452 SECTION FOUR relative risks, at least in industries they are used to, but not about absolute risk or re- quired rates of return. Therefore, they set a company- or industrywide cost of capital as a benchmark. This is not the right hurdle rate for everything the company does, but judgmental adjustments can be made for more risky or less risky ventures. SOME COMMON MISTAKES One danger with the weighted-average formula is that it tempts people to make logical errors. Think back to your estimate of the cost of capital for Big Oil: WACC = [ D × (1 – T c ) r debt ] + ( E × r equity ) VV = [.243 × (1 – .35) 9%] + (.757 × 13.5%) = 11.6% Now you might be tempted to say to yourself, “Aha! Big Oil has a good credit rating. It could easily push up its debt ratio to 50 percent. If the interest rate is 9 percent and the required return on equity is 13.5 percent, the weighted-average cost of capital would be WACC = [.50 × (1 – .35) 9%] + (.50 × 13.5%) = 9.7% At a discount rate of 9.7 percent, we can justify a lot more investment.” That reasoning will get you into trouble. First, if Big Oil increased its borrowing, the lenders would almost certainly demand a higher rate of interest on the debt. Second, as the borrowing increased, the risk of the common stock would also increase and there- fore the stockholders would demand a higher return. When you jumped to the conclusion that Big Oil could lower its weighted-average cost of capital to 9.7 percent by borrowing more, you were recognizing only the explicit cost of debt and not the implicit cost. ᭤ Self-Test 7 Jo Ann Cox’s boss has pointed out that Geothermal proposes to finance its expansion entirely by borrowing at an interest rate of 8 percent. He argues that this is therefore the appropriate discount rate for the project’s cash flows. Is he right? HOW CHANGING CAPITAL STRUCTURE AFFECTS EXPECTED RETURNS We will illustrate how changes in capital structure affect expected returns by focusing on the simplest possible case, where the corporate tax rate T c is zero. Think back to our earlier example of Geothermal. Geothermal, you may remember, has the following market-value balance sheet: Assets Liabilities and Shareholders’ Equity Assets = value of Geothermal’s $647 Debt $194 (30%) existing business Equity $453 (70%) Total value $647 Value $647 (100%) There are actually two costs of debt finance. The explicit cost of debt is the rate of interest that bondholders demand. But there is also an implicit cost, because borrowing increases the required return to equity. The Cost of Capital 453 Geothermal’s debtholders require a return of 8 percent and the shareholders require a return of 14 percent. Since we assume here that Geothermal pays no corporate tax, its weighted-average cost of capital is simply the expected return on the firm’s assets: WACC = r assets = (.3 × 8%) + (.7 × 14%) = 12.2% This is the return you would expect if you held all Geothermal’s securities and therefore owned all its assets. Now think what will happen if Geothermal borrows an additional $97 million and uses the cash to buy back and retire $97 million of its common stock. The revised mar- ket-value balance sheet is Assets Liabilities and Shareholders’ Equity Assets = value of Geothermal’s $647 Debt $291 (45%) existing business Equity 356 (55%) Total value $647 Value $647 (100%) If there are no corporate taxes, the change in capital structure does not affect the total cash that Geothermal pays out to its security holders and it does not affect the risk of those cash flows. Therefore, if investors require a return of 12.2 percent on the total package of debt and equity before the financing, they must require the same 12.2 percent return on the package afterward. The weighted-average cost of capital is there- fore unaffected by the change in the capital structure. Although the required return on the package of the debt and equity is unaffected, the change in capital structure does affect the required return on the individual securities. Since the company has more debt than before, the debt is riskier and debtholders are likely to demand a higher return. Increasing the amount of debt also makes the equity riskier and increases the return that shareholders require. WHAT HAPPENS WHEN THE CORPORATE TAX RATE IS NOT ZERO We have shown that when there are no corporate taxes the weighted-average cost of cap- ital is unaffected by a change in capital structure. Unfortunately, taxes can complicate the picture. 