of old asset depends on the relationship between its sale price and book value and on existing government tax rules.
Tax that depends on the relationship between the old asset’s sale price and book value and on existing government tax rules.
1. A brief discussion of the tax treatment of ordinary and capital gains income was presented in Chapter 2. Because corporate capital gains and ordinary income are taxed at the same rate, for convenience we do not differentiate between them in the following discussions.
Book Value
The book value of an asset is its strict accounting value. It can be calculated by the equation
The strict accounting value of an asset, calculated by subtracting its accumulated depreciation from its installed cost.
Book value = Installed cost of asset − Accumulated depreciation  (11.1) 
Example 11.2
Hudson Industries, a small electronics company, acquired a machine tool 2 years ago with an installed cost of $100,000. The asset was being depreciated under MACRS using a 5year recovery period. Table 4.2 (on page 120) shows that under MACRS for a 5year recovery period, 20% and 32% of the installed cost would be depreciated in years 1 and 2, respectively. In other words, 52% (20% + 32%) of the $100,000 cost, or $52,000 (0.52 × $100,000), would represent the accumulated depreciation at the end of year 2. Substituting into Equation 11.1, we get
Book value = $100,000 − $52,000 = 48,000
The book value of Hudson’s asset at the end of year 2 is therefore $48,000.
Basic Tax Rules
Three potential tax situations can occur when a firm sells an asset. These situations depend on the relationship between the asset’s sale price and its book value. The two key forms of taxable income and their associated tax treatments are defined and summarized in Table 11.2. The assumed tax rates used throughout this text are noted in the final column. There are three possible tax situations: The asset may be sold (1) for more than its book value, (2) for its book value, or (3) for less than its book value. An example will illustrate.
Example 11.3
My Finance Lab Solution Video
The old asset purchased 2 years ago for $100,000 by Hudson Industries has a current book value of $48,000. What will happen if the firm now decides to sell the asset and replace it? The tax consequences depend on the sale price. Figure 11.3 depicts the taxable income resulting from four possible sale prices in light of the asset’s initial purchase price of $100,000 and its current book value of $48,000. The taxable consequences of each of these sale prices are described in the following paragraphs.
TABLE 11.2 Tax Treatment on Sales of Assets
Form of taxable income  Definition  Tax treatment  Assumed tax rate 

Gain on sale of asset  Portion of the sale price that is greater than book value.  All gains above book value are taxed as ordinary income.  40% 
Loss on sale of asset  Amount by which sale price is less than book value.  If the asset is depreciable and used in business, loss is deducted from ordinary income.  40% of loss is a tax savings 
If the asset is not depreciable or is not used in business, loss is deductible only against capital gains.  40% of loss is a tax savings 
The sale of the asset for more than its book value If Hudson sells the old asset for $110,000, it realizes a gain of $62,000 ($110,000 − $48,000). Technically, this gain is made up of two parts: a capital gain and recaptured depreciation, which is the portion of the sale price that is above book value and below the initial purchase price. For Hudson, the capital gain is $10,000 ($110,000 sale price − $100,000 initial purchase price); recaptured depreciation is $52,000 (the $100,000 initial purchase price − $48,000 book value).
The portion of an asset’s sale price that is above its book value and below its initial purchase price.
FIGURE 11.3 Taxable Income from Sale of Asset
Both the $10,000 capital gain and the $52,000 recaptured depreciation are shown under the $110,000 sale price in Figure 11.3. The total gain above book value of $62,000 is taxed as ordinary income at the 40% rate, resulting in taxes of $24,800 (0.40 × $62,000). These taxes should be used in calculating the initial investment in the new asset, using the format in Table 11.1. In effect, the taxes raise the amount of the firm’s initial investment in the new asset by reducing the proceeds from the sale of the old asset.
If Hudson instead sells the old asset for $70,000, it experiences a gain above book value (in the form of recaptured depreciation) of $22,000 ($70,000 − $48,000), as shown under the $70,000 sale price in Figure 11.3. This gain is taxed as ordinary income. Because the firm is in the 40% tax bracket, the taxes on the $22,000 gain are $8,800 (0.40 × $22,000). This amount in taxes should be used in calculating the initial investment in the new asset.
The sale of the asset for its book value If the asset is sold for $48,000, its book value, the firm breaks even. There is no gain or loss, as shown under the $48,000 sale price in Figure 11.3. Because no tax results from selling an asset for its book value, there is no tax effect on the initial investment in the new asset.
The sale of the asset for less than its book value If Hudson sells the asset for $30,000, it experiences a loss of $18,000 ($48,000 − $30,000), as shown under the $30,000 sale price in Figure 11.3. The firm may use the loss to offset ordinary operating income if the asset is a depreciable asset used in the business. If the asset is not depreciable or is not used in the business, the firm can use the loss only to offset capital gains. In either case, the loss will save the firm $7,200 (0.40 × $18,000) in taxes. And, if current operating earnings or capital gains are not sufficient to offset the loss, the firm may be able to apply these losses to prior or future years’ taxes.
CHANGE IN NET WORKING CAPITAL
Net working capital is the difference between the firm’s current assets and its current liabilities. This topic is treated in depth in Chapter 15; at this point, it is important to note that changes in net working capital often accompany capital expenditure decisions. If a firm acquires new machinery to expand its level of operations, it will experience an increase in levels of cash, accounts receivable, inventories, accounts payable, and accruals. These increases result from the need for more cash to support expanded operations, more accounts receivable and inventories to support increased sales, and more accounts payable and accruals to support increased outlays made to meet expanded product demand. As noted in Chapter 4, increases in cash, accounts receivable, and inventories are outflows of cash, whereas increases in accounts payable and accruals are inflows of cash.
The difference between the firm’s current assets and its current liabilities.
Matter of fact
Europeans Squeeze Working Capital
Because, from a firm’s perspective, an increase in working capital is a cash outflow, companies around the world work hard to economize on their working capital requirements. A PWC study of European companies found that working capital was at an alltime low in 2011. According to the study, the companies that were most efficient in their use of working capital had a strong focus on process optimization and worked hard to instill a cashbased culture among their employees. In addition, these companies tended to be early adopters of new technologies, which facilitated reduced working capital needs.
The difference between the change in current assets and the change in current liabilities is the change in net working capital. Generally, when a company makes a major new investment, current assets increase by more than current liabilities, resulting in an increased investment in net working capital. This increased investment in working capital is treated as an initial outflow. If the change in net working capital were negative, it would be shown as an initial inflow. The change in net working capital—regardless of whether it is an increase or a decrease—is not taxable because it merely involves a net buildup or net reduction of current accounts.
The difference between a change in current assets and a change in current liabilities.
2. “PWC European Working Capital Annual Review” 2012.
3. When changes in net working capital apply to the initial investment associated with a proposed capital expenditure, they are for convenience assumed to be instantaneous and thereby occurring at time zero. In practice, the change in net working capital will frequently occur over a period of months as the capital expenditure is implemented.
Example 11.4
Danson Company, a metal products manufacturer, is contemplating expanding its operations. Financial analysts expect that the changes in current accounts summarized in Table 11.3 will occur and will be maintained over the life of the expansion. Current assets are expected to increase by $22,000, and current liabilities are expected to increase by $9,000, resulting in a $13,000 increase in net working capital. In this case, the change will represent an increased net working capital investment and will be treated as a cash outflow in calculating the initial investment.
TABLE 11.3 Calculation of Change in Net Working Capital for Danson Company
Current account  Change in balance  

