CHAPTER THE COST OF CAPITAL (Difficulty: E = Easy, M = Medium, and T = Tough) Multiple Choice: Conceptual Easy: Capital components Long-term debt Common stock Accounts payable and accruals Preferred stock Capital components Answer: d Diff: E For a typical firm with a given capital structure, which of the following is correct? (Note: All rates are after taxes.) a b c d e kd > ks > WACC ke > None ke > ks > WACC ke > kd > WACC > ke > ks > kd ks > WACC > kd of the statements above is correct Capital components Diff: E Which of the following is not considered a capital component for the purpose of calculating the weighted average cost of capital (WACC) as it applies to capital budgeting? a b c d Answer: c Answer: a Diff: E Which of the following statements is most correct? a If a company’s tax rate increases but the yield to maturity of its noncallable bonds remains the same, the company’s marginal cost of debt capital used to calculate its weighted average cost of capital will fall b All else equal, an increase in a company’s stock price will increase the marginal cost of retained earnings, ks c All else equal, an increase in a company’s stock price will increase the marginal cost of issuing new common equity, ke d Statements a and b are correct e Statements b and c are correct Chapter - Page Capital components Answer: c Diff: E Which of the following statements is most correct? a Since the money is readily available, the cost of retained earnings is usually a lot cheaper than the cost of debt financing b When calculating the cost of preferred stock, a company needs to adjust for taxes, because preferred stock dividends are tax deductible c When calculating the cost of debt, a company needs to adjust for taxes, because interest payments are tax deductible d Statements a and b are correct e Statements b and c are correct DCF cost of equity estimation Expected growth rate, g Dividend yield, D1/P0 Required return, ks ˆs Expected rate of return, k All of the above are equally difficult to estimate WACC Answer: d Diff: E Which of the following statements is most correct? a b c d e The WACC measures the after-tax cost of capital The WACC measures the marginal cost of capital There is no cost associated with using retained earnings Statements a and b are correct All of the statements above are correct WACC Diff: E Which of the following factors in the discounted cash flow (DCF) approach to estimating the cost of common equity is the least difficult to estimate? a b c d e Answer: b Answer: c Diff: E Which of the following statements about the cost of capital is incorrect? a A company’s target capital structure affects its weighted average cost of capital b Weighted average cost of capital calculations should be based on the after-tax costs of all the individual capital components c If a company’s tax rate increases, then, all else equal, its weighted average cost of capital will increase d Flotation costs can increase the weighted average cost of capital e An increase in the risk-free rate is likely to increase the marginal costs of both debt and equity financing Chapter - Page WACC Answer: e Diff: E Campbell Co is trying to estimate its weighted average cost of capital (WACC) Which of the following statements is most correct? a The after-tax cost of debt is generally cheaper than the after-tax cost of preferred stock b Since retained earnings are readily available, the cost of retained earnings is generally lower than the cost of debt c If the company’s beta increases, this will increase the cost of equity financing, even if the company is able to rely on only retained earnings for its equity financing d Statements a and b are correct e Statements a and c are correct Factors influencing WACC Diff: E Wyden Brothers has no retained earnings The company uses the CAPM to calculate the cost of equity capital The company’s capital structure consists of common stock, preferred stock, and debt Which of the following events will reduce the company’s WACC? a A reduction b An increase stock c An increase d An increase e An increase stock in the market risk premium in the flotation costs associated with issuing new common in the company’s beta in expected inflation in the flotation costs associated with issuing preferred WACC and capital components 10 Answer: a Answer: c Diff: E Which of the following statements is most correct? a The WACC is a measure of the before-tax cost of capital b Typically the after-tax cost of debt financing exceeds the after-tax cost of equity financing c The WACC measures the marginal after-tax cost of capital d Statements a and b are correct e Statements b and c are correct WACC and capital components 11 Answer: a Diff: E A company has a capital structure that consists of 50 percent debt and 50 percent equity Which of the following statements is most correct? a The cost of equity financing is greater than or equal to the cost of debt financing b The WACC exceeds the cost of equity financing c The WACC is calculated on a before-tax basis d The WACC represents the cost of capital based on historical averages In that sense, it does not represent the marginal cost of capital e The cost of retained earnings exceeds the cost of issuing new common stock Chapter - Page Internal vs external common equity 12 Diff: E A firm estimates that its proposed capital budget will force it to issue new common stock, which has a greater cost than the cost of retained earnings The firm, however, would like to avoid issuing costly new common stock Which of the following steps would mitigate the firm’s need to raise new common stock? a b c d e Increasing the company’s dividend payout ratio for the upcoming year Reducing the company’s debt ratio for the upcoming year Increasing the