7 For the moment, just remember • The weighted-average cost of capital is the right discount rate for average- risk capital investment projects. • The weighted-average cost of capital is the return the company needs to earn after tax in order to satisfy all its security holders. • If the firm increases its debt ratio, both the debt and the equity will become more risky. The debtholders and equity holders require a higher return to compensate for the increased risk. 7 There’s nothing wrong with our formulas and examples, provided that the tax deductibility of interest pay- ments doesn’t change the aggregate risk of the debt and equity investors. However, if the tax savings from deducting interest are treated as safe cash flows, the formulas get more complicated. If you really want to dive into the tax-adjusted formulas showing how WACC changes with capital structure, we suggest later in R. A. Brealey and S. C. Myers, Principles of Corporate Finance, 6th ed. (New York: Irwin/McGraw-Hill, 2000). 454 SECTION FOUR Flotation Costs and the Cost of Capital To raise the necessary cash for a new project, the firm may need to issue stocks, bonds, or other securities. The costs of issuing these securities to the public can easily amount to 5 percent of funds raised. For example, a firm issuing $100 million in new equity may net only $95 million after incurring the costs of the issue. Flotation costs involve real money. A new project is less attractive if the firm must spend large sums on issuing new securities. To illustrate, consider a project that will cost $900,000 to install and is expected to generate a level perpetual cash-flow stream of $90,000 a year. At a required rate of return of 10 percent, the project is just barely viable, with an NPV of zero: –$900,000 + $90,000/.10 = 0. Now suppose that the firm needs to raise equity to pay for the project, and that flotation costs are 10 percent of funds raised. To raise $900,000, the firm actually must sell $1 million of equity. Since the installed project will be worth only $90,000/.10 = $900,000, NPV including flotation costs is actually –$1 million + $900,000 = –$100,000. In our example, we recognized flotation costs as one of the incremental costs of un- dertaking the project. But instead of recognizing these costs explicitly, some companies attempt to cope with flotation costs by increasing the cost of capital used to discount project cash flows. By using a higher discount rate, project present value is reduced. This procedure is flawed on practical as well as theoretical grounds. First, on a purely practical level, it is far easier to account for flotation costs as a negative cash flow than to search for an adjustment to the discount rate that will give the right NPV. Finding the necessary adjustment is easy only when cash flows are level or will grow indefinitely at a constant trend rate. This is almost never the case in practice, however. Of course, there always exists some discount rate that will give the right measure of the project’s NPV, but this rate could no longer be interpreted as the rate of return available in the capital market for investments with the same risk as the project. Summary Why do firms compute weighted-average costs of capital? They need a standard discount rate for average-risk projects. An “average-risk” project is one that has the same risk as the firm’s existing assets and operations. What about projects that are not average? The weighted-average cost of capital can still be used as a benchmark. The benchmark is adjusted up for unusually risky projects and down for unusually safe ones. How do firms compute weighted-average costs of capital? Here’s the WACC formula one more time: The cost of capital depends only on interest rates, taxes, and the risk of the project. Flotation costs should be treated as incremental (negative) cash flows; they do not increase the required rate of return. The Cost of Capital 455 WACC = r debt × (1 – T c ) × D/V + r equity × E/V The WACC is the expected rate of return on the portfolio of debt and equity securities issued by the firm. The required rate of return on each security is weighted by its proportion of the firm’s total market value (not book value). Since interest payments reduce the firm’s income tax bill, the required rate of return on debt is measured after tax, as r debt × (1 – T c ). This WACC formula is usually written assuming the firm’s capital structure includes just two classes of securities, debt and equity. If there is another class, say preferred stock, the formula expands to include it. In other words, we would estimate r preferred , the rate of return demanded by preferred stockholders, determine P/V, the fraction of market value accounted for by preferred, and add r preferred × P/V to the equation. Of course the weights in the WACC formula always add up to 1.0. In this case D/V + P/V + E/V = 1.0. How are the costs of debt and equity calculated? The cost of debt (r debt ) is the market interest rate demanded by bondholders. In other words, it is the rate that the company would pay on new debt issued to finance its investment projects. The cost of preferred (r preferred ) is just the preferred dividend divided by the market price of a preferred share. The tricky part is estimating the cost of equity (r equity ), the expected rate of return on the firm’s shares. Financial managers use the capital asset pricing model to estimate expected return. But for mature, steady-growth companies, it can also make sense to use the constant- growth dividend discount model. Remember, estimates of expected return are less reliable for a single firm’s stock than for a sample of comparable-risk firms. Therefore, some managers also consider WACCs calculated for industries. What happens when capital structure changes? The rates of return on debt and equity will change. For example, increasing the debt ratio will increase the risk borne by both debt and equity investors and cause them to demand higher returns. However, this does not necessarily mean that the overall WACC will increase, because more weight is put on the cost of debt, which is less than the cost of equity. In fact, if we ignore taxes, the overall cost of capital will stay constant as the fractions of debt and equity change. Should WACC be adjusted for the costs of issuing securities to finance a project? No. If acceptance of a project would require the firm to issue securities, the flotation costs of the issue should be added to the investment required for the project. This reduces project NPV dollar for dollar. There is no need to adjust WACC. www.geocities.com/WallStreet/Market/1839/irates.html Incorporating risk premiums into the cost of capital www.financeadvisor.com/coc.htm Another approach to calculating cost of capital capital structure weighted-average cost of capital (WACC) 1. Cost of Debt. Micro Spinoffs, Inc., issued 20-year debt a year ago at par value with a coupon rate of 9 percent, paid annually. Today, the debt is selling at $1,050. If the firm’s tax bracket is 35 percent, what is its after-tax cost of debt? Related Web Links Key Terms Quiz 456 SECTION FOUR 2. Cost of Preferred Stock. Micro Spinoffs also has preferred stock outstanding. The stock pays a dividend of $4 per share, and the stock sells for $40. What is the cost of preferred stock? 3. Calculating WACC. Suppose Micro Spinoffs’s cost of equity is 12.5 percent. What is its WACC if equity is 50 percent, preferred stock is 20 percent, and debt is 30 percent of total capital? 4. Cost of Equity. Reliable Electric is a regulated public utility, and it is expected to provide steady growth of dividends of 5 percent per year for the indefinite future. Its last dividend was $5 per share; the stock sold for $60 per share just after the dividend was paid. What is the company’s cost of equity? 5. Calculating WACC. Reactive Industries has the following capital structure. Its corporate tax rate is 35 percent. What is its WACC? Security Market Value Required Rate of Return Debt $20 million 8% Preferred stock $10 million 10% Common stock $50 million 15% 6. Company versus Project Discount Rates. Geothermal’s WACC is 11.4 percent. Executive Fruit’s WACC is 12.3 percent. Now Executive Fruit is considering an investment in geother- mal power production. Should it discount project cash flows at 12.3 percent? Why or why not? 7. Flotation Costs. A project costs $10 million and has NPV of $+2.5 million. The NPV is computed by discounting at a WACC of 15 percent. Unfortunately, the $10 million invest- ment will have to be raised by a stock issue. The issue would incur flotation costs of $1.2 million. Should the project be undertaken? 8. WACC. The common stock of Buildwell Conservation & Construction, Inc., has a beta of .80. The Treasury bill rate is 4 percent and the market risk premium is estimated at 8 per- cent. BCCI’s capital structure is 30 percent debt paying a 5 percent interest rate, and 70 per- cent equity. What is BCCI’s cost of equity capital? Its WACC? Buildwell pays no taxes. 9. WACC and NPV. BCCI (see the previous problem) is evaluating a project with an internal rate of return of 12 percent. Should it accept the project? If the project will generate a cash flow of $100,000 a year for 7 years, what is the most BCCI should be willing to pay to ini- tiate the project? 