Cash  + $ 4,000  
Accounts receivable  + 10,000  
Inventories  + 8,000  
(1) Current assets  +$22,000  
Accounts payable  + $ 7,000  
Accruals  + 2,000  
(2) Current liabilities  + 9,000  
Change in net working capital [(1) − (2)]  +$13,000 
CALCULATING THE INITIAL INVESTMENT
A variety of tax and other considerations enter into the initial investment calculation. The following example illustrates calculation of the initial investment according to the format in Table 11.1.
Example 11.5
Powell Corporation, a large, diversified manufacturer of aircraft components, is trying to determine the initial investment required to replace an old machine with a new, more sophisticated model. The proposed machine’s purchase price is $380,000, and an additional $20,000 will be necessary to install it. It will be depreciated under MACRS using a 5year recovery period. The present (old) machine was purchased 3 years ago at a cost of $240,000 and was being depreciated under MACRS using a 5year recovery period. The firm has found a buyer willing to pay $280,000 for the present machine and to remove it at the buyer’s expense. The firm expects that a $35,000 increase in current assets and an $18,000 increase in current liabilities will accompany the replacement; these changes will result in a $17,000 ($35,000 −$18,000) increase in net working capital. The firm pays taxes at a rate of 40%.
The only component of the initial investment calculation that is difficult to obtain is taxes. The book value of the present machine can be found by using the depreciation percentages from Table 4.2 (on page 120) of 20%, 32%, and 19% for years 1, 2, and 3, respectively. The resulting book value is $240,000 − [(0.20 + 0.32 + 0.19) × $240,000], or $69,600. A gain of $210,400 ($280,000 − $69,600) is realized on the sale. The total taxes on the gain are $84,160 (0.40 × $210,400). These taxes must be subtracted from the $280,000 sale price of the present machine to calculate the aftertax proceeds from its sale.
4. Throughout the discussions of capital budgeting, all assets evaluated as candidates for replacement are assumed to be depreciable assets that are directly used in the business, so any losses on the sale of these assets can be applied against ordinary operating income. The decisions are also structured to ensure that the usable life remaining on the old asset is just equal to the life of the new asset; this assumption enables us to avoid the problem of unequal lives, which is discussed in Chapter 12.
Substituting the relevant amounts into the format in Table 11.1 results in an initial investment of $221,160, which represents the net cash outflow required at time zero.
REVIEW QUESTIONS
11.3 Finding the Operating Cash Flows
LG 5
As the name implies, operating cash flows are the incremental, aftertax cash flows that occur after a new investment is made. In this section, we use the income statement format to clarify what we mean by incremental, aftertax cash flows.
INTERPRETING THE TERM AFTERTAX
Benefits that result from capital expenditures must be measured on an aftertax basis because the firm will not have the use of any benefits until it has satisfied the government’s tax claims. These claims depend on the firm’s taxable income, so deducting taxes before making comparisons between proposed investments is necessary for consistency when evaluating capital expenditure alternatives.
INTERPRETING THE TERM CASH FLOWS
All costs and benefits expected from a proposed project must be measured on a cash flow basis. Cash outflows represent costs incurred by the firm, and cash inflows represent dollars that can be spent by the firm. Cash flows generally are not equal to accounting profits. One of the main reasons that accounting profits do not equal cash flows is because accounting does not allow firms to fully deduct or expense the cost of fixed assets at the time of purchase. Instead, firms expense a portion of the cost of fixed assets through depreciation deductions over the useful life of the fixed asset. As a result, when a firm pays cash for a fixed asset, the firm’s profits will not fully reflect the cost of the asset in the year of purchase. In subsequent years, firms reduce their profits by taking depreciation expenses, even though there are no cash outlays tied to those depreciation charges.
There is a simple technique for converting aftertax net profits into operating cash flows. The calculation requires adding depreciation and any other noncash charges (amortization and depletion) deducted as expenses on the firm’s income statement back to net profits after taxes. Recognize that depreciation expenses are not actually cash inflows themselves. Adding depreciation to profit simply recognizes that the profit calculation requires firms to deduct an expense that is not tied to a specific cash outlay. In a sense, adding depreciation to profit “corrects” this issue and provides a number that better matches the actual cash inflows and outflows.
Example 11.6
Powell Corporation’s estimates of its revenue and expenses (excluding depreciation and interest), with and without the proposed new machine described in Example 11.5, are given in Table 11.4. Note that both the expected usable life of the proposed machine and the remaining usable life of the present machine are 5 years. The amount to be depreciated with the proposed machine is calculated by summing the purchase price of $380,000 and the installation costs of $20,000. The proposed machine is to be depreciated under MACRS using a 5year recovery period.^{5} The resulting depreciation on this machine for each of the 6 years, as well as the remaining 3 years of depreciation (years 4, 5, and 6) on the present machine, are calculated in Table 11.5.^{6}
TABLE 11.4 Powell Corporation’s Revenue and Expenses (Excluding Depreciation and Interest) for Proposed and Present Machines
With proposed machine