company’s proposed capital budget All of the statements above are correct None of the statements above is correct Risk and project selection 13 Answer: e Answer: c Diff: E Dick Boe Enterprises, an all-equity firm, has a corporate beta coefficient of 1.5 The financial manager is evaluating a project with an expected return of 21 percent, before any risk adjustment The risk-free rate is 10 percent, and the required rate of return on the market is 16 percent The project being evaluated is riskier than Boe’s average project, in terms of both beta risk and total risk Which of the following statements is most correct? a The project should be accepted since its expected return (before risk adjustment) is greater than its required return b The project should be rejected since its expected return (before risk adjustment) is less than its required return c The accept/reject decision depends on the risk-adjustment policy of the firm If the firm’s policy were to reduce a riskier-than-average project’s expected return by percentage point, then the project should be accepted d Riskier-than-average projects should have their expected returns increased to reflect their added riskiness Clearly, this would make the project acceptable regardless of the amount of the adjustment e Projects should be evaluated on the basis of their total risk alone Thus, there is insufficient information in the problem to make an accept/reject decision Risk and project selection 14 Answer: b Diff: E A company estimates that an average-risk project has a WACC of 10 percent, a below-average risk project has a WACC of percent, and an above-average risk project has a WACC of 12 percent Which of the following independent projects should the company accept? a b c d e Project A has average risk and a return of percent Project B has below-average risk and a return of 8.5 percent Project C has above-average risk and a return of 11 percent All of the projects above should be accepted None of the projects above should be accepted Chapter - Page Divisional risk 15 Answer: a Division A Division B Division B Statements Statements project project project a and c b and d with an 11 percent return with a 12 percent return with a 13 percent return are correct are correct Retained earnings break point Diff: E An increase in its net income An increase in its dividend payout An increase in the amount of equity in its capital structure An increase in its capital budget All of the statements above are correct Retained earnings break point Answer: b Diff: E Which of the following actions will increase the retained earnings break point? a b c d e An increase in the dividend payout ratio An increase in the debt ratio An increase in the capital budget An increase in flotation costs All of the statements above are correct Miscellaneous cost of capital concepts 18 Answer: a Which of the following will increase a company’s retained earnings break point? a b c d e 17 N Conglomerate Inc consists of divisions of equal size, and Conglomerate is 100 percent equity financed Division A’s cost of equity capital is 9.8 percent, while Division B’s cost of equity capital is 14 percent Conglomerate’s composite WACC is 11.9 percent Assume that all Division A projects have the same risk and that all Division B projects have the same risk However, the projects in Division A are not the same risk as those in Division B Which of the following projects should Conglomerate accept? a b c d e 16 Diff: E Answer: c Diff: E N Which of the following statements is most correct? a Since debt capital is riskier than equity capital, the cost of debt is always greater than the WACC b Because of the risk of bankruptcy, the cost of debt capital is always higher than the cost of equity capital c If a company assigns the same cost of capital to all of its projects regardless of the project’s risk, then it follows that the company will generally reject too many safe projects and accept too many risky projects d Because you are able to avoid flotation costs, the cost of retained earnings is generally lower than the cost of debt e Higher flotation costs tend to reduce the cost of equity capital Chapter - Page Miscellaneous concepts 19 Answer: e Diff: E Which of the following statements is most correct? a Higher flotation costs reduce investor returns, and therefore reduce a company’s WACC b The WACC represents the historical cost of capital and is usually calculated on a before-tax basis c The cost of retained earnings is zero because retained earnings are readily available and not require the payment of flotation costs d All of the statements above are correct e None of the statements above is correct Medium: Capital components 20 Answer: e Diff: M Which of the following statements is most correct? a In the weighted average cost of capital calculation, we must adjust the cost of preferred stock for the tax exclusion of 70 percent of dividend income b We ideally would like to use historical measures of the component costs from prior financings in estimating the appropriate weighted average cost of capital c The cost of a new equity issuance (ke) could possibly be lower than the cost of retained earnings (ks) if the market risk premium and risk-free rate decline by a substantial amount d Statements b and c are correct e None of the statements above is correct Capital components 21 Answer: a Diff: M Which of the following statements is most correct? a The cost of retained earnings is the rate of return stockholders require on a firm’s common stock b The component cost of preferred stock is expressed as kp(1 - T), because preferred stock dividends are treated as fixed charges, similar to the treatment of debt interest c The bond-yield-plus-risk-premium approach to estimating a