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# Calculus: Practice Problems MAC 2233

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This 214 page Study Guide was uploaded by Giancarlos on Wednesday February 10, 2016. The Study Guide belongs to MAC 2233 at Florida International University taught by Goldstein in Summer 2015. Since its upload, it has received 22 views. For similar materials see Calculus for Business in Math at Florida International University.

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Problem 4-16 Return on Equity Central City Construction (CCC) needs $2 million of assets to get started, and it expects to have a basic earning power ratio of 30%. CCC will own no securities, so all of its income will be operating income. If it chooses to, CCC can finance up to 60% of its assets with debt, which will have an 7% interest rate. Assuming a 35% tax rate on all taxable income, what is the difference between CCC's expected ROE if it finances with 60% debt versus its expected ROE if it finances entirely with common stock? Round your answer to two decimal places. 22.43% TA = $2,000,000; Int. rate = 7%; T = 35%; BEP = 0.3 = EBIT/Total assets, so EBIT = 0.3($2,000,000) = $600,000; D/A = 0.6 = 60%, so Equity = $2,000,000. No debt Debt = 60% EBIT $600,000 $600,000 Interest 0 84,000 * EBT $600,000 $516,000 Tax (35%) 210,000 180,600 NI 390,000 335,400 Difference in ROE = 41.93% - 19.5% = 22.43%. *Debt = 0.6 x 2,000,000 = $1,200,000. At an 7% interest rate, INT = $1,200,000 x 0.07 = $84,000. Problem 3-14 Income Statement Hermann Industries is forecasting the following income statement: Sales $7,000,000 Operating costs excluding depreciation & amortization 3,850,000 EBITDA $3,150,000 Depreciation and amortization 420,000 EBIT $2,730,000 Interest 630,000 EBT $2,100,000 Taxes (40%) 840,000 Net income $1,260,000 The CEO would like to see higher sales and a forecasted net income of $2,016,000. Assume that operating costs (excluding depreciation and amortization) are 55% of sales and that depreciation and amortization and interest expenses will increase by 6%. The tax rate, which is 40%, will remain the same. What level of sales would generate $2,016,000 in net income? If necessary, round your answer to the nearest dollar at the end of the calculations. *$9,940,000 Sales $9,940,000 S - 0.55 Sales - Deprec. = EBIT Operating costs (excl. Deprec.) 5,467,000 $9,940,000 x 0.55 Depreciation 445,200 $420,000 x 1.06 EBIT 4,027,800 $3,360,000 + $667,800 or EBT + Interest Interest 667,800 $630,000 x 1.06 EBT 3,360,000 NI / (1 - T ) = $2,016,000 / (1-0.4) Taxes (40%) 1,344,000 $3,360,000 x 0.40 Net income 2,016,000 Chapter 10 The Cost of Capital Problem 10-1 After-tax Cost of Debt The Heuser Company's currently outstanding bonds have a 10% coupon and a 12% yield to maturity. Heuser believes it could issue new bonds at par that would provide a similar yield to maturity. If its marginal tax rate is 35%, what is Heuser's after-tax cost of debt? Round your answer to two decimal places. 7.80% Rd(1-T) = 0.12 (1-0.35) = 7.8% Problem 10-2 Cost of Preferred Stock Tunney Industries can issue perpetual preferred stock at a price of $59.00 a share. The stock would pay a constant annual dividend of $5.50 a share. What is the company's cost of preferred stock, rp? Round your answer to two decimal places. 9.32% Pp = $59.00; Dp = $5.50; rp = ? rp = Dp/Pp = $5.50/$59.00 = 9.32% Problem 10-3 Cost of Common Equity Percy Motors has a target capital structure of 30% debt and 70% common equity, with no preferred stock. The yield to maturity on the company's outstanding bonds is 12%, and its tax rate is 40%. Percy's CFO estimates that the company's WACC is 13.50%. What is Percy's cost of common equity? Round your answer to two decimal places. 16.20% 30% Debt; 70% Common equity; rd = 12%; T = 40%; WACC = 13.50%; rs = ? WACC = (wd)(rd)(1 - T) + (wc)(rs) 0.1350 = (0.30)(0.12)(1 - 0.4) + (0.70)rs 0.1350 = 0.0216 + (0.70)rs 0.1134 = (0.70)rs rs = 16.20%. Problem 10-4 Cost of Equity with and without Flotation Javits & Sons' common stock currently trades at $24.00 a share. It is expected to pay an annual dividend of $2.00 a share at the end of the year (D1 = $2.00), and the constant growth rate is 4% a year. a. What is the company's cost of common equity if all of its equity comes from retained earnings? Round your answer to two decimal places. 12.33% P0 = $24.00; D1 = $2.00; g = 4.00%; rs = ? rs = D1/P0 + g = $2.00/$24.00 + 0.04 = 12.33%. b. If the company were to issue new stock, it would incur a 9% flotation cost. What would the cost of equity from new stock be? Round your answer to two decimal places. 13.16% b.F = 9%; re = ? re = D1/(P0(1 - F)) + g = $2.00/($24.00(1 - 0.09)) + 0.04 = 13.16% Problem 10-5 Project Selection Midwest Water Works estimates that its WACC is 10.55%. The company is considering the following capital budgeting projects. Assume that each of these projects is just as risky as the firm's existing assets and that the firm may accept all the projects or only some of them. Which set of projects should be accepted? Project Size Rate of Return A $1 million 12.0% accept B 2 million 11.5 accept C 2 million 11.2 accept D 2 million 11.0 accept E 1 million 10.7 accept F 1 million 10.3 don’t accept G 1 million 10.2 don’t accept Projects A, B, C, D, and E would be accepted since each project's return is greater than the firm's WACC. Problem 10-6 Cost of Common Equity The future earnings, dividends, and common stock price of Carpetto Technologies Inc. are expected to grow 7% per year. Carpetto's common stock currently sells for $27.75 per share; its last dividend was $2.00; and it will pay a $2.14 dividend at the end of the current year. a.Using the DCF approach, what is its cost of common equity? Round your answer to two decimal places. 14.71% rs = D1/P0 + g = $2.14/$27.75 + 7.00% = 7.71% + 7.00% = 14.71%. b.If the firm's beta is 1.10, the risk-free rate is 5%, and the average return on the market is 12%, what will be the firm's cost of common equity using the CAPM approach? Round your answer to two decimal places. 12.70% rs = rRF + (rM - rRF)b = 5% + (12% - 5%) 1.10 = 5% + (7%) 1.10 = 5% + 7.70% = 12.70%. c.If the firm's bonds earn a return of 8%, based on the bond-yield-plus-risk-premium approach, what will be rs? Use the midpoint of the risk premium range discussed in Section 10-5 in your calculations. Round your answer to two decimal places. 12.00% rs = Bond rate + Risk premium = 8% + 4% = 12.00%. d.If you have equal confidence in the inputs used for the three approaches, what is your estimate of Carpetto's cost of common equity? Round your answer to two decimal places. 