With present machine



Year  Revenue (1)  Expenses (excl. depr. and int.) (2)  Year  Revenue (1)  Expenses (excl. depr. and int.) (2) 
1  $2,520,000  $2,300,000  1  $2,200,000  $1,990,000 
2  2,520,000  2,300,000  2  2,300,000  2,110,000 
3  2,520,000  2,300,000  3  2,400,000  2,230,000 
4  2,520,000  2,300,000  4  2,400,000  2,250,000 
5  2,520,000  2,300,000  5  2,250,000  2,120,000 
5. As noted in Chapter 4, it takes n + 1 years to depreciate an nyear class asset under current tax law. Therefore, MACRS percentages are given for each of 6 years for use in depreciating an asset with a 5year recovery period.
6. It is important to recognize that although both machines will provide 5 years of use, the proposed new machine will be depreciated over the 6year period, whereas the present machine, as noted in the preceding example, has been depreciated over 3 years and therefore has remaining only its final 3 years (years 4, 5, and 6) of depreciation (12%, 12%, and 5%, respectively, under MACRS).
The operating cash flows each year can be calculated by using the income statement format shown in Table 11.6. Note that we exclude interest because we are focusing purely on the “investment decision.” The interest is relevant to the “financing decision,” which is separately considered. Because we exclude interest expense, “earnings before interest and taxes” (EBIT) is equivalent to “net profits before taxes,” and the calculation of “operating cash flow” (OCF) in Table 11.6 is identical to the definition that we provided in Chapter 4 (defined in Equation 4.3, on page 125). Simply stated, the income statement format calculates the OCF.
TABLE 11.5 Depreciation Expense for Proposed and Present Machines for Powell Corporation
TABLE 11.6 Calculation of Operating Cash Flows Using the Income Statement Format
Substituting the data from Tables 11.4 and 11.5 into this format and assuming a 40% tax rate, we get Table 11.7, which demonstrates the calculation of operating cash flows for each year for both the proposed and the present machine. Because the proposed machine is depreciated over 6 years, the analysis must be performed over the 6year period to capture fully the tax effect of its year6 depreciation. The resulting operating cash flows appear in the final row of Table 11.7 for each machine. The $8,000 year6 operating cash inflow for the proposed machine results solely from the tax benefit of its year6 depreciation deduction.^{7}
TABLE 11.7 Calculation of Operating Cash Flows for Powell Corporation’s Proposed and Present Machines
INTERPRETING THE TERM INCREMENTAL
The final step in estimating the operating cash flows for a proposed replacement project is to calculate the incremental (relevant) cash flows. Incremental operating cash flows are needed because our concern is only with the change in operating cash flows that result from the proposed project. Clearly, if it were an expansion project, the project’s cash flows would be the incremental cash flows.
7. Although here we have calculated the year6 operating cash flow for the proposed machine, this cash flow will later be eliminated as a result of the assumed sale of the machine at the end of year 5.
TABLE 11.8 Incremental (Relevant) Operating Cash Flows for Powell Corporation
Operating cash flows  