firm’s cost of common equity involves adding a subjectively determined risk premium to the market risk-free bond rate d The higher the firm’s flotation cost for new common stock, the more likely the firm is to use preferred stock, which has no flotation cost e None of the statements above is correct Chapter - Page Cost of capital estimation 22 Answer: c Diff: M Which of the following statements is correct? a The cost of capital used to evaluate a project should be the cost of the specific type of financing used to fund that project b The cost of debt used to calculate the weighted average cost of capital is based on an average of the cost of debt already issued by the firm and the cost of new debt c One problem with the CAPM approach in estimating the cost of equity capital is that if a firm’s stockholders are, in fact, not well diversified, beta may be a poor measure of the firm’s true investment risk d The bond-yield-plus-risk-premium approach is the most sophisticated and objective method of estimating a firm’s cost of equity capital e The cost of equity capital is generally easier to measure than the cost of debt, which varies daily with interest rates, or the cost of preferred stock since preferred stock is issued infrequently Cost of equity estimation 23 Answer: d Diff: M Which of the following statements is correct? a Although some methods of estimating the cost of equity capital encounter severe difficulties, the CAPM is a simple and reliable model that provides great accuracy and consistency in estimating the cost of equity capital b The DCF model is preferred over other models to estimate the cost of equity because of the ease with which a firm’s growth rate is obtained c The bond-yield-plus-risk-premium approach to estimating the cost of equity is not always accurate but its advantages are that it is a standardized and objective model d Depreciation-generated funds are an additional source of capital and, in fact, represent the largest single source of funds for some firms e None of the statements above is correct CAPM cost of equity estimation 24 Answer: e Diff: M In applying the CAPM to estimate the cost of equity capital, which of the following elements is not subject to dispute or controversy? a b c d e The The The The All expected rate of return on the market, kM stock’s beta coefficient, bi risk-free rate, kRF market risk premium (RPM) of the above are subject to dispute Chapter - Page CAPM and DCF estimation 25 Answer: a Diff: M Which of the following statements is most correct? a Beta measures market risk, but if a firm’s stockholders are not well diversified, beta may not accurately measure stand-alone risk b If the calculated beta underestimates the firm’s true investment risk, then the CAPM method will overestimate ks c The discounted cash flow method of estimating the cost of equity can’t be used unless the growth component, g, is constant during the analysis period d An advantage shared by both the DCF and CAPM methods of estimating the cost of equity capital, is that they yield precise estimates and require little or no judgement e None of the statements above is correct WACC 26 Answer: d Diff: M Which of the following statements is most correct? a The weighted average cost of capital for a given capital budget level is a weighted average of the marginal cost of each relevant capital component that makes up the firm’s target capital structure b The weighted average cost of capital is calculated on a before-tax basis c An increase in the risk-free rate is likely to increase the marginal costs of both debt and equity financing d Statements a and c are correct e All of the statements above are correct WACC 27 Answer: d Diff: M Which of the following statements is correct? a The WACC should include only after-tax component costs Therefore, the required rates of return (or “market rates”) on debt, preferred, and common equity (kd, kp, and ks) must be adjusted to an after-tax basis before they are used in the WACC equation b The cost of retained earnings is generally higher than the cost of new common stock c Preferred stock is riskier to investors than is debt Therefore, if someone told you that the market rates showed kd > kp for a given company, that person must have made a mistake d If a company with a debt ratio of 50 percent were suddenly exempted from all future income taxes, then, all other things held constant, this would cause its WACC to increase e None of the statements above is correct Chapter - Page WACC 28 Answer: e Diff: M Which of the following statements is most correct? a An increase in flotation costs incurred in selling new stock will increase the cost of retained earnings b The WACC should include only after-tax component costs Therefore, the required rates of return (or “market rates”) on debt, preferred, and common equity (kd, kp, and ks) must be adjusted to an after-tax basis before they are used in the WACC equation c An increase in a firm’s corporate tax rate will increase the firm’s cost of debt capital, as long as the yield to maturity on the company’s bonds remains constant or falls d Statements b and c are correct e None of the statements above is correct WACC 29 Answer: e Diff: M Which of the following statements is most correct? a Since stockholders not generally pay corporate taxes, corporations should focus on before-tax cash flows when calculating the weighted average cost of capital (WACC) b All else equal, an increase in flotation costs will increase the cost of retained earnings c When calculating the weighted average cost of capital, firms should rely on historical costs rather than marginal costs of capital d Statements a and b are correct e None of the statements above is correct WACC and capital components 