10. Calculating WACC. Find the WACC of William Tell Computers. The total book value of the firm’s equity is $10 million; book value per share is $20. The stock sells for a price of $30 per share, and the cost of equity is 15 percent. The firm’s bonds have a par value of $5 mil- lion and sell at a price of 110 percent of par. The yield to maturity on the bonds is 9 percent, and the firm’s tax rate is 40 percent. 11. WACC. Nodebt, Inc., is a firm with all-equity financing. Its equity beta is .80. The Treasury bill rate is 5 percent and the market risk premium is expected to be 10 percent. What is Nodebt’s asset beta? What is Nodebt’s weighted-average cost of capital? The firm is exempt from paying taxes. 12. Cost of Capital. A financial analyst at Dawn Chemical notes that the firm’s total interest payments this year were $10 million while total debt outstanding was $80 million, and he concludes that the cost of debt was 12.5 percent. What is wrong with this conclusion? 13. Cost of Equity. Bunkhouse Electronics is a recently incorporated firm that makes electronic entertainment systems. Its earnings and dividends have been growing at a rate of 30 percent, Practice Problems The Cost of Capital 457 and the current dividend yield is 2 percent. Its beta is 1.2, the market risk premium is 8 per- cent, and the risk-free rate is 4 percent. a. Calculate two estimates of the firm’s cost of equity. b. Which estimate seems more reasonable to you? Why? 14. Cost of Debt. Olympic Sports has two issues of debt outstanding. One is a 9 percent coupon bond with a face value of $20 million, a maturity of 10 years, and a yield to maturity of 10 percent. The coupons are paid annually. The other bond issue has a maturity of 15 years, with coupons also paid annually, and a coupon rate of 10 percent. The face value of the issue is $25 million, and the issue sells for 92.8 percent of par value. The firm’s tax rate is 35 percent. a. What is the before-tax cost of debt for Olympic? b. What is Olympic’s after-tax cost of debt? 15. Capital Structure. Examine the following book-value balance sheet for University Prod- ucts, Inc. What is the capital structure of the firm based on market values? The preferred stock currently sells for $15 per share and the common stock for $20 per share. There are one million common shares outstanding. BOOK VALUE BALANCE SHEET (all values in millions) Assets Liabilities and Net Worth Cash and short-term securities $ 1 Bonds, coupon = 8%, paid $10.0 annually (maturity = 10 years, current yield to maturity = 9%) Accounts receivable 3 Preferred stock (par value $20 2.0 per share) Inventories 7 Common stock (par value $.10) .1 Plant and equipment 21 Additional paid in stockholders’ 9.9 capital Retained earnings 10.0 Total $32 Total $32.0 16. Calculating WACC. Turn back to University Products’s balance sheet from the previous problem. If the preferred stock pays a dividend of $2 per share, the beta of the stock is .8, the market risk premium is 10 percent, the risk-free rate is 6 percent, and the firm’s tax rate is 40 percent, what is University’s weighted-average cost of capital? 17. Project Discount Rate. University Products is evaluating a new venture into home com- puter systems (see problems 15 and 16). The internal rate of return on the new venture is estimated at 13.4 percent. WACCs of firms in the personal computer industry tend to average around 14 percent. Should the new project be pursued? Will University Products make the correct decision if it discounts cash flows on the proposed venture at the firm’s WACC? 18. Cost of Capital. The total market value of Okefenokee Real Estate Company is $6 million, and the total value of its debt is $4 million. The treasurer estimates that the beta of the stock currently is 1.5 and that the expected risk premium on the market is 10 percent. The Trea- sury bill rate is 4 percent. a. What is the required rate of return on Okefenokee stock? b. What is the beta of the company’s existing portfolio of assets? The debt is perceived to be virtually risk-free. 458 SECTION FOUR c. Estimate the weighted-average cost of capital assuming a tax rate of 40 percent. d. Estimate the discount rate for an expansion of the company’s present business. e. Suppose the company wants to diversify into the manufacture of rose-colored glasses. The beta of optical manufacturers with no debt outstanding is 1.2. What is the required rate of return on Okefenokee’s new venture? 19. Changes in Capital Structure. Look again at our calculation of Big Oil’s WACC. Suppose Big Oil is excused from paying taxes. How would its WACC change? Now suppose Big Oil makes a large stock issue and uses the proceeds to pay off all its debt. How would the cost of equity change? 