13.14% Since you have equal confidence in the inputs used for the three approaches, an average of the three methodologies probably would be warranted. rs = (14.71% + 12.70% + 12.00%)/3 = 13.14%. Problem 10-7 Cost of Common Equity with and without Flotation The Evanec Company's next expected dividend, D1, is $2.74; its growth rate is 5%; and its common stock now sells for $34. New stock (external equity) can be sold to net $30.60 per share. a. What is Evanec's cost of retained earnings, rs? Round your answer to two decimal places. rs = 13.06% a.rs = D1/P0 + g = $2.74/$34.00 + 0.05 = 13.06% b. What is Evanec's percentage flotation cost, F? Round your answer to two decimal places. F = 10.00 % b.F = ($34.00 - $30.60)/$34.00 = $3.40/$34.00 = 10.00% c. What is Evanec's cost of new common stock, re? Round your answer to two decimal places. re = 13.95% c.re = D1/(P0(1 - F)) + g = $2.74/$30.60 + 5.00% = $8.95% + 5.00% = 13.95% Problem 10-8 Cost of Common Equity and WACC Patton Paints Corporation has a target capital structure of 35% debt and 65% common equity, with no preferred stock. Its before-tax cost of debt is 10% and its marginal tax rate is 40%. The current stock price is P0 = $33.50. The last dividend was D0 = $3.50, and it is expected to grow at a 5% constant rate. What is its cost of common equity and its WACC? Round your answers to two decimal places. Debt = 35%, Common equity = 65%. a. rs = 15.97% P0 = $33.50, D0 = $3.50, D1 = $3.50(1.05) = $3.68, g = 5%. rs = D1/P0 + g = $3.68/$33.50 + 5.00% = 15.97%. b. WACC = 12.48% WACC = (0.35)(0.10)(1 - 0.4) + (0.65)(0.1597) = 0.021000 + 0.103806 = 12.48%. Problem 10-9 WACC The Patrick Company's year-end balance sheet is shown below. Its cost of common equity is 14%, its before-tax cost of debt is 8%, and its marginal tax rate is 40%. Assume that the firm's long-term debt sells at par value. The firm’s total debt, which is the sum of the company’s short-term debt and long- term debt, equals $1,097. The firm has 576 shares of common stock outstanding that sell for $4.00 per share. Calculate Patrick's WACC using market value weights. Round your answer to two decimal places. Assets Liabilities And Equity Cash $ 120 Accounts payable and accruals $ 10 Accounts receivable 240 Short-term debt 47 Inventories 360 Long-term debt $1,050 Plant and equipment, net 2,160 Common equity 1,773 Total assets $2,880 Total liabilities and equity $2,880 11.03% BV total debt = Short-term debt + Long-term debt = MV total debt = $1,097; P0 = $4.00; Shares outstanding = 576; T = 40% MV Equity = $4.00 x 576 shares = $2,304. Capital Sources Market Value Market Value Weight Long-term debt $ 1,097 $1,097/$3,401 = 32.26% Common Equity 2,304 $2,304/$3,401 = 67.74% Total capital $3,401 100.00% WACC = (wd)(rd)(1 - T) + (wc)(rs) = (0.3226)(0.08)(0.6) + (0.6774)(0.14) = 0.01548 + 0.09484 = 11.03% Problem 10-10 WACC Klose Outfitters Inc. believes that its optimal capital structure consists of 40% common equity and 60% debt, and its tax rate is 40%. Klose must raise additional capital to fund its upcoming expansion. The firm will have $1 million of retained earnings with a cost of rs = 14%. New common stock in an amount up to $7 million would have a cost of re = 16%. Furthermore, Klose can raise up to $3 million of debt at an interest rate of rd = 10%, and an additional $3 million of debt at rd = 13%. The CFO estimates that a proposed expansion would require an investment of $3.0 million. What is the WACC for the last dollar raised to complete the expansion? Round your answer to two decimal places. 10.0% If the investment requires $3.0 million, that means that it requires $1.20 million (40%) of common equity and $1.8 million (60%) of debt. In this scenario, the firm would exhaust its $1 million of retained earnings and be forced to raise new stock at a cost of 16%. Needing $1.8 million in debt, the firm could get by raising debt at only 10%. Therefore, its weighted average cost of capital is: WACC = 0.60(10%)(1 - 0.4) + 0.40(16%) = 10.00%. Problem 10-11 WACC and Percentage of Debt Financing Hook Industries' capital structure consists solely of debt and common equity. It can issue debt at rd = 9%, and its common stock currently pays a $3.75 dividend per share (D0 = $3.75). The stock's price is currently $25.75, its dividend is expected to grow at a constant rate of 7% per year, its tax rate is 40%, and its WACC is 15.85%. What percentage of the company's capital structure consists of debt? Round your answer to two decimal places. 39.18% rs = D1/P0 + g = ($3.75)(1.07)/$25.75 + 7% = 15.58% + 7% = 22.58% WACC = wd(rd)(1 - T) + wc(rs); wc = 1 - wd. 15.85% = (wd)(9%)(1 - 0.40) + (1 - wd)(22.58%) 0.1585 = 0.0540wd + 0.2258 - 0.2258wd -0.0673 = -0.1718wd wd = 0.3918 = 39.18% Problem 10-12 WACC Midwest Electric Company (MEC) uses only debt and common equity. It can borrow unlimited amounts at an interest rate of rd = 10% as long as it finances at its target capital structure, which calls for 50% debt and 50% common equity. Its last dividend (D0) was $2.25, its expected constant growth rate is 4%, and its common stock sells for $25. MEC's tax rate is 40%. Two projects are available: Project A has a rate of return of 13%, while Project B's return is 8%. These two projects are equally risky and about as risky as the firm's existing assets. a.What is its cost of common equity? Round your answer to two decimal places. 13.36% rd = 10%, rd(1 - T) = 10%(0.6) = 6.0%. wd = 50%; D0 = $2.25; g = 4%; P0 = $25; T = 40%. Project A: Rate of return = 13%. Project B: Rate of return = 8%. rs = $2.25(1.04)/$25 + 4% = 13.36%. b.What is the WACC? Round your answer to two decimal places. 9.68% WACC = 0.50(6.0%) + 0.50(13.36%) = 9.68% c.Which projects should Midwest accept? Project A Since the firm's WACC is 9.68% and each of the projects is equally risky and as risky as the firm's other assets, MEC should accept Project A. Its rate of return is greater than the firm's WACC. Project B should not be accepted, since its rate of return is less than MEC's WACC. Problem 10-13 Cost of Common Equity with Flotation Ballack Co.’s common stock currently sells for $36.50 per share. The growth rate is a constant 12.8%, and the company has an expected dividend yield of 3%. The expected long-run dividend payout ratio is 20%, and the expected return on equity (ROE) is 16%. New stock can be sold to the public at the current price, but a flotation cost of 5% would be incurred. What would be the cost of new equity? Round your answer to two decimal places. 15.96% If the firm's dividend yield is 3% and its stock price is $36.50, the next expected annual dividend can be calculated. Dividend yield = D1/P0 3% = D1/$36.50 D1 = $1.0950 Next, the firm's cost of new common stock can be determined from the DCF approach for the cost of equity. re = D1/[P0(1 - F)] + g = $1.0950/[$36.50(1 - 0.05)] + 0.128 = 15.96% Problem 10-14 Cost of Preferred Stock Including Flotation Trivoli Industries plans to issue perpetual preferred stock with an $11.00 dividend. The stock is currently selling for $90.00; but flotation costs will be 7% of the market price, so the net price will be $83.70 per share. What is the cost of the preferred stock, including flotation? Round your answer to two decimal places. 13.14% rp = $11/$83.70 = 13.14%. Problem 10-15 WACC and Cost of Common Equity Kahn Inc. has a target capital structure of 50% common equity and 50% debt to fund its $10 billion in operating assets. Furthermore, Kahn Inc. has a WACC of 15%, a before-tax cost of debt of 8%, and a tax rate of 40%. The company's retained earnings are adequate to provide the common equity portion of its capital budget. Its expected dividend next year (D1) is $4 and the current stock price is $30. a. What is the company's expected growth rate? Round your answer to two decimal places at the end of the calculations. 