30 Answer: b Diff: M Which of the following statements is correct? a Because we often need to make comparisons among firms that are in different income tax brackets, it is best to calculate the WACC on a before-tax basis b If a firm has been suffering accounting losses and is expected to continue suffering such losses, and therefore its tax rate is zero, it is possible that its after-tax component cost of preferred stock as used to calculate the WACC will be less than its after-tax component cost of debt c Normally, the cost of external equity raised by issuing new common stock is above the cost of retained earnings Moreover, the higher the growth rate is relative to the dividend yield, the more the cost of external equity will exceed the cost of retained earnings d The lower a company’s tax rate, the greater the advantage of using debt in terms of lowering its WACC e None of the statements above is correct Chapter - Page Risk-adjusted cost of capital 31 Answer: c Diff: M Kemp Consolidated has two divisions of equal size: a computer division and a restaurant division Stand-alone restaurant companies typically have a cost of capital of percent, while stand-alone computer companies typically have a 12 percent cost of capital Kemp’s restaurant division has the same risk as a typical restaurant company, and its computer division has the same risk as a typical computer company Consequently, Kemp estimates that its composite corporate cost of capital is 10 percent The company’s consultant has suggested that they use an percent hurdle rate for the restaurant division and a 12 percent hurdle rate for the computer division However, Kemp has chosen to ignore its consultant, and instead, chooses to assign a 10 percent cost of capital to all projects in both divisions Which of the following statements is most correct? a While Kemp’s decision to not risk adjust its cost of capital will lead it to accept more projects in its computer division and fewer projects in its restaurant division, this should not affect the overall value of the company b Kemp’s decision to not risk adjust means that it is effectively subsidizing its restaurant division, which means that its restaurant division is likely to become a larger part of the overall company over time c Kemp’s decision to not risk adjust means that the company will accept too many projects in the computer business and too few projects in the restaurant business This will lead to a reduction in the overall value of the company d Statements a and b are correct e Statements b and c are correct Risk-adjusted cost of capital 32 Answer: b Diff: M The Barabas Company has an equal amount of low-risk projects, average-risk projects, and high-risk projects Barabas estimates that the overall company’s WACC is 12 percent This is also the correct cost of capital for the company’s average-risk projects The company’s CFO argues that, even though the company’s projects have different risks, the cost of capital for each project should be the same because the company obtains its capital from the same sources If the company follows the CFO’s advice, what is likely to happen over time? a The company will take on too many low-risk projects and reject too many high-risk projects b The company will take on too many high-risk projects and reject too many low-risk projects c Things will generally even out over time, and therefore, the risk of the firm should remain constant over time d Statements a and c are correct e Statements b and c are correct Chapter - Page 10 29 WACC Answer: e Diff: M Statement e is the correct answer After-tax cash flows must be considered in order to account for the tax deductibility of interest payments on corporate debt An increase in flotation costs will leave the cost of retained earnings unchanged, but will raise the cost of new equity issues The marginal, not the embedded, cost of capital is the relevant cost of capital 30 WACC and capital components Answer: b Diff: M Because corporations can exclude dividends for tax purposes, preferred stock often has a before-tax market return that is less than the issuing company’s before-tax cost of debt Then, if the issuer’s tax rate is zero, its component cost of preferred would be less than its after-tax cost of debt 31 Risk-adjusted cost of capital Answer: c Diff: M By Kemp not making the risk adjustment, it is true that the company will accept more projects in the computer division, and fewer projects in the restaurant division However, this will make the company riskier overall, raising its cost of equity Investors will discount their cash flows at a higher rate, and the company’s value will fall In addition, some of the computer projects might not exceed the appropriate risk-adjusted hurdle rate, and will actually be negative NPV projects, further destroying value Therefore, statement a is false Because fewer of the restaurant projects will be accepted, the restaurant division will become a smaller part of the overall company Therefore, statement b is false As explained above, statement c is true 32 Risk-adjusted cost of capital Answer: b Diff: M By not risk adjusting the cost of capital, the firm will tend to reject low-risk projects since their returns will be lower than the average cost of capital, and it will take on high-risk projects since their returns will be higher than the average cost of capital 33 Risk-adjusted cost of capital Answer: e Diff: M 34 Risk-adjusted cost of capital Answer: a Diff: M 35 Division WACCs and risk Answer: e Diff: M If the company uses the 10 percent WACC, it will turn down all projects with a return of less than 10 percent but more than percent Thus, these “safer” projects will no longer be taken, and the company will increase the proportion