Year  Proposed machine^{a} (1)  Present machine^{a} (2)  Incremental (relevant) [(1) − (2)] (3) 
1  $164,000  $137,520  $26,480 
2  183,200  125,520  57,680 
3  162,400  106,800  55,600 
4  151,200  90,000  61,200 
5  151,200  78,000  73,200 
6  8,000  0  8,000 
Example 11.7
Table 11.8 demonstrates the calculation of Powell Corporation’s incremental (relevant) operating cash flows for each year. The estimates of operating cash flows developed in Table 11.7 appear in columns 1 and 2. Column 2 values represent the amount of operating cash flows that Powell Corporation will receive if it does not replace the present machine. If the proposed machine replaces the present machine, the firm’s operating cash flows for each year will be those shown in column 1. Subtracting the present machine’s operating cash flows from the proposed machine’s operating cash flows, we get the incremental operating cash flows for each year, shown in column 3. These cash flows represent the amounts by which each respective year’s cash flows will increase as a result of the replacement. For example, in year 1, Powell Corporation’s cash flows would increase by $26,480 if the proposed project were undertaken. Clearly, these are the relevant inflows to be considered when evaluating the benefits of making a capital expenditure for the proposed machine.^{8}
8. The following equation can be used to calculate more directly the incremental cash flow in year t, ICI_{t}:
ICI_{t} = [ΔEBDIT_{t} × (1 − T)] + (ΔD_{t} × T)
where
ΔEBDIT_{t}  =  change in earnings before depreciation, interest, and taxes [revenues − expenses (excl. depr. and int.)] in year t 
T  =  firm’s marginal tax rate 
ΔD_{t}  =  change in depreciation expense in year t 
Applying this formula to the Powell Corporation data given in Tables 11.4 and 11.5 for year 3, we get the following values of variables:
Substituting into the equation yields
The $55,600 of incremental cash inflow for year 3 is the same value as that calculated for year 3 in column 3 of Table 11.8.
REVIEW QUESTIONS
11.4 Finding the Terminal Cash Flow
LG 6
Terminal cash flow is the cash flow resulting from termination and liquidation of a project at the end of its economic life. It represents the aftertax cash flow, exclusive of operating cash flows, that occurs in the final year of the project. When it applies, this flow can significantly affect the capital expenditure decision. Terminal cash flow can be calculated for replacement projects by using the basic format presented in Table 11.9.
PROCEEDS FROM SALE OF ASSETS
The proceeds from sale of the new and the old asset, often called “salvage value,” represent the amount net of any removal or cleanup costs expected on termination of the project. For replacement projects, proceeds from both the new asset and the old asset must be considered. For expansion and renewal types of capital expenditures, the proceeds from the old asset are zero. Of course, it is not unusual for the value of an asset to be zero at the termination of a project.
TABLE 11.9 The Basic Format for Determining Terminal Cash Flow
TAXES ON SALE OF ASSETS
When the investment being analyzed involves replacing an old asset with a new one, there are two key elements in finding the terminal cash flow. First, at the end of the project’s life, the firm will dispose of the new asset, possibly by selling it, so the aftertax proceeds from selling the new asset represent a cash inflow. However, remember that if the firm had not replaced the old asset, the firm would have received proceeds from sale of the old asset at the end of the project (rather than counting those proceeds up front as part of the initial investment). Therefore, we must count as a cash outflow the aftertax proceeds that the firm would have received from disposal of the old asset. Taxes come into play whenever an asset is sold for a value different from its book value. If the net proceeds from the sale are expected to exceed book value, a tax payment shown as an outflow (deduction from sale proceeds) will occur. When the net proceeds from the sale are less than book value, a tax benefit shown as a cash inflow (addition to sale proceeds) will result. For assets sold to net exactly book value, no taxes will be due.
CHANGE IN NET WORKING CAPITAL
When we calculated the initial investment, we took into account any change in net working capital that is attributable to the new asset. Now, when we calculate the terminal cash flow, the change in net working capital represents the reversion of any initial net working capital investment. Most often, this will show up as a cash inflow due to the reduction in net working capital; with termination of the project, the need for the increased net working capital investment is assumed to end. Because the net working capital investment is in no way consumed, the amount recovered at termination will equal the amount shown in the calculation of the initial investment. Tax considerations are not involved.
Calculating the terminal cash flow involves the same procedures as those used to find the initial investment. In the following example, the terminal cash flow is calculated for a replacement decision.
Example 11.8
Continuing with the Powell Corporation example, assume that the firm expects to be able to liquidate the new machine at the end of its 5year usable life to net $50,000 after paying removal and cleanup costs. Had it not been replaced by the new machine, the old machine would have been liquidated at the end of the 5 years to net $10,000. The firm expects to recover its $17,000 net working capital investment upon termination of the project. The firm pays taxes at a rate of 40%.
From the analysis of the operating cash flows presented earlier, we can see that the proposed (new) machine will have a book value of $20,000 (equal to the year6 depreciation) at the end of 5 years. The present (old) machine would have been fully depreciated and therefore would have a book value of zero at the end of the 5 years. Because the sale price of $50,000 for the proposed (new) machine is below its initial installed cost of $400,000 but greater than its book value of $20,000, taxes will have to be paid only on the recaptured depreciation of $30,000 ($50,000 sale proceeds − $20,000 book value). Applying the ordinary tax rate of 40% to this $30,000 results in a tax of $12,000 (0.40 × $30,000) on the sale of the proposed machine. Its aftertax sale proceeds would therefore equal $38,000 ($50,000 sale proceeds − $12,000 taxes). Because the old machine would have been sold for $10,000 at termination, which is less than its original purchase price of $240,000 and above its book value of zero, it would have experienced a taxable gain of $10,000 ($10,000 sale price − $0 book value). Applying the 40% tax rate to the $10,000 gain, the firm would have owed a tax of $4,000 (0.40 × $10,000) on the sale of the old machine at the end of year 5. Its aftertax sale proceeds from the old machine would have equaled $6,000 ($10,000 sale price − $4,000 taxes). Substituting the appropriate values into the format in Table 11.9 results in the terminal cash inflow of $49,000.
9. As noted earlier, the change in net working capital is for convenience assumed to occur instantaneously, in this case, on termination of the project.
REVIEW QUESTION
11.5 Summarizing the Relevant Cash Flows
LG 3
LG 5
LG 6
The initial investment, operating cash flows, and terminal cash flow together represent a project’s relevant cash flows. These cash flows can be viewed as the incremental aftertax cash flows attributable to the proposed project. They represent, in a cash flow sense, how much better or worse off the firm will be if it chooses to implement the proposal.
Example 11.9
The relevant cash flows for Powell Corporation’s proposed replacement expenditure can be shown graphically, on a time line. Note that because the new asset is assumed to be sold at the end of its 5year usable life, the year6 incremental operating cash inflow calculated in Table 11.8 has no relevance; the terminal cash flow effectively replaces this value in the analysis.
With these cash flow estimates in hand, a financial manager could then calculate the investment’s NPV or IRR using the techniques covered in Chapter 10.
Personal Finance Example 11.10
After receiving a sizable bonus from her employer, Tina Talor is contemplating the purchase of a new car. She believes that by estimating and analyzing the cash flows, she could make a more rational decision about whether to make this large purchase. Tina’s cash flow estimates for the car purchase are as follows:
Negotiated price of new car  $23,500 
Taxes and fees on new car purchase  $ 1,650 
Proceeds from sale of old car  $ 9,750 
Estimated value of new car in 3 years  $10,500 
Estimated value of old car in 3 years  $ 5,700 
Estimated annual repair costs on new car  0 (in warranty) 
Estimated annual repair costs on old car  $ 400 
Using the cash flow estimates, Tina calculates the initial investment, operating cash flows, terminal cash flow, and a summary of all cash flows for the car purchase.
Initial Investment  
Total cost of new car  
Cost of car  $23,500  
+ Taxes and fees  1,650  $25,150  
− Proceeds from sale of old car  9,750  
Initial investment  $15,400  
Operating Cash Flows  Year 1  Year 2  Year 3 
Cost of repairs on new car  $ 0  $ 0  $ 0 
− Cost of repairs on old car  400  400  400 
Operating cash flows (savings)  $400  $400  $400 