11.87% Examining the DCF approach to the cost of retained earnings, the expected growth rate can be determined from the cost of common equity, price, and expected dividend. However, first, this Problem requires that the formula for WACC be used to determine the cost of common equity. WACC = wd(rd)(1 - T) + wc(rs) 15.0% = 0.50(8%)(1 - 0.4) + 0.50(rs) 12.60% = 0.50rs rs = 0.2520 or 25.20% From the cost of common equity, the expected growth rate can now be determined. rs = D1/P0 + g 0.2520 = $4/$30 + g g = 0.1187 or 11.87% b. If the firm's net income is expected to be $1.6 billion, what portion of its net income is the firm expected to pay out as dividends? (Hint: Refer to Equation below.) Growth rate = (1 - Payout ratio)ROE Round your answer to two decimal places at the end of the calculations. 62.92% From the formula for the long-run growth rate: g = (1 - Div. payout ratio) × ROE = (1 - Div. payout ratio) × (NI/Equity) 0.118667 = (1 - Div. payout ratio) × ($1,600 million/$5,000 million) 0.118667 = (1 - Div. payout ratio) × 0.320000 0.370833 = (1 - Div. payout ratio) Div. payout ratio = 0.6292 or 62.92% Problem 10-16 Cost of Common Equity The Bouchard Company's EPS was $6.50 in 2014, up from $4.42 in 2009. The company pays out 50% of its earnings as dividends, and its common stock sells for $32. a. Calculate the past growth rate in earnings. (Hint: This is a 5-year growth period.) Round your answer to two decimal places. 8.00% With a financial calculator, input N = 5, PV = -4.42, PMT = 0, FV = 6.5, and then solve for I/YR = g = 8.02% ≈ 8.00%. b. The last dividend was D0 = 0.50($6.50) = $3.25. Calculate the next expected dividend, D1, assuming that the past growth rate continues. Round your answer to the nearest cent. $3.51 D1 = D0(1 + g) = $3.25(1.08) = $3.51 c. What is Bouchard's cost of retained earnings, rs? Round your answer to two decimal places. 18.99% rs = D1/P0 + g = $3.51/$32.00 + 8.02% = 18.99%. Problem 10-17 Calculation of g and EPS Sidman Products' common stock currently sells for $74 a share. The firm is expected to earn $7.40 per share this year and to pay a year-end dividend of $4.00, and it finances only with common equity. a.If investors require a 10% return, what is the expected growth rate? Round your answer to two decimal places. 4.59% rs = D1 / P0 + g 0.1 = $4.00 / $74.00 + g 0.1 = 0.05 + g g = 4.59%. b.If Sidman reinvests retained earnings in projects whose average return is equal to the stock's expected rate of return, what will be next year's EPS? (Hint: g = (1 - Payout rate)(ROE).) Round your answer to the nearest cent. $7.74 per share. Current EPS $7.400 Less: Dividends per share 4.000 Retained earnings per share $3.400 Rate of return x 0.100 Increase in EPS $0.340 Plus: Current EPS 7.400 Next year's EPS $7.740 Alternatively: EPS1 = EPS0(1 + g) = $7.40(1.05) = $7.740. Problem 10-18 WACC and optimal capital budget Adams Corporation is considering four average-risk projects with the following costs and rates of return: Project Cost Expected Rate of Return 1 $2,000 16.00% 2 3,000 15.00 3 5,000 13.75 4 2,000 12.50 The company estimates that it can issue debt at a rate of rd = 10%, and its tax rate is 30%. It can issue preferred stock that pays a constant dividend of $4 per year at $59 per share. Also, its common stock currently sells for $40 per share; the next expected dividend, D1, is $5.00; and the dividend is expected to grow at a constant rate of 5% per year. The target capital structure consists of 75% common stock, 15% debt, and 10% preferred stock. a.What is the cost of each of the capital components? Round your answers to two decimal places. Cost of debt 7.00% rd(1 - T) = 0.1(1 - 0.3) = 7.00%. Cost of preferred stock 6.78% rp = $4/$59 = 6.78%. Cost of retained earnings 17.50% rs = $5/$40 + 5% = 17.50%. b.What is Adams' WACC? Round your answer to two decimal places. 14.85% WACC Component Weight x After-Tax Cost = Weighted Cost Debt 0.15 7.00% 1.05% Preferred stock 0.10 6.78 0.68 Common stock 0.75 17.50 13.13 WACC = 14.85% c.Only projects with expected returns that exceed WACC will be accepted. Which projects should Adams accept? Project 1 accept Project 2 accept Project 3 reject Project 4 reject Projects 1 and 2 will be accepted since their rates of return exceed the WACC Problem 10-19 Adjusting cost of capital for risk Ziege Systems is considering the following independent projects for the coming year. Project Required Investment Rate of Return Risk A $4 million 13% High B 5 million 10.5 High C 3 million 8.5 Low D 2 million 8.25 Average E 6 million 11.5 High F 5 million 11.5 Average G 6 million 6.25 Low H 3 million 10 Low Ziege's WACC is 9.00%, but it adjusts for risk by adding 2% to the WACC for high-risk projects and subtracting 2% for low-risk projects. a.Which projects should Ziege accept if it faces no capital constraints? Project A -Select-accept Project B -Select-reject Project C -Select-accept Project D -Select-reject Project E -Select-accept Project F -Select-accept Project G -Select-reject Project H -Select-accept If all project decisions are independent, the firm should accept all projects whose returns exceed their risk-adjusted costs of capital. The appropriate costs of capital are summarized below: Project Required Investment Rate of Return Cost of Capital A $4 million 13 % 11 % B 5 million 10.5 11 C 3 million 8.5 7 D 2 million 8.25 9 E 6 million 11.5 11 F 5 million 11.5 9 G 6 million 6.25 7 H 3 million 10 7 Therefore, Ziege should accept projects A, C, E, F, H. b.If Ziege can only invest a total of $13 million, which projects should it accept? Project A -Select-accept Project B -Select-reject Project C -Select-reject Project D -Select-reject Project E -Select-reject Project F -Select-accept Project G -Select-reject Project H -Select-accept If Ziege can only invest a total of $13 million, what would be the dollar size of its capital budget? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. $12 million With only $13 million to invest in its capital budget, Ziege must choose the best combination of Projects A, C, E, F, H. Collectively, the projects would account for an investment of $21 million, so naturally not all these projects may be accepted. Looking at the excess return created by the projects (rate of return minus the cost of capital), we see that the excess returns for Projects A, C, E, F, and H are 2%, 1.5%, 0.5%, 2.5%, and 3%. The firm should accept the projects which provide the greatest excess returns. By that rationale, the first project to be eliminated from consideration is Project E. This brings the total investment required down to $15 million, therefore one more project must be eliminated. The next lowest excess return is Project C. Therefore, Ziege's optimal capital budget consists of Projects A, F, and H, and it amounts to $12 million. c.Suppose Ziege can raise additional funds beyond the $13 million, but each new increment (or partial increment) of $5 million of new capital will cause the WACC to increase by 1%. Assuming that Ziege uses the same method of risk adjustment, which projects should it now accept? Project A -Select-accept Project B -Select-reject Project C -Select-accept Project D -Select-reject Project E -Select-reject Project F -Select-accept Project G -Select-reject Project H -Select-accept What would be the dollar size of its capital budget? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. $15 million Since Projects A, F, and H are already accepted projects, we must adjust the costs of capital for the other two value producing projects (C and E). Project Required Investment Rate of Return Cost of Capital C 3 million 8.5 % 7%+1%=8% E 6 million 11.5 11%+1%=12% If new capital must be issued, Project E ceases to be an acceptable project. On the other hand, Project C's expected rate of return still exceeds the risk-adjusted cost of capital even after raising additional capital. Hence, Ziege's new capital budget should consist of Projects A, C, F, and H and requires $15 million of capital, so an additional $2 million must be raised above the initial $13 million constraint. Problem 10-20 WACC The following table gives Foust Company's earnings per share for the last 10 years. The common stock, 6.1 million shares outstanding, is now (1/1/15) selling for $56 per share. The expected dividend at the end of the current year (12/31/15) is 65% of the 2014 EPS. Because investors expect past trends to continue, g may be based on the historical earnings growth rate. (Note that 9 years of growth are reflected in the 10 years of data.) Year EPS Year EPS 2005 $3.90 2010 $5.73 2006 4.21 2011 6.19 2007 4.55 2012 6.68 2008 4.91 2013 7.22 2009 5.31 2014 7.80 The current interest rate on new debt is 10%; Foust's marginal tax rate is 40%; and its target capital structure is 35% debt and 65% equity. a.Calculate Foust's after-tax cost of debt. Round your answer to two decimal places. 6.00% a.After-tax cost of new debt: rd(1 - T) = 0.10(1 - 0.4) = 6.00%. Calculate Foust's cost of common equity. Calculate the cost of equity as rs = D1/P0 + g. Round your answer to two decimal places. 17.06% Cost of common equity: Calculate g as follows: With a financial calculator, input N = 9, PV = -3.90, PMT = 0, FV = 7.80, and then solve for I/YR = g = 8.006%. rs = D1/P0 + g = (0.65)($7.80)/$56.00 + 0.08 = $5.07/$56.00 + 0.08 = 0.1706 or 17.06% b.Find Foust's WACC. Round your answer to two decimal places. 13.19% WACC calculation: Component Target Weight x After-Tax Cost = Weighted Cost Debt 0.35 6.00% 2.10% Common equity (RE) 0.65 17.06 11.09 WACC = 13.19% Chapter 11 The Basic of Capital Budgeting Problem 11-1 NPV Project K costs $50,000, its expected cash inflows are $15,000 per year for 6 years, and its WACC is 10%. What is the project's NPV? Round your answer to the nearest cent. $15,328.91 Financial calculator solution: Input CF0 = -50,000, CF1-6 = 15,000, I/YR = 10, and then solve for NPV = $15,328.91. Problem 11-2 IRR Project K costs $43,580.14, its expected cash inflows are $9,000 per year for 10 years, and its WACC is 14%. What is the project's IRR? Round your answer to two decimal places. 15.95% Financial calculator solution: Input CF0 = -43,580.14, CF1-10 = 9,000, and then solve for IRR = 15.95%. Problem 11-3 MIRR Project K costs $60,000, its expected cash inflows are $13,000 per year for 8 years, and its WACC is 12%. What is the project's MIRR? Round your answer to two decimal places. 13.03% MIRR: PV costs = $60,000. FV inflows: PV 0 1 2 3 4 5 6 7 8 12% 13,000 13,000 13,000 13,000 13,000 13,000 13,000 13,000 x 1.12 14,560 x (1.12)2 16,307 x (1.12)3 18,264 x (1.12)4 20,456 x (1.12)5 22,910 x (1.12)6 25,660 x (1.12)7 28,739 60,000 MIRR = 13.03% 159,896 Financial calculator solution: Obtain the FVA by inputting N = 8, I/YR = 12, PV = 0, PMT = 13,000, and then solve for FV = $159,896. The MIRR can be obtained by inputting N = 8, PV = 60,000, PMT = 0, FV = 159,896, and then solving for I/YR = 13.03%. Problem 11-4 Payback period Project K costs $55,000, its expected cash inflows are $12,000 per year for 10 years, and its WACC is 13%. What is the project's payback? Round your answer to two decimal places. 5 Years Since the cash flows are a constant $12,000, calculate the payback period as: $55,000/$12,000 = 4.5833, so the payback is about 5 years. Problem 11-5 Discounted payback Project K costs $40,000, its expected cash inflows are $9,000 per year for 8 years, and its WACC is 11%. What is the project's discounted payback? Round your answer to two decimal places. 6.44 years Project K's discounted payback period is calculated as follows: Annual Discounted @11% Period Cash Flows Cash Flows Cumulative 0 -$40,000 -$40,000.00 -$40,000.00 1 9,000 8,108.11 -31,891.89 2 9,000 7,304.60 -24,587.29 3 9,000 6,580.72 -18,006.57 4 9,000 5,928.58 -12,077.99 5 9,000 5,341.06 -6,736.93 6 9,000 4,811.77 -1,925.16 7 9,000 4,334.93 2,409.77 8 9,000 3,905.34 6,315.10 The discounted payback period is 6 + 1,925.16 / 4,334.93 years, or 6.44 years. Problem 11-6 NPV Your division is considering two projects with the following cash flows (in millions): 0 1 2 3 Project A -$20 $5 $9 $12 Project B -$13 $8 $7 $3 a.What are the projects' NPVs assuming the WACC is 5%? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Project A $3.29 million Project A: Using a financial calculator, enter the following: CF0 = -20, CF1 = 5, CF2 = 9, CF3 = 12, I/YR = 5; NPV = $3.29. Project B $3.56 million Project B: Using a financial calculator, enter the following: CF0 = -13, CF1 = 8, CF2 = 7, CF3 = 3, I/YR = 5; NPV = $3.56. What are the projects' NPVs assuming the WACC is 10%? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Project A $1.00 million Change I/YR = 5 to I/YR = 10; NPV = $1.00. Project B $2.31 million Change I/YR = 5 to I/YR = 10; NPV = $2.31. What are the projects' NPVs assuming the WACC is 15%? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Project A $-0.96 million Change I/YR = 10 to I/YR = 15; NPV = $-0.96. Project B $1.22 million Change I/YR = 10 to I/YR = 15; NPV = $1.22. b.What are the projects' IRRs assuming the WACC is 5%? Round your answer to two decimal places. Project A 12.46% Using the data for Project A, enter the cash flows into a financial calculator and solve for IRRA = 12.46%. The IRR is independent of the WACC, so it doesn’t change when the WACC changes. Project B 21.49 % Using the data for Project B, enter the cash flows into a financial calculator and solve for IRRB = 21.49%. Again, the IRR is independent of the WACC, so it doesn’t change when the WACC changes. What are the projects' IRRs assuming the WACC is 10%? Round your answer to two decimal places. Project A 12.46% Using the data for Project A, enter the cash flows into a financial calculator and solve for IRRA = 12.46%. The IRR is independent of the WACC, so it doesn’t change when the WACC changes. Project B 21.49% Using the data for Project B, enter the cash flows into a financial calculator and solve for IRRB = 21.49%. Again, the IRR is independent of the WACC, so it doesn’t change when the WACC changes. What are the projects' IRRs assuming the WACC is 15%? Round your answer to two decimal places. Project A 12.46% Using the data for Project A, enter the cash flows into a financial calculator and solve for IRRA = 12.46%. The IRR is independent of the WACC, so it doesn’t change when the WACC changes. Project B 21.49 % Using the data for Project B, enter the cash flows into a financial calculator and solve for IRRB = 21.49%. Again, the IRR is independent of the WACC, so it doesn’t change when the WACC changes. c.If the WACC were 5% and A and B were mutually exclusive, which would you choose? (Hint: The crossover rate is 3.86%.) Project B At a WACC = 5%, NPVA < NPVB, so choose Project B. If the WACC were 10% and A and B were mutually exclusive, which would you choose? (Hint: The crossover rate is 