20. Changes in Capital Structure. Refer again to problem 19. Suppose Big Oil starts from the financing mix in Table 4.13, and then borrows an additional $200 million from the bank. It then pays out a special $200 million dividend, leaving its assets and operations unchanged. What happens to Big Oil’s WACC, still assuming it pays no taxes? What happens to the cost of equity? 21. WACC and Taxes. “The after-tax cost of debt is lower when the firm’s tax rate is higher; therefore, the WACC falls when the tax rate rises. Thus, with a lower discount rate, the firm must be worth more if its tax rate is higher.” Explain why this argument is wrong. 22. Cost of Capital. An analyst at Dawn Chemical notes that its cost of debt is far below that of equity. He concludes that it is important for the firm to maintain the ability to increase its borrowing because if it cannot borrow, it will be forced to use more expensive equity to fi- nance some projects. This might lead it to reject some projects that would have seemed at- tractive if evaluated at the lower cost of debt. Comment on this reasoning. 1 Hot Rocks’s 4 million common shares are worth $40 million. Its market value balance sheet is: Assets Liabilities and Shareholders’ Equity Assets $90 Debt $50 (56%) Equity 40 (44%) Value $90 Value $90 WACC = (.56 × 9%) + (.44 × 17%) = 12.5% We use Hot Rocks’s pretax return on debt because the company pays no taxes. 2 Burg’s 6 million shares are now worth only 6 million × $4 = $24 million. The debt is sell- ing for 80 percent of book, or $20 million. The market value balance sheet is: Assets Liabilities and Shareholders’ Equity Assets $44 Debt $20 (45%) Equity 24 (55%) Value $44 Value $44 WACC = (.45 × 14%) + (.55 × 20%) = 17.3% Note that this question ignores taxes. Challenge Problems Solutions to Self-Test Questions The Cost of Capital 459 3 Compare the two income statements, one for Criss-cross Industries and the other for a firm with identical EBIT but no debt in its capital structure. (All figures in millions.) Criss-cross Firm with No Debt EBIT $10.0 $10.0 Interest expense 2.0 0.0 Taxable income 8.0 10.0 Taxes owed 2.8 3.5 Net income 5.2 6.5 Total income accruing to debt & equity holders 7.2 6.5 Notice that Criss-cross pays $.7 million less in taxes than its debt-free counterpart. Ac- cordingly, the total income available to debt plus equity holders is $.7 million higher. 4 For Hot Rocks, WACC = [.56 × 9 × (1 – .35)] + (.44 × 17) = 10.76% For Burg Associates, WACC = [.45 × 14 × (1 – .35)] + (.55 × 20) = 15.1% 5 WACC measures the expected rate of return demanded by debt and equity investors in the firm (plus a tax adjustment capturing the tax-deductibility of interest payments). Thus the calculation must be based on what investors are actually paying for the firm’s debt and eq- uity securities. In other words, it must be based on market values. 6 From the CAPM: r equity = r f + β equity (r m – r f ) = 6% + 1.20(9%) = 16.8% WACC = .3(1 – .35) 8% + .7(16.8%) = 13.3% 7 Jo Ann’s boss is wrong. The ability to borrow at 8 percent does not mean that the cost of capital is 8 percent. This analysis ignores the side effects of the borrowing, for example, that at the higher indebtedness of the firm the equity will be riskier, and therefore the equity- holders will demand a higher rate of return on their investment. MINICASE Bernice Mountaindog was glad to be back at Sea Shore Salt. Employees were treated well. When she had asked a year ago for a leave of absence to complete her degree in finance, top man- agement promptly agreed. When she returned with an honors de- gree, she was promoted from administrative assistant (she had been secretary to Joe-Bob Brinepool, the president) to treasury analyst. Bernice thought the company’s prospects were good. Sure, table salt was a mature business, but Sea Shore Salt had grown steadily at the expense of its less well-known competitors. The company’s brand name was an important advantage, despite the difficulty most customers had in pronouncing it rapidly. Bernice started work on January 2, 2000. The first two weeks went smoothly. Then Mr. Brinepool’s cost of capital memo as- signed her to explain Sea Shore Salt’s weighted-average cost of capital to other managers. The memo came as a surprise to Ber- nice, so she stayed late to prepare for the questions that would surely come the next day. Bernice first examined Sea Shore Salt’s most recent balance sheet, summarized in Table 4.14. Then she jotted down the fol- lowing additional points: • The company’s bank charged interest at current