of risky projects it undertakes Therefore, statement a is true If Division A’s projects have lower returns than Division B’s because they have less risk, fewer and fewer projects will be accepted from Division A and more projects will be accepted from Division B Therefore, Division B will grow and Division A will shrink Therefore, statement b is true If the company becomes riskier, then its cost of equity will increase causing WACC to increase Therefore, statement c is true Because all of the statements are true, the correct choice is statement e Chapter - Page 41 36 Divisional risk and project selection Answer: e Diff: M N The correct answer is statement e Statement a is correct; the firms have the same size and capital structure, so the WACC of the merged company is just a simple average of their separate WACCs Statement b is correct; Project X has an IRR of 10.5% and its appropriate cost of capital is 10%, therefore, the project has a positive net present value Statement c is also correct; Project X should be accepted because of the previous argument Project Y should be rejected because it has an 11.5% return and its appropriate cost of capital is 12% Therefore, statement e is the correct choice 37 Beta and project risk Answer: a Diff: M 38 Miscellaneous concepts Answer: a Diff: M 39 Cost of new equity Answer: b Diff: E Answer: d Diff: E ke = 40 $2.00(1.05) + 5% = 9.94% $50(1 - 0.15) Cost of new equity The firm must issue new equity to fund its capital projects, so we need to find the cost of new equity capital, ke: ke = D1/(P0 - F) + g = $2.50/($50 - $3) + 4% = $2.50/$47 + 4% = 5.32% + 4% = 9.32% 41 Cost of retained earnings Answer: d Diff: E Answer: a Diff: E Answer: a Diff: E Use the dividend growth model to calculate ks: D (1  g) $2.20(1.06) ks = + g = + 0.06 P0 $28 = 0.0833 + 0.06 = 0.1433  14.3% 42 WACC WACC = wdkd(1 - T) + wcke kd is given = 9% ke = D1/[P0(1 - F)] + g = $0.8/[$25(1 - 0.1)] + 0.09 = 0.125556 Find ke: Now you can calculate WACC: WACC = (0.3)(0.09)(0.6) + (0.7)(0.125556) = 10.41% 43 WACC WACC = [0.3  0.084 = 10.73% Chapter - Page 42  (1 - 0.4)] + [0.7  ($2.5/($45  (1 - 0.1)) + 0.07)] 44 WACC Answer: b Diff: E Answer: c Diff: E WACC = wdkd(1 - T) + wcks ks = kRF + RPM(b) ks = 5.5% + 5%(1.4) ks = 5.5% + 7% = 12.5% WACC = wdkd(1 - T) + wcks WACC = 0.4(9%)(1 - 0.4) + (0.6)12.5% WACC = 9.66% 45 Divisional risk kYD = 10% + 2% = 12% However, for a low-risk project, Dandy Product subtracts percentage points Therefore, the required rate of return is 10 percent kYD,Low-risk project = 10% + 2% - 2% = 10% 46 Retained earnings break point Answer: e Diff: E Additions to retained earnings will be: $3.0 million  0.4 = $1.2 million The retained earnings breakpoint is $1.2 million/0.2 = $6 million 47 Cost of retained earnings The ks = = = 48 Answer: d Diff: M cost of retained earnings as calculated from the CAPM is kRF + (kM - kRF)b 5% + (6%)1.2 12.2% Cost of external equity Answer: d Diff: M Answer: b Diff: M D0 = $2; D1 = $2(1.07) = $2.14 ke = D1/[P0(1 - F)] + g = $2.14/($42 - $1) + 7% = 12.22% 49 Component cost of debt Time line: kd = ? | | PMT = 20 V B = 686.86 | 20 | 20 | 20 80 | 20 FV = 1,000 • • • Quarters Financial calculator solution: Calculate the nominal YTM of bond: Inputs: N = 80; PV = -686.86; PMT = 20; FV = 1000 Output: I = 3.05% periodic rate Nominal annual rate = 3.05%  = 12.20% Calculate kd after-tax: kd,AT = 12.20(1 - T) = 12.20(1 - 0.4) = 7.32% Chapter - Page 43 50 WACC Answer: e Diff: M N Data given: kRF = 6%; RPM = 5%; b = 1.2; T = 40%; wd = 0.3; wc = 0.7 WACC = wdkd(1 - T) + wcks Step 1: Determine the firm’s costs of debt and equity: Enter the following data as inputs in your calculator: N = 26; PV = -920; PMT = 75; FV = 1000; and then solve for I = kd = 8.2567% ks = kRF + (RPM)b = 6% + (5%)1.2 = 12% Step 2: 51 Given the firm’s component costs of capital, calculate the firm’s WACC: WACC = wdkd(1 - T) + wcks = 0.3(8.2567%)(1 - 0.4) + 0.7(12%) = 1.4862% + 8.4% = 9.8862%  9.89% WACC Answer: a Diff: M Find the dividend, D1 = [(0.5)$40,000]/# of Shares = $20,000/10,000 = $2.00 Since the firm will not have enough retained earnings to fund the equity portion of its capital budget, the firm will have to issue new common stock Find the cost of new common stock: ke = D1/[P0(1 - F)] + g = $2.00/[$25(1 - 0.15)] + 0% = 0.0941 = 9.41% Finally, calculate WACC, using ke = 0.0941, and kd = 0.08, so WACC = (D/A)(1 - Tax rate)kd + (E/A)ke = 0.4(0.08)(1 - 0.4) + 0.6(0.0941) = 0.0757  7.6% 52 WACC Answer: b Diff: M AT cost of debt = 0.07(1 - 0.40) = 0.042 = 4.2% Cost of preferred stock = $4/$42 = 0.0952 = 9.52% Cost of retained earnings = $2/$28 + 0.07 = 0.1414 = 14.14% WACC = 0.40(0.042) + 0.10(0.0952) + 0.50(0.1414) = 0.0970 = 9.70% 53 WACC Answer: a AT cost of debt = 0.08(1 - 0.40) = 0.048 = 4.80% Cost of retained earnings = $2.12/$32 + 0.06 = 0.1263 = 12.63% WACC = 0.75(0.1263) + 0.25(0.048) = 10.67% Chapter - Page 44 Diff: M 54 WACC Cost Cost Cost WACC 55 Answer: c Diff: M of debt = 0.084(1 - 0.30) = 0.0588 = 5.88% of preferred stock = 0.09 = 9% of retained earnings = kRF + (RPM)b = 6.57% + (5%)1.3 = 13.07% = 0.4(0.0588) + 0.10(0.09) + 0.50(0.1307) = 9.79% WACC Answer: b Diff: M Cost of debt = 0.09(1 - 0.35) = 0.0585 = 5.85% Cost of retained earnings = kRF + (RPM)b = 6% + 6%(1.5) = 15% WACC = 0.60(0.0585) + 0.40(0.1500) = 0.0951 = 9.51% 56 WACC Answer: e Diff: M The firm will not be issuing new equity because there are adequate retained earnings available to fund available projects Therefore, WACC should be calculated using ks rather than ke ks = D1/P0 + g = $3.00/$60.00 + 0.07 = 0.12 = 12% WACC = wdkd(1 - T) + wcks = (0.6)(0.08)(1 - 0.4) + (0.4)(0.12) = 0.0768 = 7.68% 57 WACC Answer: d Diff: M AT cost of debt = 7%(1 - 0.3) = 4.9% Retained earnings breakpoint = $500,000/0.5 = $1,000,000 Thus, to finance its optimal capital budget, Longstreet must issue some new equity and flotation costs of 10% will be incurred Cost of new equity = [$5(1.10)/$75(1 - 0.1)] + 10% = 8.15% + 10% = 18.15% WACC = 4.9%(0.3) + 9%(0.2) + 18.15%(0.5) = 12.34% 58 WACC Answer: a Diff: M WACC = [(0.7)(kd)(1 - T)] + [(0.3)(ks)] Use bond information to solve for kd: N = 20; PV = -1273.8564; PMT = 120; FV = 1000; and then solve for kd = 9% To solve for ks, we can use the SML equation, but we need to find beta Using Market and J-Mart return information and a calculator’s regression feature we find b = 1.3585 ks = 0.0635 + (0.1135 - 0.0635)(1.3585) = 0.1314 = 13.14% Plug these values into the WACC equation and solve: WACC = [(0.7)(0.09)(1 - 0.35)] + [(0.3)(0.1314)] = 0.0804 = 8.04% Chapter - Page 45 59 60 WACC Answer: c Diff: M Step 1: Find the cost of debt: Enter the following input data in the calculator: N = 15; PV = -1075; PMT = 80; FV = 1000; and then solve for I = kd = 7.1678% Step 2: Find the cost of equity: ks = kRF + (kM - kRF)b = 5% + 4%(1.1) = 5% + 4.4% = 9.4% Step 3: Calculate the firm’s WACC: WACC = wdkd(1 - T) + wcks = (0.3)(7.1678%)(1 - 0.38) + (0.7)(9.4%) = 1.3332% + 6.58% = 7.9132%  7.91% WACC Answer: d Diff: M wd = 0.4; wc = 0.6 Step 1: Calculate kd: Use the information about the company’s existing bonds to enter the following input data in the calculator: N = 20; PV = -1075; PMT = 90; FV = 1000; and then solve for I = 8.2234% Step 2: Calculate ks: kRF = 5%; kM - kRF = 4%; b = 0.8 ks = kRF + (kM - kRF)b = 5% + (4%)0.8 = 8.2% Step 3: 61 Calculate WACC: WACC = wdkd(1 - T) + wcks = (0.4)(8.2234%)(1 - 0.4) + (0.6)(8.2%) = 6.89% WACC Answer: c Diff: M N WACC = wdkd(1 - T) + wcks Step 1: Calculate the cost of common equity using the CAPM equation: ks = 5% + (6%)1.2 = 12.20% Step 2: Calculate the cost of debt using a financial calculator by entering the following input data: N = 20; PV = -1200; PMT = 120; FV = 1000; and then solve for I = kd = 9.7% Step 3: Calculate the firm’s WACC by substituting the values calculated above in the WACC equation: WACC = (0.25)9.7%(1 - 0.40) + (0.75)12.20% = 10.61% Chapter - Page 46 62 63 WACC and dividend growth rate Solve for ks: WACC = wdkd(1 - T) + wcks 11.5% = 0.45(0.09)(0.70) + 0.55ks ks = 15.75% Solve for g: 15.75% 15.75% g Diff: M Answer: e Diff: M = D1/P0 + g = $5/$45 + g = 4.64% WACC and optimal capital budget Rate of Return 16% 14 12 11 10 10 Project A B C D E F G Answer: c Risk-Adjusted Cost of Capital 13% 11 13 11 9 Projects A, B, and C are profitable because their returns surpass their risk-adjusted costs of capital D is not profitable because its return (11%) is less than its risk-adjusted cost of capital (13%) E is not acceptable for the same reason: Its return (10%) is less than its riskadjusted cost of capital (11%) F is accepted since it is low risk and its return (10%) surpasses the risk-adjusted cost of capital of 9% G is rejected because its return (7%) is less than the risk-adjusted cost of capital (9%) 64 CAPM, beta, and WACC Answer: e Diff: M Data given: wd = 0.3; wc = 0.7; kd = 8%; WACC = 10%; T = 40%; kRF = 5.5%, kM - kRF = 5% 65 Step 1: Determine the firm’s cost of equity using the WACC equation: WACC = wdkd(1 - T) + wcks 10% = (0.3)(8%)(1 - 0.4) + (0.7)ks 8.56% = (0.7)ks ks = 12.2286% Step 2: Calculate the firm’s beta using the CAPM equation: ks = kRF + (kM - kRF)b 12.2286% = 5.5% + (5%)b 6.7286% = 5%b b = 1.3457  1.35 Required rate of return bOld, kOld, bNew, kNew, kNew, firm firm firm firm = = = = assets Answer: c Diff: M 1.25 0.07 + (0.14 – 0.07)1.25 = 15.75% 0.9(1.25) + 0.1(1.1) = 1.235 0.07 + 1.235(0.07) = 15.645% = 0.07 + 1.1(0.07) = 14.7% Chapter - Page 47 66 Beta risk Old assets = 1.0 Old required rate: 18% = 7% + (5%)b beta = 2.2 Answer: b Diff: M New assets = 0.5 Total assets = 1.5 New required rate: 16% = 7% + (5%)b beta = 1.8 New b must not be greater than 1.8, therefore 0.5 (2.2) + (b) = 1.8 1.5 1.5 0.3333(b) = 0.3333 b = 1.0 Therefore, beta of the new division cannot exceed 1.0 67 WACC Answer: b Diff: T Capital structure: 40% D, 10% P, 50% E WACC = 12.30% (given) kd = 11% (given) WACC = 0.4(kd)(1 - T) + 0.1(kp) + 0.5(ke) Because the firm has insufficient retained earnings to fund the equity portion of the firm’s capital budget, use ke in the WACC calculation a Calculate ke: $2(1.08) ke = + 8% = 8.47% + 8% = 16.47% $30(0.85) b Calculate kp: Dp $2 kp = = = 11.11% Pp $20(0.9) c Find T by substituting values for kd, kp, and ke in the WACC equation: 0.1230 = 0.4(0.11)(1 - T) + 0.1(0.1111) + 0.5(0.1647) 0.1230 = 0.044(1 - T) + 0.0111 + 0.08235 0.02954 = 0.044(1 - T) 0.671364 = - T 0.328636 = T Chapter - Page 48 68 WACC and cost of preferred stock Answer: b Diff: T We need to find kp at the point where all projects are accepted In other words, the capital budget = $2,000 + $3,000 + $5,000 + $3,000 = $13,000 The WACC at that point is equal to IRRD = 9.5% 69 Step 1: Find the retained earnings break point to determine whether ks or ke is used in the WACC calculation: $1,000 BPRE = = $2,500 0.4 Since the capital budget > the retained earnings break point, ke is used in the WACC calculation Step 2: Calculate ke: $3.00 ke = + 5% = 12.80% $42.75(0.9) Step 3: Find kp: 9.5% = 0.4(10%)(0.65) + 0.2(kp) + 0.4(12.80%) 9.5% = 2.60% + 0.2(kp) + 5.12% 1.78% = 0.2kp 8.90% = kp Cost of retained earnings ks = 70 71 Diff: E Answer: b Diff: E Answer: d Diff: E $0.90(1.05) + 0.05 = 0.1600 = 16.00% $8.59 Cost of external equity ke = Answer: e $0.90(1.05) + 0.05 = 0.1722 = 17.22% $8.59(1 - 0.10) WACC Since the firm can fund the equity portion of its capital budget with retained earnings, use ks in WACC WACC = = = = 72 Cost of external equity ke = 73 wdkd(1 - T) + wcks 0.3(0.12)(1 - 0.4) + 0.7(0.16) 