3.86%.) Project B At a WACC = 10%, NPVA < NPVB, so choose Project B. If the WACC were 15% and A and B were mutually exclusive, which would you choose? (Hint: The crossover rate is 3.86%.) Project B At a WACC = 15%, NPVA < NPVB, so choose Project B. Problem 11-7 Capital budgeting criteria A firm with a 14% WACC is evaluating two projects for this year's capital budget. After-tax cash flows, including depreciation, are as follows: 0 1 2 3 4 5 Project A -$12,000 $4,000 $4,000 $4,000 $4,000 $4,000 Project B -$36,000 $11,200 $11,200 $11,200 $11,200 $11,200 a. Calculate NPV for each project. Round your answers to the nearest cent. Project A $1,732.32 CF0 = -12,000; CF1-5 = 4,000; I/YR = 14. Solve for NPVA = $1,732.32. Project B $2,450.51 CF0 = -36,000; CF1-5 = 11,200; I/YR = 14. Solve for NPVB = $2,450.51. Calculate IRR for each project. Round your answers to two decimal places. Project A 19.86% CF0 = -12,000; CF1-5 = 4,000; I/YR = 14. Solve for NPVA = $1,732.32. IRRA = 19.86%. Project B 16.80% Solve for NPVB = $2,450.51. IRRB = 16.80%. Calculate MIRR for each project. Round your answers to two decimal places. Project A 17.12 % MIRR calculation: 0 1 2 3 4 5 14% -12,000 4,000 4,000 4,000 4,000 4,000 x 1.14 4,560.00 x (1.14)2 5,198.40 x (1.14)3 5,926.18 x (1.14)4 6,755.84 26,440.42 Using a financial calculator, enter N = 5; PV = -12,000; PMT = 0; FV = 26,440.42; and solve for MIRRA = I/YR = 17.12%. Project B 15.51% MIRR calculation: 0 1 2 3 4 5 14% -36,000 11,200 11,200 11,200 11,200 11,200 x 1.14 12,768.00 x (1.14)2 14,555.52 x (1.14)3 16,593.29 x (1.14)4 18,916.35 74,033.17 Using a financial calculator, enter N = 5; PV = -36,000; PMT = 0; FV = 74,033.17; and solve for MIRRB = I/YR = 15.51%. Calculate payback for each project. Round your answers to two decimal places. Project A 3.00 years Project B 4.16 years Calculate discounted payback for each project. Round your answers to two decimal places. Project A 3.21 years Project B 4.56 years Project A Project B NPV $1,732.32 $2,450.51 IRR 19.86 % 16.80 % MIRR 17.12 % 15.51 % Payback 3.00 years 3.21 years Discounted payback 4.16 years 4.56 years b. Assuming the projects are independent, which one or ones would you recommend? -Select-Both projects would be accepted since both of their NPV's are positive. Only Project A would be accepted because IRR(A) > IRR(B).Both projects would be rejected since both of their NPV's are negative.Only Project A would be accepted because NPV(A) > NPV(B).Only Project B would be accepted because NPV(B) > NPV(A). c. If the projects are mutually exclusive, which would you recommend? -Select-If the projects are mutually exclusive, the project with the shortest Payback Period is chosen. Accept Project A.If the projects are mutually exclusive, the project with the highest positive IRR is chosen. Accept Project B.If the projects are mutually exclusive, the project with the highest positive NPV is chosen. Accept Project B.If the projects are mutually exclusive, the project with the highest positive IRR is chosen. Accept Project A.If the projects are mutually exclusive, the project with the highest positive MIRR is chosen. Accept Project A. d. Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR? -Select-The conflict between NPV and IRR occurs due to the difference in the size of the projects.The conflict between NPV and IRR is due to the relatively high discount rate.The conflict between NPV and IRR is due to the fact that the cash flows are in the form of an annuity.The conflict between NPV and IRR is due to the difference in the timing of the cash flows.There is no conflict between NPV and IRR. Problem 11-8 Capital budgeting criteria: ethical considerations A mining company is considering a new project. Because the mine has received a permit, the project would be legal; but it would cause significant harm to a nearby river. The firm could spend an additional $10.33 million at Year 0 to mitigate the environmental Problem, but it would not be required to do so. Developing the mine (without mitigation) would cost $63 million, and the expected net cash inflows would be $21 million per year for 5 years. If the firm does invest in mitigation, the annual inflows would be $22 million. The risk adjusted WACC is 13%. a. Calculate the NPV and IRR with mitigation. Round your answers to two decimal places. Enter your answer for NPV in millions. For example, an answer of $10,550,000 should be entered as 10.55. NPV $4.05 million IRR 15.24% With mitigation analysis (in millions of dollars): 0 1 2 3 4 5 13% -73.33 22 22 22 22 22 Using a financial calculator, enter the data as follows: CF0 = -73.33; CF1-5 = 22; I/YR = 13. Solve for NPV = $4.05 million and IRR = 15.24%. Calculate the NPV and IRR without mitigation. Round your answers to two decimal places. Enter your answer for NPV in millions. For example, an answer of $10,550,000 should be entered as 10.55. NPV $10.86 million IRR 19.86 % No mitigation analysis (in millions of dollars): 0 1 2 3 4 5 13% -63 21 21 21 21 21 Using a financial calculator, enter the data as follows: CF0 = -63; CF1-5 = 21; I/YR = 13. Solve for NPV = $10.86 million and IRR = 19.86%. b.How should the environmental effects be dealt with when this project is evaluated? I.The environmental effects if not mitigated could result in additional loss of cash flows and/or fines and penalties due to ill will among customers, community, etc. Therefore, even though the mine is legal without mitigation, the company needs to make sure that they have anticipated all costs in the "no mitigation" analysis from not doing the environmental mitigation. II.The environmental effects should be ignored since the mine is legal without mitigation. III.The environmental effects should be treated as a sunk cost and therefore ignored. IV.The environmental effects if not mitigated would result in additional cash flows. Therefore, since the mine is legal without mitigation, there are no benefits to performing a "no mitigation" analysis. V.The environmental effects should be treated as a remote possibility and should only be considered at the time in which they actually occur. c.Should this project be undertaken? -Select--Select-Even when mitigation is considered the project has a positive IRR, so it should be undertaken.The project should not be undertaken under the "no mitigation" assumption.The project should be undertaken only under the "no mitigation" assumption.The project should not be undertaken under the "mitigation" assumption.Even when mitigation is considered the project has a positive NPV, so it should be undertaken. If so, should the firm do the mitigation? I.Under the assumption that all costs have been considered, the company would mitigate for the environmental impact of the project since its IRR with mitigation is greater than its IRR when mitigation costs are not included in the analysis. II.Under the assumption that all costs have been considered, the company would not mitigate for the environmental impact of the project since its NPV with mitigation is greater than its NPV when mitigation costs are not included in the analysis. III.Under the assumption that all costs have been considered, the company would not mitigate for the environmental impact of the project since its IRR without mitigation is greater than its IRR when mitigation costs are included in the