Terminal Cash Flow: End of Year 3  
Proceeds from sale of new car  $10,500  
− Proceeds from sale of old car  5,700  
Terminal cash flow  $ 4,800  
Summary of Cash Flows  
End of Year  Cash Flow  
0  −$15,400  
1  + 400  
2  + 400  
3  + 5,200  ($400 + $4,800) 
The cash flows associated with Tina’s car purchase decision reflect her net costs of the new car over the assumed 3year ownership period, but they ignore the many intangible benefits of owning a car. Whereas the fuel cost and basic transportation service provided are assumed to be the same with the new car as with the old car, Tina will have to decide if the cost of moving up to a new car can be justified in terms of intangibles, such as luxury and prestige.
REVIEW QUESTION
Summary
FOCUS ON VALUE
A key responsibility of financial managers is to review and analyze proposed investment decisions to make sure that the firm undertakes only those that contribute positively to the value of the firm. Using a variety of tools and techniques, financial managers estimate the cash flows that a proposed investment will generate and then apply decision techniques to assess the investment’s impact on the firm’s value. The most difficult and important aspect of this capital budgeting process is developing good estimates of the relevant cash flows.
The relevant cash flows are the incremental aftertax cash flows resulting from a proposed investment. These estimates represent the cash flow benefits that are likely to accrue to the firm as a result of implementing the investment. By applying to the cash flows decision techniques that capture the time value of money and risk factors, the financial manager can estimate how the investment will affect the firm’s share price. Consistent application of capital budgeting procedures to proposed longterm investments should therefore allow the firm to maximize its stock price.
REVIEW OF LEARNING GOALS
LG 1 Discuss the three major cash flow components. The three major cash flow components of any project can include (1) an initial investment, (2) operating cash flows, and (3) terminal cash flow. The initial investment occurs at time zero, the operating cash flows occur during the project’s life, and the terminal cash flow occurs at the end of the project.
LG 2 Discuss relevant cash flows, expansion versus replacement decisions, sunk costs and opportunity costs, and international capital budgeting. The relevant cash flows for capital budgeting decisions are the initial investment, the operating cash flows, and the terminal cash flow. For replacement decisions, these flows are the difference between the cash flows of the new asset and the old asset. Expansion decisions are viewed as replacement decisions in which all cash flows from the old asset are zero. When estimating relevant cash flows, ignore sunk costs and include opportunity costs as cash outflows. In international capital budgeting, currency risks and political risks can be minimized through careful planning.
LG 3 Calculate the initial investment associated with a proposed capital expenditure. The initial investment is the initial outflow required, taking into account the installed cost of the new asset, the aftertax proceeds from the sale of the old asset, and any change in net working capital. The initial investment is reduced by finding the aftertax proceeds from sale of the old asset. The book value of an asset is used to determine the taxes owed as a result of its sale. Either of two forms of taxable income—a gain or a loss—can result from sale of an asset, depending on whether the asset is sold for (1) more than book value, (2) book value, or (3) less than book value. The change in net working capital is the difference between the change in current assets and the change in current liabilities expected to accompany a given capital expenditure.
LG 4 Discuss the tax implications associated with the sale of an old asset. There is typically a tax implication from the sale of an old asset. The tax implication depends on the relationship between its sale price and book value and on existing government tax rules. Generally, if the old asset is sold for an amount greater than its book value, the difference is subject to a capital gains tax, and if the old asset is sold for an amount less than its book value, the company is entitled to a tax deduction equal to the difference.
LG 5 Find the relevant operating cash flows associated with a proposed capital expenditure. The operating cash flows are the incremental aftertax cash flows expected to result from a project. The income statement format involves adding depreciation back to net operating profit after taxes and gives the operating cash inflows, which are the same as operating cash flows (OCF), associated with the proposed and present projects. The relevant (incremental) cash flows for a replacement project are the difference between the operating cash flows of the proposed project and those of the present project.
LG 6 Determine the terminal cash flow associated with a proposed capital expenditure. The terminal cash flow represents the aftertax cash flow (exclusive of operating cash inflows) that is expected from liquidation of a project. It is calculated for replacement projects by finding the difference between the aftertax proceeds from sale of the new and the old asset at termination and then adjusting this difference for any change in net working capital. Sale price and depreciation data are used to find the taxes and the aftertax sale proceeds on the new and old assets. The change in net working capital typically represents the reversion of any initial net working capital investment.
OpenerinReview
The chapter opener talked about Diamond Comic Distributor’s attempt to reduce the cost of opening a retail comic book store. Suppose that the current cost of opening such a store is $400,000 and that $250,000 of that initial investment is the cost of stocking the shelves with new inventory. Suppose also that the annual operating cash inflow from running an average comic book store is about $62,000 before taxes and that the tax rate is 35%.
 a. Assuming that the average comic book store has a life of about 10 years, what is the NPV of opening a new store if the required rate of return in this business is 10%? You may assume that the $250,000 in initial inventory will be recovered at the end of the tenth year (in addition to the annual operating cash flow for that year). What is the IRR that one can earn by opening up a new store?
 b. Assume that by offering merchandise discounts to customers who are opening new stores Diamond can reduce the required initial inventory investment from $250,000 to $150,000. Maintaining all other assumptions as previously stated, how will that affect the NPV and IRR earned on a new comic book store?
SelfTest Problems
(Solutions in Appendix)
LG 3
LG 4
 a. Calculate the book value of the old piece of equipment.
 b. Determine the taxes, if any, attributable to the sale of the old equipment.
 c. Find the initial investment associated with the proposed equipment replacement.
LG 3
LG 4
LG 5
LG 6
 a. Determine the initial investment associated with the proposed replacement decision.
 b. Calculate the incremental operating cash flows for years 1 to 4 associated with the proposed replacement. (Note: Only depreciation cash flows must be considered in year 4.)
 c. Calculate the terminal cash flow associated with the proposed replacement decision. (Note: This decision is made at the end of year 3.)
 d. Depict on a time line the relevant cash flows found in parts a, b, and c that are associated with the proposed replacement decision, assuming that it is terminated at the end of year 3.
WarmUp Exercises
All problems are available in MyFinanceLab.
LG 2
LG 2
LG 3
LG 3
LG 4
LG 3
LG 4
Problems
All problems are available in MyFinanceLab.
LG 2
 a. An initial lease payment of $5,000 for electronic pointofsale cash register systems
 b. An outlay of $20,000 to purchase patent rights from an inventor
 c. An outlay of $80,000 for a major research and development program
 d. An $80,000 investment in a portfolio of marketable securities
 e. A $300 outlay for an office machine
 f. An outlay of $2,000 for a new machine tool
 g. An outlay of $240,000 for a new building
 h. An outlay of $1,000 for a marketing research report
LG 1
LG 2
 a. A project that requires an initial investment of $120,000 and will generate annual operating cash inflows of $25,000 for the next 18 years. In each of the 18 years, maintenance of the project will require a $5,000 cash outflow.
 b. A new machine with an installed cost of $85,000. Sale of the old machine will yield $30,000 after taxes. Operating cash inflows generated by the replacement will exceed the operating cash inflows of the old machine by $20,000 in each year of a 6year period. At the end of year 6, liquidation of the new machine will yield $20,000 after taxes, which is $10,000 greater than the aftertax proceeds expected from the old machine had it been retained and liquidated at the end of year 6.
 c. An asset that requires an initial investment of $2 million and will yield annual operating cash inflows of $300,000 for each of the next 10 years. Operating cash outlays will be $20,000 for each year except year 6, when an overhaul requiring an additional cash outlay of $500,000 will be required. The asset’s liquidation value at the end of year 10 is expected to be zero.
LG 2
Project A  Project B  