market rates, and the long-term debt had just been issued. Book and market values could not differ by much. • But the preferred stock had been issued 35 years ago, when 460 SECTION FOUR interest rates were much lower. The preferred stock was now trading for only $70 per share. • The common stock traded for $40 per share. Next year’s earn- ings per share would be about $4.00 and dividends per share probably $2.00. Sea Shore Salt had traditionally paid out 50 percent of earnings as dividends and plowed back the rest. • Earnings and dividends had grown steadily at 6 to 7 percent per year, in line with the company’s sustainable growth rate: Sustainable = return × plowback growth rate on equity ratio = 4.00/30 × .5 = .067, or 6.7% • Sea Shore Salt’s beta had averaged about .5, which made sense, Bernice thought, for a stable, steady-growth business. She made a quick cost of equity calculation using the capital asset pricing model (CAPM). With current interest rates of about 7 percent, and a market risk premium of 8 percent, CAPM cost of equity = r E = r f + β(r m – r f ) = 7% + .5(8%) = 11% This cost of equity was significantly less than the 16 percent decreed in Mr. Brinepool’s memo. Bernice scanned her notes ap- prehensively. What if Mr. Brinepool’s cost of equity was wrong? Was there some other way to estimate the cost of equity as a check on the CAPM calculation? Could there be other errors in his calculations? Bernice resolved to complete her analysis that night. If neces- sary, she would try to speak with Mr. Brinepool when he arrived at his office the next morning. Her job was not just finding the right number. She also had to figure out how to explain it all to Mr. Brinepool. TABLE 4.14 Sea Shore Salt’s balance sheet, taken from the company’s 1999 balance sheet (figures in millions) Assets Liabilities and Net Worth Working capital $200 Bank loan $120 Plant and equipment 360 Long-term debt 80 Other assets 40 Preferred stock 100 Common stock, including retained earnings 300 Total $600 Total $600 Notes: 1. At year-end 1999, Sea Shore Salt had 10 million common shares outstanding. 2. The company had also issued 1 million preferred shares with book value of $100 per share. Each share receives an annual dividend of $6.00. The Cost of Capital 461 Sea Shore Salt Company Spring Vacation Beach, Florida CONFIDENTIAL MEMORANDUM DATE: January 15, 2000 TO: S.S.S. Management FROM: Joe-Bob Brinepool, President SUBJECT: Cost of Capital This memo states and clarifies our company’s long-standing policy regarding hurdle rates for capital investment decisions. There have been many recent questions, and some evident confusion, on this matter. Sea Shore Salt evaluates replacement and expansion investments by discounted cash flow. The discount or hurdle rate is the company’s after-tax weighted-average cost of capital. The weighted-average cost of capital is simply a blend of the rates of return expected by investors in our company. These investors include banks, bond holders, and preferred stock investors in addition to common stockholders. Of course many of you are, or soon will be, stockholders of our company. The following table summarizes the composition of Sea Shore Salt’s financing. Amount (in millions) Percent of Total Rate of Return Bank loan $120 20% 8% Bond issue 80 13.3 7.75 Preferred stock 100 16.7 6 Common stock 300 50 16 $600 100% The rates of return on the bank loan and bond issue are of course just the interest rates we pay. However, interest is tax-deductible, so the after-tax interest rates are lower than shown above. For example, the after-tax cost of our bank financing, given our 35% tax rate, is 8(1 – .35) = 5.2%. The rate of return on preferred stock is 6%. Sea Shore Salt pays a $6 dividend on each $100 preferred share. Our target rate of return on equity has been 16% for many years. I know that some newcomers think this target is too high for the safe and mature salt business. But we must all aspire to superior profitability. Once this background is absorbed, the calculation of Sea Shore Salt’s weighted-average cost of capital (WACC) is elementary: WACC = 8(1 – .35)(.2) + 7.75(1 – .35)(.133) + 6(.167) + 16(.50) = 10.7% The official corporate hurdle rate is therefore 10.7%. If you have further questions about these calculations, please direct them to our new Treasury Analyst, Ms. Bernice Mountaindog. It is a pleasure to have Bernice back at Sea Shore Salt after a year’s leave of absence to complete her degree in finance. [...]