0.0216 + 0.112 0.1336 = 13.36% WACC Answer: a Diff: E Answer: b Diff: E $2.00(1.05) + 0.05 = 17% $21.88(1 - 0.2) WACC = 0.4(0.14)(1 - 0.4) + 0.6(0.17) = 0.1356 = 13.56%  13.6% Chapter - Page 49 74 Cost of debt Answer: e Time line: k d/2 = ? | | PMT = 60 V B = 1,000 | 60 | 60 | 60 Diff: E 40 6-month | Periods 60 FV = 1,000 • • • Since the bond sells at par of $1,000, its YTM and coupon rate (12 percent) are equal Thus, the before-tax cost of debt to Rollins is 12.0 percent The after-tax cost of debt equals: kd,After-tax = 12.0%(1 - 0.40) = 7.2% Financial calculator solution: Inputs: N = 40; PV = -1000; PMT = 60; FV = 1000; Output: I = 6.0% = kd/2 kd = 6.0%  = 12% kd(1 - T) = 12.0%(0.6) = 7.2% 75 Cost of preferred stock Cost of preferred stock: 76 Answer: d Diff: E Answer: c Diff: E Answer: c Diff: E Answer: c Diff: E kp = $12/$100(0.95) = 12.6% Cost of equity: CAPM Cost of retained earnings (CAPM approach): ks = 10% + (5%)1.2 = 16.0% 77 Cost of equity: DCF Cost of retained earnings (DCF approach): $2.00(1.08) ks = + 8% = 16.0% $27 78 Cost of equity: risk premium Cost of retained earnings (bond yield-plus-risk-premium approach): ks = 12.0% + 4.0% = 16.0% 79 WACC Calculate ke: Answer: b ke = Diff: E $2.00(1.08) + 8% = 16.89% $27(1  0.1) WACC = wdkd(1 - T) + wpkp + wcke = 0.2(12.0%)(0.6) + 0.2(12.6%) + 0.6(16.89%) = 14.09  14.1% 80 Stock price constant growth ks = 10% + (4%)1.5 = 16% $3.00(1.10) P0 = = $55.00 0.16 - 0.10 Chapter - Page 50 Answer: d Diff: E 81 Cost of external equity Answer: b Diff: E Answer: e Diff: M Answer: d Diff: E Answer: c Diff: E Answer: d Diff: E Answer: b Diff: E Answer: d Diff: E Cost of new common equity: $3.30 ke = + 0.10 = 16.32% $55.00(0.95) 82 Cost of retained earnings EBIT Interest EBT Taxes (40%) Net income $1,000,000 400,000 $ 600,000 240,000 $ 360,000 EPS1 = $360,000/100,000 = $3.60 D1 = $3.60(0.5) = $1.80 ks = ($1.80/$40.00) + 0.125 = 17.0% 83 Cost of external equity Cost of new common equity: $1.80 ke = + 0.125 = 17.5% ($40)(0.90) 84 Cost of retained earnings ks = 85 $2.00(1.10) + 0.10 = 15.5% $40.00 Cost of external equity Cost of new common equity: $2.20 ke = + 0.10 = 0.1647  16.5% $34.00 86 Cost of preferred stock kp = 87 $10 = 12.5% $80 WACC Since the firm has sufficient retained earnings to fund the equity portion of its capital budget, use ks in WACC equation WACC = wdkd(1 - T) + wpkp + wcks = 0.4(6%) + 0.1(12.5%) + 0.5(15.5%) = 11.4% Chapter - Page 51 88 Cost of debt Answer: b Diff: E N To determine the cost of debt, use market values and the bond information given Enter the following data as inputs into your calculator as follows: N = 15; PV = -1150; PMT = 120; FV = 1000; and then solve for I = kd = 10.03% The after-tax cost of debt is 10.03%(1 - Tax rate) = 10.03%(0.6) = 6.02%  6% 89 Cost of common equity: CAPM Using the CAPM equation: Answer: e Diff: E N ks = kRF + (kM – kRF)b ks = 5% + (5%)1.4 ks = 12% Since equity costs are not tax-deductible, this is also the after-tax cost of equity 90 WACC Answer: c Diff: E N Use the target debt and equity ratios and the WACC equation as follows: WACC = wdkd(1 – T) + wcks = (0.40)(0.06) + (0.60)(0.12) = 0.096, or 9.6% 91 Cost of debt Answer: b Diff: M N The after-tax cost of debt is found by using the firm’s bond information to solve for the YTM on bonds outstanding Then, the YTM needs to be converted to an after-tax yield N = 20; PV = -945; PMT = 85; FV = 1000; and then solve for kd = I = 9.11% AT kd = 9.11%(1 - 0.4) = 5.46% 92 Cost of preferred stock Answer: d Diff: E N The after-tax cost of preferred stock can be derived by simply dividing the preferred dividend paid by the price of preferred stock kp = Dp Pp kp = $2/$25 kp = 8.0% 93 Cost of common equity: CAPM Answer: d Diff: E N The cost of common equity can be found in a variety of ways In this case, we have been given information about the market risk premium and beta Therefore, we can use the CAPM to value the cost of common equity ks = kRF + (kM – kRF)b ks = 6% + (5%)1.2 ks = 12.0% Chapter - Page 52 94 WACC Answer: c Diff: E N The WACC is merely a weighted-average of the capital component costs WACC = wdkd(1 – T) + wpkp + wcks WACC = 0.4(9.11%)(1 - 0.4) + 0.2(8%)+ 0.4(12%) WACC = 8.59% 95 After-tax cost of debt Answer: c Diff: E N To find the cost of debt, enter the following data into your calculator: N = 25; PV = -1252; PMT = 120; FV = 1000; and then solve for I = 9.3594%, which is the before-tax cost of debt To calculate the after-tax cost of debt, multiply by (1 – T) as follows: (1 - 0.40)  9.3594% = 5.6156%  5.62% 96 Cost of common equity: CAPM Answer: c Diff: E N Answer: b Diff: E N ks = 5% + (6%)1.6 = 14.6% 97 WACC WACC = (0.40)(5.6156%) + (0.60)(14.6%) = 11.0062%  11.0% Chapter - Page 53 WEB APPENDIX 9A SOLUTIONS 9A-1 Risk and divisional costs of capital Answer: a Diff: E N The correct answer is statement a The composite WACC will be the average of the two divisional WACCs Since there is no debt, the WACC = ks There is no cost of equity given, but it can be calculated from the beta, the risk-free rate, and the market risk premium using CAPM The beta of the entire company is the weighted average of the two divisions’ betas (0.5  0.8 + 0.5  1.2 = 1.0) The firm’s cost of equity will be equal to 11% (ks = kRF + (RPM)b = 6% + 5%  1.0 = 11%) Therefore, the WACC is 11%, and statement a is correct Division B has a higher beta, therefore its cost of capital will be higher than A’s Therefore, statement b is false If both divisions were assigned the same hurdle rate, this rate would reflect the required return on projects with a beta of 1.0 Since Division A’s average projects have a beta of 0.8, they would tend to have a lower return Therefore, fewer of them would meet the hurdle rate of 11%, and the company would choose too