Initial investment  $40,000  $12,000^{a} 
Year  Operating cash inflows  
1  $10,000  $ 6,000 
2  12,000  6,000 
3  14,000  6,000 
4  16,000  6,000 
5  10,000  6,000 
 a. If project A were actually a replacement for project B and the $12,000 initial investment shown for project B were the aftertax cash inflow expected from liquidating it, what would be the relevant cash flows for this replacement decision?
 b. How can an expansion decision such as project A be viewed as a special form of a replacement decision? Explain.
LG 2
 a. How should the $1,000,000 in development costs be classified?
 b. How should the $250,000 sale price for the existing line be classified?
 c. Depict all the known relevant cash flows on a time line.
LG 2
 a. Covol would be able to use the same tooling, which had a book value of $40,000, on the new machine tool as it had used on the old one.
 b. Covol would be able to use its existing computer system to develop programs for operating the new machine tool. The old machine tool did not require these programs. Although the firm’s computer has excess capacity available, the capacity could be leased to another firm for an annual fee of $17,000.
 c. Covol would have to obtain additional floor space to accommodate the larger new machine tool. The space that would be used is currently being leased to another company for $10,000 per year.
 d. Covol would use a small storage facility to store the increased output of the new machine tool. The storage facility was built by Covol 3 years earlier at a cost of $120,000. Because of its unique configuration and location, it is currently of no use to either Covol or any other firm.
 e. Covol would retain an existing overhead crane, which it had planned to sell for its $180,000 market value. Although the crane was not needed with the old machine tool, it would be used to position raw materials on the new machine tool.
Personal Finance Problem
LG 2
The house should be ready to rent after that. In reviewing the financial situation, Dave views all the expenditures as being relevant, so he plans to net out the estimated expenditures discussed above from the rental income.
 a. Do Dave and Ann understand the difference between sunk costs and opportunity costs? Explain the two concepts to them.
 b. Which of the expenditures should be classified as sunk cash flows, and which should be viewed as opportunity cash flows?
LG 4
LG 5
Asset  Installed cost  Recovery period (years)  Elapsed time since purchase (years) 