analysis. IV.Under the assumption that all costs have been considered, the company would mitigate for the environmental impact of the project since its NPV with mitigation is greater than its NPV when mitigation costs are not included in the analysis. V.Under the assumption that all costs have been considered, the company would not mitigate for the environmental impact of the project since its NPV without mitigation is greater than its NPV when mitigation costs are included in the analysis. Problem 11-9 Capital budgeting criteria: ethical considerations An electric utility is considering a new power plant in northern Arizona. Power from the plant would be sold in the Phoenix area, where it is badly needed. Because the firm has received a permit, the plant would be legal; but it would cause some air pollution. The company could spend an additional $40 million at Year 0 to mitigate the environmental Problem, but it would not be required to do so. The plant without mitigation would cost $240.31 million, and the expected cash inflows would be $80 million per year for 5 years. If the firm does invest in mitigation, the annual inflows would be $84.93 million. Unemployment in the area where the plant would be built is high, and the plant would provide about 350 good jobs. The risk adjusted WACC is 16%. a. Calculate the NPV and IRR with mitigation. Round your answers to two decimal places. Enter your answer for NPV in millions. For example, an answer of $10,550,000 should be entered as 10.55. NPV $-2.22 million IRR 15.66% With mitigation analysis (in millions of dollars): 0 1 2 3 4 5 16% -280.31 84.93 84.93 84.93 84.93 84.93 Using a financial calculator, enter the data as follows: CF0 = -280.31; CF1-5 = 84.93; I/YR = 16. Solve for NPV = -$2.22 million and IRR = 15.66%. No mitigation analysis (in millions of dollars): Calculate the NPV and IRR without mitigation. Round your answers to two decimal places. Enter your answer for NPV in millions. For example, an answer of $10,550,000 should be entered as 10.55. NPV $21.64 million IRR 19.80% 0 1 2 3 4 5 16% -240.31 80 80 80 80 80 Using a financial calculator, enter the data as follows: CF0 = -240.31; CF1-5 = 80; I/YR = 16. Solve for NPV = $21.64 million and IRR = 19.80%. b. How should the environmental effects be dealt with when evaluating this project? I.If the utility mitigates for the environmental effects, the project is not acceptable. However, before the company chooses to do the project without mitigation, it needs to make sure that any costs of "ill will" for not mitigating for the environmental effects have been considered in that analysis. II.The environmental effects should be treated as a remote possibility and should only be considered at the time in which they actually occur. III.The environmental effects if not mitigated would result in additional cash flows. Therefore, since the plant is legal without mitigation, there are no benefits to performing a "no mitigation" analysis. IV.The environmental effects should be ignored since the plant is legal without mitigation. V.The environmental effects should be treated as a sunk cost and therefore ignored. c. Should this project be undertaken? I.The project should be undertaken since the IRR is positive under both the "mitigation" and "no mitigation" assumptions. II.The project should be undertaken since the NPV is positive under both the "mitigation" and "no mitigation" assumptions. III.Even when no mitigation is considered the project has a negative NPV, so it should not be undertaken. IV.The project should be undertaken only if they do not mitigate for the environmental effects. However, they want to make sure that they've done the analysis properly due to any "ill will" that might result from undertaking the project without concern for the environmental impacts. V.The project should be undertaken only under the "mitigation" assumption. Problem 11-10 Capital budgeting criteria: mutually exclusive projects A firm with a WACC of 10% is considering the following mutually exclusive projects: 0 1 2 3 4 5 Project A -$400 $45 $45 $45 $205 $205 Project B -$650 $350 $350 $40 $40 $40 Which project would you recommend? I. Both Projects A and B, since both projects have NPV's > 0. II. Project A, since the NPVA > NPVB. III. Neither A or B, since each project's NPV < 0. IV. Project B, since the NPVB > NPVA. V. Both Projects A and B, since both projects have IRR's > 0. Project A: Using a financial calculator, enter the following data: CF0 = -400; CF1-3 = 45; CF4-5 = 205; I/YR = 10. Solve for NPV = $-20.79. Project B: Using a financial calculator, enter the following data: CF0 = -650; CF1-2 = 350; CF3-5 = 40; I/YR = 10. Solve for NPV = $39.65. The decision rule for mutually exclusive projects is to accept the project with the highest positive NPV. In this situation, the firm would accept Project B since NPVB = $39.65 is greater than NPVA = $-20.79. Problem 11-11 Capital budgeting criteria: mutually exclusive projects Project S costs $11,000 and its expected cash flows would be $4,500 per year for 5 years. Mutually exclusive Project L costs $46,500 and its expected cash flows would be $12,300 per year for 5 years. If both projects have a WACC of 12%, which project would you recommend? I. Both Projects S and L, since both projects have NPV's > 0. II. Project S, since the NPVS > NPVL. III. Project L, since the NPVL > NPVS. IV. Neither S or L, since each project's NPV < 0. V. Both Projects S and L, since both projects have IRR's > 0. Project S: Using a financial calculator, enter the following data: CF0 = -11,000; CF1-5 = 4,500; I/YR = 12. NPVS = $5,221.49. Project L: Using a financial calculator, enter the following data: CF0 = -46,500; CF1-5 = 12,300; I/YR = 12. NPVL = $-2,161.25. The decision rule for mutually exclusive projects is to accept the project with the highest positive NPV. In this situation, the firm would accept Project S since NPVS = $5,221.49 is greater than NPVL = $- 2,161.25. Problem 11-12 IRR and NPV A company is analyzing two mutually exclusive projects, S and L, with the following cash flows: 0 1 2 3 4 Project -$1,000 $888.13 $250 $5 $10 Project L -$1,000 $5 $240 $400 $845.68 The company's WACC is 8.0%. What is the IRR of the better project? (Hint: The better project may or may not be the one with the higher IRR.) Round your answer to two decimal places. 12.60% Input the appropriate cash flows into the cash flow register, and then calculate NPV at 8% and the IRR of each of the projects: Project S: CF0 = -1000; CF1 = 888.13; CF2 = 250; CF3 = 5; CF4 = 10; I/YR = 8. Solve for NPVS = $48.00; IRRS = 12.20%. Project L: CF0 = -1000; CF1 = 5; CF2 = 240; CF3 = 400; CF4 = 845.68; I/YR = 8. Solve for NPVL = $149.52; IRRL = 12.60%. Since Project L has the higher NPV, it is the better project, even though its IRR is less than Project S's IRR. The IRR of the better project is IRRL = 12.60%. Problem 11-13 MIRR A firm is considering two mutually exclusive projects, X and Y, with the following cash flows: 0 1 2 3 4 Project X -$1,000 $110 $280 $400 $650 Project Y -$1,000 $1,000 $100 $50 $45 The projects are equally risky, and their WACC is 10.0%. What is the MIRR of the project that maximizes shareholder value? Round your answer to two decimal places. 