... Investment Sales Variable cost as percent of sales Fixed cost 6,200,000 14,000,000 5,400,000 16,000,000 5,000,000 18, 000,000 –121,000 –1,2 18, 000 +4 78, 000 +4 78, 000 +7 78, 000 +2,174,000 83 2,100,000 81 .25 2,000,000 80 1,900,000 – 788 ,000 +26,000 +4 78, 000 +4 78, 000 +1, 382 ,000 +930,000 or perhaps you will need to undertake costly landscaping The greatest dangers often lie in these unknown unknowns, or “unk-unks,”... by 1 percent, and profits will increase by 01 × (sales – variable costs) = 01 × (profits + fixed costs) Now recall the definition of DOL: 4 DOL = percentage change in profits change in profits/level of profits percentage change in sales = 01 = 100 × = 1+ change in profits 01 × (profits + fixed costs) = 100 × level of profits level of profits fixed costs profits Project Analysis 481 Flexibility in Capital... project has an NPV of –$1.2 18 million If variable costs are 83 percent of sales (and all other forecasts are unchanged), then the project has an NPV of –$ 788 ,000 ᭤ Self-Test 1 Recalculate cash flow as in Table 5.1 if variable costs are 83 percent of sales Confirm that NPV will be –$ 788 ,000 Value of Information Now that you know the project could be thrown badly off course by a poor estimate of sales, you... 7) Present value of cash flows NPV Competing Store Scenarioa $16,000,000 13,000,000 2,000,000 450,000 550,000 220,000 330,000 780 ,000 $13,600,000 11,152,000 2,000,000 450,000 –2,000 80 0 –1,200 4 48, 800 5 ,87 8,000 4 78, 000 3, 382 ,000 –2,0 18, 000 a Assumptions: Competing store causes (1) a 15 percent reduction in sales, and (2) variable costs to increase to 82 percent of sales scenario of lower sales and... 12.5 4 78 SECTION FIVE Thus Lophead needs to sell about 46 planes a year, or a total of about 280 planes over the 6 years to show a profit Notice that we obtain the same result if we attack the problem in terms of the breakeven level of revenue The variable cost of each plane is $8. 5 million, which is 54 .8 percent of the $15.5 million price Therefore, each dollar of sales increases pretax profits by... with sales, and the profit on each extra sale Managers often face a trade-off between these 3 The true break-even point for the TriStar program is estimated in U E Reinhardt, “Break-Even Analysis for Lockheed’s TriStar: An Application of Financial Theory,” Journal of Finance 28 (September 1973), pp 82 1 83 8 Project Analysis OPERATING LEVERAGE Degree to which costs are fixed DEGREE OF OPERATING LEVERAGE... million –$7.69 million + 84 78 × sales = $5.4 million sales = 5.4 + 7.69 = $15.4 million 84 78 This implies that the store needs sales of $15.4 million a year for the investment to have a zero NPV This is more than 18 percent higher than the point at which the project has zero profit Figure 5.2 is a plot of the present value of the inflows and outflows from the superstore as a function of annual sales The... MacCaugh invest $200,000 now to obtain a 50 percent chance of a project with an NPV of $2 million a year later? If payoffs of zero and $2 million are equally likely, the expected payoff is (.5 × 0) + (.5 × 2 million) = $1 million Thus the pilot project offers an expected payoff of $1 million on an investment of $200,000 At any reasonable cost of capital this is a good deal THE OPTION TO EXPAND Notice... are 81 .25 percent of sales So, for each additional dollar of sales, costs increase by only $ .81 25 We can easily determine how much business the superstore needs to attract to avoid losses If the store sells nothing, the income statement will show fixed costs of $2 million and depreciation of $450,000 Thus there will be a loss of $2.45 million Each dollar of sales reduces this loss by $1.00 – $ .81 25... end of the 12 years you could sell off the land and buildings As an experienced financial manager, you recognize immediately that these cash flows constitute an annuity and therefore you calculate present value by multiplying the $ 780 ,000 cash flow by the 12-year annuity factor If the cost of capital is 8 percent, present value is PV = $ 780 ,000 × 12-year annuity factor = $ 780 ,000 × 7.536 = $5 .87 8 million . 5,000,000 –121,000 +4 78, 000 +7 78, 000 Sales 14,000,000 16,000,000 18, 000,000 –1,2 18, 000 +4 78, 000 +2,174,000 Variable cost as percent of sales 83 81 .25 80 – 788 ,000 +4 78, 000 +1, 382 ,000 Fixed cost 2,100,000. then the project has an NPV of –$1.2 18 million. If variable costs are 83 percent of sales (and all other forecasts are unchanged), then the project has an NPV of –$ 788 ,000. ᭤ Self-Test 1 Recalculate. variable costs are 83 percent of sales. Confirm that NPV will be –$ 788 ,000. Value of Information. Now that you know the project could be thrown badly off course by a poor estimate of sales, you might