A  $ 950,000  5  3 
B  40,000  3  1 
C  96,000  5  4 
D  350,000  5  1 
E  1,500,000  7  5 
LG 3
LG 4
 a. What is the book value of the machine?
 b. Calculate the firm’s tax liability if it sold the machine for each of the following amounts: $100,000; $56,000; $23,200; and $15,000.
LG 3
LG 4
 a. The asset is sold for $220,000.
 b. The asset is sold for $150,000.
 c. The asset is sold for $96,000.
 d. The asset is sold for $80,000.
LG 3
Account  Change 

Accruals  +$ 40,000 
Marketable securities  0 
Inventories  − 10,000 
Accounts payable  + 90,000 
Notes payable  0 
Accounts receivable  + 150,000 
Cash  + 15,000 
 a. Using the information given, calculate any change in net working capital that is expected to result from the proposed replacement action.
 b. Explain why a change in these current accounts would be relevant in determining the initial investment for the proposed capital expenditure.
 c. Would the change in net working capital enter into any of the other cash flow components that make up the relevant cash flows? Explain.
LG 3
LG 4
 a. Calculate the book value of the existing computer system.
 b. Calculate the aftertax proceeds of its sale for $200,000.
 c. Calculate the initial investment associated with the replacement project.
LG 3
LG 4
LG 3
LG 4
 a. EMC sells the old machine for $11,000.
 b. EMC sells the old machine for $7,000.
 c. EMC sells the old machine for $2,900.
 d. EMC sells the old machine for $1,500.
LG 3
LG 4
 a. What is the book value of the existing roaster?
 b. Calculate the aftertax proceeds of the sale of the existing roaster.
 c. Calculate the change in net working capital using the figures given in the following table.
Anticipated Changes in Current Assets and Current Liabilities Accruals −$20,000 Inventory + 50,000 Accounts payable + 40,000 Accounts receivable + 70,000 Cash 0 Notes payable + 15,000  d. Calculate the initial investment associated with the proposed new roaster.
LG 5
LG 5
 a. What incremental earnings before depreciation, interest, and taxes will result from the renewal?
 b. What incremental net operating profits after taxes will result from the renewal?
 c. What incremental operating cash flows will result from the renewal?
Personal Finance Problem
LG 5
 There are 5 years of remaining useful life on the old mower.
 The old mower has a zero book value.
 The new mower is expected to last 5 years.
 The Thomsons will follow a 5year MACRS recovery period for the new mower.
 Depreciable value of the new mower is $1,800.
 They are subject to a 40% tax rate.
 The new mower is expected to be more fuel efficient, maneuverable, and durable than previous models and can result in reduced operating expenses of $500 per year.
 The Thomsons will buy a maintenance contract that calls for annual payments of $120.
Create an incremental operating cash flow statement for the replacement of Richard and Linda’s John Deere riding mower. Show the incremental operating cash flow for the next 6 years.
LG 5
LG 5
New lathe

Old lathe



Year  Revenue  Expenses (excluding depreciation and interest)  Revenue  Expenses (excluding depreciation and interest) 
1  $40,000  $30,000  $35,000  $25,000 
2  41,000  30,000  35,000  25,000 
3  42,000  30,000  35,000  25,000 
4  43,000  30,000  35,000  25,000 
5  44,000  30,000  35,000  25,000 
 a. Calculate the operating cash flows associated with each lathe. (Note: Be sure to consider the depreciation in year 6.)
 b. Calculate the incremental (relevant) operating cash flows resulting from the proposed lathe replacement.
 c. Depict on a time line the incremental operating cash flows calculated in part b.
LG 5
Year  



1  2  3  4  5  6  
With the proposed new buses  
Revenue  $1,850,000  $1,850,000  $1,830,000  $1,825,000  $1,815,000  $1,800,000 
Expenses (excluding depreciation and interest)  460,000  460,000  468,000  472,000  485,000  500,000 
With the present buses  
Revenue  $1,800,000  $1,800,000  $1,790,000  $1,785,000  $1,775,000  $1,750,000 
Expenses (excluding depreciation and interest)  500,000  510,000  520,000  520,000  530,000  535,000 
LG 6
 a. Calculate the terminal cash flow for a usable life of (1) 3 years, (2) 5 years, and (3) 7 years.
 b. Discuss the effect of usable life on terminal cash flows using your findings in part
 c. Assuming a 5year usable life, calculate the terminal cash flow if the machine were sold to net (1) $9,000 or (2) $170,000 (before taxes) at the end of 5 years.
 d. Discuss the effect of sale price on terminal cash flow using your findings in part c.
LG 6
Marcus Tube Income Statement for the Year Ended December 31, 2015  

Sales revenue  $20,000,000 
Less: Cost of goods sold (80%)  16,000,000 
Gross profits  $ 4,000,000 
Less: Operating expenses  
General and administrative expense (10%)  $ 2,000,000 
Depreciation expense  500,000 
Total operating expense  $ 2,500,000 
Earnings before interest and taxes  $ 1,500,000 
Less: Taxes (rate 5 40%)  600,000 
Net operating profit after taxes  900,000 
Marcus Tube Sales Forecast  

Year  Sales revenue 
2016  $20,500,000 
2017  21,000,000 
2018  21,500,000 
2019  22,500,000 
2020  23,500,000 
LG 3
LG 4
LG 5
LG 6
LG 3
LG 4
LG 5
New machine

Old machine



Year  Revenue  Expenses (excl. depr. and int.)  Revenue  Expenses (excl. depr. and int.) 
1  $750,000  $720,000  $674,000  $660,000 
2  750,000  720,000  676,000  660,000 
3  750,000  720,000  680,000  660,000 
4  750,000  720,000  678,000  660,000 
5  750,000  720,000  674,000  660,000 
 a. Calculate the initial investment associated with replacement of the old machine by the new one.
 b. Determine the incremental operating cash flows associated with the proposed replacement. (Note: Be sure to consider the depreciation in year 6.)
 c. Depict on a time line the relevant cash flows found in parts a and b associated with the proposed replacement decision.
LG 3
LG 4
LG 5
LG 6
Earnings before depreciation, interest, and taxes  