12.03% Because both projects are the same size you can just calculate each project’s MIRR and choose the project with the higher MIRR. Project X: 0 1 2 3 4 -1,000 110 280 400 650.00 x 1.1 440.00 x (1.1)2 338.80 x (1.1)3 146.41 1,000 12.03% = MIRRX 1,575.21 $1,000 = $1,575.21/(1 + MIRRX)4. MIRRX = 12.03% Project Y: 0 1 2 3 4 -1,000 1,000 100 50 45.00 x 1.1 55.00 x (1.1)2 121.00 x (1.1)3 1,331.00 1,000 11.62% = MIRRY 1,552.00 $1,000 = $1,552.00/(1 + MIRRY)4. MIRRY = 11.62% Thus, since MIRRX > MIRRY, Project X should be chosen. Alternate step: You could calculate the NPVs, see that Project X has the higher NPV, and just calculate MIRRX. NPVX = $75.89 and NPVY = $60.04. Problem 11-14 Choosing mandatory projects on the basis of least cost Kim Inc. must install a new air conditioning unit in its main plant. Kim must install one or the other of the units; otherwise, the highly profitable plant would have to shut down. Two units are available, HCC and LCC (for high and low capital costs, respectively). HCC has a high capital cost but relatively low operating costs, while LCC has a low capital cost but higher operating costs because it uses more electricity. The costs of the units are shown here. Kim's WACC is 5%. 0 1 2 3 4 5 HCC -$590,000 -$50,000 -$50,000 -$50,000 -$50,000 -$50,000 LCC -$110,000 -$175,000 -$175,000 -$175,000 -$175,000 -$175,000 a. Which unit would you recommend? I.Since we are examining costs, the unit chosen would be the one that had the lower PV of costs. Since LCC's PV of costs is lower than HCC's, LCC would be chosen. II.Since we are examining costs, the unit chosen would be the one that had the lower PV of costs. Since HCC's PV of costs is lower than LCC's, HCC would be chosen. III.Since all of the cash flows are negative, the IRR's will be negative and we do not accept any project that has a negative IRR. IV.Since all of the cash flows are negative, the NPV's cannot be calculated and an alternative method must be employed. V.Since all of the cash flows are negative, the NPV's will be negative and we do not accept any project that has a negative NPV. HCC: Using a financial calculator, enter the following data: CF0 = -590,000; CF1-5 = -50,000; I/YR = 5. Solve for NPV = -$806,473.83. LCC: Using a financial calculator, enter the following data: CF0 = -110,000; CF1-5 = -175,000; I/YR = 5. Solve for NPV = -$867,658.42. Since we are examining costs, the unit chosen would be the one that has the lower PV of costs. Since HCC's PV of costs is lower than LCC's, HCC would be chosen. b.If Kim's controller wanted to know the IRRs of the two projects, what would you tell him? I.The IRR cannot be calculated because the cash flows are all one sign. A change of sign would be needed in order to calculate the IRR. II.The IRR cannot be calculated because the cash flows are in the form of an annuity. III.The IRR of each project will be positive at a lower WACC. IV.There are multiple IRR's for each project. V.The IRR of each project is negative and therefore not useful for decision-making. c. If the WACC rose to 10% would this affect your recommendation? I.When the WACC increases to 10%, the IRR for LCC is greater than the IRR for HCC, LCC would be chosen. II.When the WACC increases to 10%, the IRR for HCC is greater than the IRR for LCC, HCC would be chosen. III.Since all of the cash flows are negative, the NPV's will be negative and we do not accept any project that has a negative NPV. IV.When the WACC increases to 10%, the PV of costs are now lower for LCC than HCC. V.When the WACC increases to 10%, the PV of costs are now lower for HCC than LCC. HCC: I/YR = 10; solve for NPV = -$779,539.34. LCC: I/YR = 10; solve for NPV = -$773,387.68. Explain your answer and why this result occurred. I.The reason is that when you discount at a higher rate you are making negative CFs higher thus improving the IRR. II.The reason is that when you discount at a higher rate you are making negative CFs higher thus improving the NPV. III.The reason is that when you discount at a higher rate you are making negative CFs higher and this lowers the NPV. IV.The reason is that when you discount at a higher rate you are making negative CFs smaller and this lowers the NPV. V.The reason is that when you discount at a higher rate you are making negative CFs smaller thus improving the NPV. When the WACC increases from 5% to 10%, the PV of costs are now lower for LCC than HCC. The reason is that when you discount at a higher rate you are making negative CFs smaller and thus improving the results, unknowingly. Thus, if you were trying to risk adjust for a riskier project that consisted just of negative CFs then you would use a lower cost of capital rather than a higher cost of capital and this would properly adjust for the risk of a project with only negative CFs. Problem 11-15 NPV profiles: timing differences An oil drilling company must choose between two mutually exclusive extraction projects, and each costs $11.8 million. Under Plan A, all the oil would be extracted in 1 year, producing a cash flow at t = 1 of $14.16 million. Under Plan B, cash flows would be $2.0967 million per year for 20 years. The firm's WACC is 11.8%. a. Construct NPV profiles for Plans A and B. Round your answers to two decimal places. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Discount Rate NPV Plan A NPV Plan B 0% $ million $ million 5 $ million $ million 10 $ million $ million 12 $ million $ million 15 $ million $ million 17 $ million $ million 20 $ million $ million Identify each project's IRR. Round your answers to two decimal places. Project A % Project B % Find the crossover rate. Round your answer to two decimal places. % b.Is it logical to assume that the firm would take on all available independent, average-risk projects with returns greater than 11.8%? -Select-yesno If all available projects with returns greater than 11.8% have been undertaken, does this mean that cash flows from past investments have an opportunity cost of only 11.8%, because all the company can do with these cash flows is to replace money that has a cost of 11.8%? -Select-yesno Does this imply that the WACC is the correct reinvestment rate assumption for a project's cash flows? -Select-yesno Problem 11-17 Capital budgeting criteria A company has a 13% WACC and is considering two mutually exclusive investments (that cannot be repeated) with the following cash flows: 0 1 2 3 4 5 6 7 Project A -$300 -$387 -$193 - $100 $600 $600 $850 -$180 Project B -$400 $134 $134 $134 $134 $134 $134 $0 a. What is each project's NPV? Round your answer to the nearest cent. Project A $162.48 Project B $135.67 Using a financial calculator and entering each project's cash flows into the cash flow registers and entering I/YR = 13, you would calculate each project's NPV. At WACC = 13%, Project A has the greater NPV, specifically $162.48 as compared to Project B's NPV of $135.67. b. What is each project's IRR? Round your answer to two decimal places. Project A 18.10% Project B 24.51% Using a financial calculator and entering each project's cash flows into the cash flow registers, you would calculate each project's IRR. IRRA = 18.1%; IRRB = 24.51%. c. What is each project's MIRR? (Hint: Consider Period 7 as the end of Project B's life.) Round your answer to two decimal places. Project A 15.60% Here is the MIRR for Project A when WACC = 13%: PV costs = $300 + $387/(1.13)1 + $193/(1.13)2 + $100/(1.13)3 + $180/(1.13)7 = $939.44. TV inflows = $600(1.13)3 + $600(1.13)2 + $850(1.13)1 = $2,592.38. MIRR is the discount rate that forces the TV of $2,592.38 in 7 years to equal $939.44. Using a financial calculator enter the following inputs: N = 7, PV = -939.44, PMT = 0, and FV = 2,592.38. Then, solve for I/YR = MIRRA = 15.60%. Project B 17.81% Here is the MIRR for Project B when WACC = 13%: PV costs = $400. TV inflows = $134(1.13)6 + $134(1.13)5 + $134(1.13)4 + $134(1.13)3 + $134(1.13)2 + $134(1.13) = $1,260.22. MIRR is the discount rate that forces the TV of $1,260.22 in 7 years to equal $400. Using a financial calculator enter the following inputs: N = 7; PV = -400; PMT = 0; and FV = 1,260.22. Then, solve for I/YR = MIRRB = 17.81%. d.From your answers to parts a-c, which project would be selected? Project A WACC = 13% criteria: Project A Project B NPV $162.48 $135.67 IRR 18.10% 24.51% MIRR 15.60% 17.81% The correct decision is that Project A should be chosen because NPVA > NPVB. If the WACC was 18%, which project would be selected? Project B At WACC = 18%, using your financial calculator enter the cash flows for each project, enter I/YR = WACC = 18, and then solve for each Project’s NPV. NPVA = $2.66; NPVB = $68.68. At WACC = 18%, NPVB > NPVA so Project B would be chosen e.Construct NPV profiles for Plans A and B. Round your answers to the nearest cent. Discount Rate NPV Plan A NPV Plan B 0% $890.00 $ 404.00 5 $540.09 $ 280.14 10 $283.34 $183.60 12 $200.41 $ 150.93 15 $ 92.96 $ 107.12 18.1 $ -0.09 $ 67.48 24.51 $ -147.63 $ -0.02 f. Calculate the crossover rate where the two projects' NPVs are equal. Round your answer to two decimal places. 14.28% To calculate the crossover rate, create Project Δ which represents the cash flow differences between the two projects. The IRR of Project Δ is the crossover rate. Year CFA CFB CFΔ = CFA - CFB 0 -300 -400 100 1 -387 134 -521 2 -193 134 -327 3 -100 134 -234 4 600 134 466 5 600 134 466 6 850 134 716 7 - 180 0 -180 Enter the data for Project Δ into the cash flow registers and solve for IRRΔ = 14.28%. Note that when using your calculator you may receive an ERROR message. In order to find the IRR, you will need to store a guess for IRR, say 10%, by ■ STO 10 and then calculate IRR, IRR = 14.28%. g.What is each project's MIRR at a WACC of 18%? Round your answer to two decimal places. Project A 18.05% Here is the MIRR for Project A when WACC = 18%: PV costs = $300 + $387/(1.18)1 + $193/(1.18)2 + $100/(1.18)3 + $180/(1.18)7 = $883.95. TV inflows = $600(1.18)3 + $600(1.18)2 + $850(1.18)1 = $2,824.26. MIRR is the discount rate that forces the TV of $2,824.26 in 7 years to equal $883.95. Using a financial calculator enter the following inputs: N = 7; PV = -883.95; PMT = 0; and FV = 2,824.26. Then, solve for I/YR = MIRRA = 18.05%. Project B 20.70% Here is the MIRR for Project B when WACC = 18%: PV costs = $400. TV inflows = $134(1.18)6 + $134(1.18)5 + $134(1.18)4 + $134(1.18)3 + $134(1.18)2 + $134(1.18) = $1,492.96. MIRR is the discount rate that forces the TV of $1,492.96 in 7 years to equal $400. Using a financial calculator enter the following inputs: N = 7; PV = -400; PMT = 0; and FV = 1,492.96. Then, solve for I/YR = MIRRB = 20.70%. Problem 11-20 NPV A project has annual cash flows of $5,000 for the next 10 years and then $6,000 each year for the following 10 years. The IRR of this 20-year project is 13.51%. If the firm's WACC is 9%, what is the project's NPV? Round your answer to the nearest cent. $12,781.68 Because the IRR is the discount rate at which the NPV of a project equals zero, the project's inflows can be evaluated at the IRR and the present value of these inflows must equal the initial investment. Using a financial calculator enter the following: CF0 = 0; CF1 = 5,000; Nj = 10; CF2 = 6,000; Nj = 10; I/YR = 13.51. NPV = $35,571.93. Therefore, the initial investment for this project is $35,571.93. Using a calculator, the project's NPV at the firm's WACC can now be solved. CF0 = -35,571.93; CF1 = 5,000; Nj = 10; CF2 = 6,000; Nj = 10; I/YR = 9. NPV = $12,781.68. Problem 11-21 MIRR Project X costs $2,000, and its cash flows are the same in Years 1 through 10. Its IRR is 18%, and its WACC is 11%. What is the project's MIRR? Round your answer to two decimal places. 14.04% Step 1: Determine the PMT: 0 1 10 18% ... -2,000 PMT PMT The IRR is the discount rate at which the NPV of a project equals zero. Since we know the project's initial investment, its IRR, the length of time that the cash flows occur, and that each cash flow is the same, then we can determine the project's cash flows by setting it up as a 10-year annuity. With a financial calculator, input N = 10, I/YR = 18, PV = -2,000, and FV = 0 to obtain PMT = $445.03. Step 2: Since we've been given the WACC, once we have the project’s cash flows we can now determine the project's MIRR. 0 1 2 9 10 11% ... -2,000 445.03 445.03 445.03 445.03 x 1.11 493.98 . . . x (1.11)8 1,025.59 x (1.11)9 1,138.40 2,000 14.04% = MIRR TV = 7,441.78 FV of inflows: With a financial calculator, input N = 10, I/YR = 11, PV = 0, and PMT = 445.03 to obtain FV = $7,441.78. Calculate MIRR: Then input N = 10, PV = -2,000, PMT = 0, and FV = 7,441.78 to obtain I/YR = MIRR = 14.04%. Problem 11-22 MIRR A project has the following cash flows: 0 1 2 3 4 5 -$700 $220 -$X $209 $380 $478 This project requires two outflows at Years 0 and 2, but the remaining cash flows are positive. Its WACC is 14%, and its MIRR is 16.05%. What is the Year 2 cash outflow? Round your answer to the nearest cent. $50.00 The MIRR can be solved with a financial calculator by finding the terminal future value of the cash inflows and the initial present value of cash outflows, and solving for the discount rate that equates these two values. In this instance, the MIRR is given, but a cash outflow is missing and must be calculated. Therefore, if the terminal future value of the cash inflows is found, it can be entered into a financial calculator, along with the number of years the project lasts and the MIRR, to solve for the initial present value of the cash outflows. One of these cash outflows occurs in Year 0 and the remaining value must be the present value of the missing cash outflow in Year 2. Cash Inflows Compounding Rate FV in Year 5 @ 14% CF1 = $220 x (1.14)4 $371.57 CF3 = 209 x (1.14)2 271.62 CF4 = 380 x 1.14 433.20 CF5 = 478 x 1.00 478.00 1,554.39 Using the financial calculator to solve for the present value of cash outflows: N = 5; I/YR = 16.05; PV = ?; PMT = 0; FV = 1,554.39. Solve for PV = $738.47. The total present value of cash outflows is $738.47, and since the outflow for Year 0 is $700, the present value of the Year 2 cash outflow is $38.47. Therefore, the missing cash outflow for Year 2 is $38.47 x (1.14)2 = $50.00. Practice Exam # 2 Chapter 6 Interest Rates Problem 6-1 1). Yield Curves TERM RATE 6 months 4.65% 1 year 5.48% 2 years5.54% 3 years5.8% 4 years5.81% 5 years6.04% 10 years 6.33% 20 years 6.69% 30 years 6.79% Plot a yield curve based on these data. The correct sketch is A. What type of yield curve is shown? The yield curve is upward sloping. What information does this graph tell you? This yield curve tells us generally that either inflation is expected to increase or there is an increasing maturity risk premium. Bas

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