few of them Conversely, the company would choose too many projects in Division B Therefore, statement c is false 9A-2 Risk and project betas Answer: d Diff: M 9A-3 SML and capital budgeting Answer: a Diff: M 9A-4 Project cost of capital Answer: c Diff: E ˆ Calculate the required return, ks, and compare to the expected return, k s ˆ k s = 7% ks = kRF + (kM - kRF)b = 7% + (10% - 7%)0.5 = 8.5% ˆ ; 8.5% > 7.0%; reject the investment ks > k s 9A-5 Project cost of capital Answer: e Diff: M Calculate the beta of the firm, and use to calculate project beta: ks = 0.16 = 0.10 + (0.05)bFirm bFirm = 1.2 bProject = (bFirm)1.5 (bProject is 50% greater than current bFirm) bProject = (1.2)1.5 = 1.8 Calculate required return on project, kProject, and compare to expected return: Project: kProject = 0.10 + (0.05)1.8 = 0.19 = 19% Expected return = 0.18 = 18% Since the required return is one percentage point greater than the expected return, the firm should not accept the new project Chapter - Page 54 WEB APPENDIX 9B SOLUTIONS 9B-1 Pure play method Answer: b 9B-2 Corporate WACC for firm with divisions For Division A: kA = kRF + (kM – kRF)bA kA = 5% + (6%)0.8 kA = 9.8% For Division B: kB = kRF + (kM – kRF)bB kB = 5% + (6%)1.5 kB = 14% Answer: c Diff: M Diff: E N WACC = wAkA + wBkB = (0.50)(0.098) + (0.50)(0.14) = 0.119, or 11.9% 9B-3 Pure play method Answer: b Diff: M Calculate the required return, ks, and use to calculate the WACC: ks = 10% + 1.38(5%) = 16.9% WACC = 0.5(12.0%)(0.6) + 0.5(16.9%) = 12.05% ˆ Compare expected project return, k Project , to WACC: ˆ But k = 13.0% Project ˆ Accept the project since k Project  WACC : 13.0% > 12.05% Chapter - Page 55 [...]... firm’s beta, then the required return on the asset is greater than the required return on the firm c If the beta of the asset is greater than the firm’s beta prior to the addition of that asset, then the firm’s beta after the purchase of the asset will be smaller than the original firm’s beta d If the beta of an asset is larger than the firm’s beta prior to the addition of that asset, then the required... return of 10.75 percent and a beta of 1.25 The investment, if undertaken, will double the firm’s total assets If kRF is 7 percent and the market return is 10 percent, should the firm undertake the investment? (Choose the best answer.) a Yes; the expected return of the asset (7%) exceeds the required return (6.5%) b Yes; the beta of the asset will reduce the risk of the firm c No; the expected return of the. .. less than the required return (8.5%) d No; the risk of the asset (beta) will increase the firm’s beta e No; the expected return of the asset is less than the firm’s required return, which is 10.75% Chapter 9 - Page 34 Medium: Project cost of capital 9A-5 Answer: e Diff: M Assume you are the director of capital budgeting for an all-equity firm The firm’s current cost of equity is 16 percent; the risk-free... Diff: M If the firm is being operated so as to maximize shareholder wealth, and if our basic assumptions concerning the relationship between risk and return are true, then which of the following should be true? a If the beta of the asset is larger than the firm’s beta, then the required return on the asset is less than the required return on the firm b If the beta of the asset is smaller than the firm’s... 10 percent If the company raises capital through a new equity issuance, the flotation costs are 10 percent The cost of preferred stock is 9 percent and the cost of debt is 7 percent (Assume debt and preferred stock have no flotation costs.) What is the weighted average cost of capital at the firm’s optimal capital budget? a b c d e 12.58% 18.15% 12.18% 12.34% 11.94% Chapter 9 - Page 20 WACC 58 Answer:... face value of $1,000, and a current price of $1,252 The company uses the CAPM to calculate the cost of common stock Currently, the risk-free rate is 5 percent and the market risk premium, (kM - kRF), equals 6 percent The company’s common stock has a beta of 1.6 The company’s tax rate is 40 percent After-tax cost of debt 95 Diff: E N Answer: c Diff: E N What is the company’s after-tax cost of debt? a... coupon of 7.5 percent The bonds have a face value of $1,000 and sell in the market today for $920 The risk-free rate is 6 percent The market risk premium is 5 percent The stock’s beta is 1.2 The company’s tax rate is 40 percent The company’s target capital structure consists of 70 percent equity and 30 percent debt The company uses the CAPM to estimate the cost of equity and does not include flotation costs... company estimates that if the divisions operated as independent companies Division A would have a cost of capital of 8 percent, while Division B would have a cost of capital of 12 percent Since the two divisions are the same size, Pearson’s composite weighted average cost of capital (WACC) is 10 percent In the past, Pearson has assigned separate hurdle rates to each division based on their relative risk... must, therefore, issue new common stock The new stock has an estimated flotation cost of $3 per share What is the company’s cost of equity capital? a 10.14% b 9.21% c 9.45% d 9.32% e 9.00% Chapter 9 - Page 13 Cost of retained earnings 41 Answer: d Diff: E Allison Engines Corporation has established a target capital structure of 40 percent debt and 60 percent common equity The current market price of the. .. required return on the firm will be greater after the purchase of that asset than prior to its purchase e None of the statements above is correct Chapter 9 - Page 33 SML and capital budgeting 9A-3 Answer: a Diff: M Using the Security Market Line concept in capital budgeting, which of the following is correct? a If the expected rate of return on a given capital project lies above the SML, the project should