Year  New grinder  Existing grinder 
1  $43,000  $26,000 
2  43,000  24,000 
3  43,000  22,000 
4  43,000  20,000 
5  43,000  18,000 
 a. Calculate the initial investment associated with the replacement of the existing grinder by the new one.
 b. Determine the incremental operating cash flows associated with the proposed grinder replacement. (Note: Be sure to consider the depreciation in year 6.)
 c. Determine the terminal cash flow expected at the end of year 5 from the proposed grinder replacement.
 d. Depict on a time line the relevant cash flows associated with the proposed grinder replacement decision.
Personal Finance Problem
LG 3
LG 4
LG 5
LG 6
Negotiated price of the new boat  $70,000 
Sales tax rate (applicable to purchase price)  6.5% 
Boat tradein  0 
Estimated value of new boat in 4 years  $40,000 
Estimated monthly repair and maintenance  $800 
Estimated monthly docking fee  $500 
Using these cash flow estimates, calculate the following:
 a. The initial investment
 b. Operating cash flow
 c. Terminal cash flow
 d. Summary of annual cash flow
 e. Based on their disposable annual income, what advice would you give Jan and Deana regarding the proposed boat purchase?
LG 3
LG 4
LG 5
LG 6
Increased investments in net working capital will accompany the decision to acquire hoist A or hoist B. Purchase of hoist A would result in a $4,000 increase in net working capital; hoist B would result in a $6,000 increase in net working capital. The projected earnings before depreciation, interest, and taxes with each alternative hoist and the existing hoist are given in the following table.
Earnings before depreciation, interest, and taxes  



Year  With hoist A  With hoist B  With existing hoist 
1  $21,000  $22,000  $14,000 
2  21,000  24,000  14,000 
3  21,000  26,000  14,000 
4  21,000  26,000  14,000 
5  21,000  26,000  14,000 
The existing hoist can currently be sold for $18,000 and will not incur any removal or cleanup costs. At the end of 5 years, the existing hoist can be sold to net $1,000 before taxes. Hoists A and B can be sold to net $12,000 and $20,000 before taxes, respectively, at the end of the 5year period. The firm is subject to a 40% tax rate. (See Table 4.2 on page 120 for the applicable depreciation percentages.)
 a. Calculate the initial investment associated with each alternative.
 b. Calculate the incremental operating cash flows associated with each alternative. (Note: Be sure to consider the depreciation in year 6.)
 c. Calculate the terminal cash flow at the end of year 5 associated with each alternative.
 d. Depict on a time line the relevant cash flows associated with each alternative.
LG 1
LG 2
LG 3
LG 4
LG 5
LG 6
Wells Printing’s cost of capital is 11%. (Note: Assume that the old and the new presses will each have a terminal value of $0 at the end of year 6.)
 a. Determine the initial investment required by the new press.
 b. Determine the operating cash flows attributable to the new press. (Note: Be sure to consider the depreciation in year 6.)
 c. Determine the payback period.
 d. Determine the net present value (NPV) and the internal rate of return (IRR) related to the proposed new press.
 e. Make a recommendation to accept or reject the new press, and justify your answer.
LG 1
LG 2
LG 3
LG 4
LG 5
LG 6
 a. Develop the relevant cash flows needed to analyze the proposed replacement.
 b. Determine the net present value (NPV) of the proposal.
 c. Determine the internal rate of return (IRR) of the proposal.
 d. Make a recommendation to accept or reject the replacement proposal, and justify your answer.
 e. What is the highest cost of capital that the firm could have and still accept the proposal? Explain.
LG 2
Spreadsheet Exercise
Damon Corporation, a sports equipment manufacturer, has a machine currently in use that was originally purchased 3 years ago for $120,000. The firm depreciates the machine under MACRS using a 5year recovery period. Once removal and cleanup costs are taken into consideration, the expected net selling price for the present machine will be $70,000.
Damon can buy a new machine for a net price of $160,000 (including installation costs of $15,000). The proposed machine will be depreciated under MACRS using a 5year recovery period. If the firm acquires the new machine, its working capital needs will change: Accounts receivable will increase $15,000, inventory will increase $19,000, and accounts payable will increase $16,000.
Earnings before depreciation, interest, and taxes (EBDIT) for the present machine are expected to be $95,000 for each of the successive 5 years. For the proposed machine, the expected EBDIT for each of the next 5 years are $105,000, $110,000, $120,000, $120,000, and $120,000, respectively. The corporate tax rate (T) for the firm is 40%. (Table 4.2 on page 120 contains the applicable MACRS depreciation percentages.)
Damon expects to be able to liquidate the proposed machine at the end of its 5year usable life for $24,000 (after paying removal and cleanup costs). The present machine is expected to net $8,000 upon liquidation at the end of the same period. Damon expects to recover its net working capital investment upon termination of the project. The firm is subject to a tax rate of 40%.
TO DO
Create a spreadsheet similar to Tables 11.1, 11.5, 11.7, and 11.9 to answer the following:
 a. Create a spreadsheet to calculate the initial investment.
 b. Create a spreadsheet to prepare a depreciation schedule for both the proposed and the present machine. Both machines are depreciated under MACRS using a 5year recovery period. Remember that the present machine has only 3 years of depreciation remaining.
 c. Create a spreadsheet to calculate the operating cash flows for Damon Corporation for both the proposed and the present machine.
 d. Create a spreadsheet to calculate the terminal cash flow associated with the project.
Visit www.myfinancelab.com for Chapter Case: Developing Relevant Cash Flows for Clark Upholstery Company’s Machine Renewal or Replacement Decision, Group Exercises, and numerous online resources.