final 9 fundamentals of corporate finance, 4th edition brealey

AK/ADMS 3530.03 Finance Final Exam Summer 2006 Solutions provided at the end of the paper You are expected to pay $1,883.33 per month on a one-year loan with a principal of $20,000 What is the EAR of this loan? A) B) C) D) 13.00% 13.80% 23.19% 25.82% You are planning to buy a $240,000 home with a $105,000 mortgage at 6% APR for 25 years What is your monthly payment? A) B) C) D) $470.49 $671.83 $940.97 $1,343.66 ABC Corp has a 10% coupon (semi-annual payments) bond with years to maturity selling at 104% of par (par value =$1,000) What is the bond’s effective annual yield (i.e EAR)? A) 9.21% B) 9.42% C) 9.62% D) 10.00% Based on the following information about yesterday’s trading activity which appears in today’s Globe and Mail for IC Inc., what was the closing price the day-before-yesterday on IC’s $1,000 face value 7.875% bond? Bond prices are quoted as percentage of face value Bond IC Inc 7.875 A) B) C) D) Current Yield 9.4 Volume 10 Close ? Net Change -0.5 83.25 83.75 84.25 94.00 Big Sell Computers has planned dividend payments of $6.50, $5.00, $3.00 and $2.00 over the next four years If the required rate of return on the stock is 16%, what is the current share price if dividends are expected to grow at a constant rate of 5% infinitely after the fourth year? A) B) C) D) $6.82 $14.22 $19.09 $22.89 Given that XYZ Inc is projecting a dividend growth of 25% annually over the next years, 18% in the fourth year and 8% annually thereafter, what is the projected dividend for next year based upon an expected 15% return on the stock and a current share price of $60? A) B) C) D) $2.00 $2.38 $2.65 $2.98 If a project has a positive NPV, what is true about its discounted payback? A) B) C) D) The discounted payback will be less than the project life The discounted payback may not fall within the project The NPV of the project will equal the discounted payback More information is needed in order to arrive at an answer The PI is: A) B) C) D) the measure of the NPV of a project’s net income the NPV of cash flows relative to the project’s initial cost the discount rate that causes the NPV of a series of cash flows to be identically zero the indexed measure of all future cash flows relative to the firm’s discount rate A firm is facing a hard capital rationing Given the firm’s required rate of return of 9%, apply the PI decision rule to the following two projects Which project would you accept? Year A) B) C) D) Project I Cash Flow -$20,000 $10,000 $10,000 $10,000 Project II Cash Flow -$3,000 $2,500 $2,500 $2,500 Neither project should be accepted More information is needed before a decision can be made Project I Project II 10 A firm using a discount rate of 12% calculated expected annual cash flows on a new 4year project, whose expected initial cost is $8,000, to be $7,000, $7,500, $8,000, and $8,500, respectively What is the discounted payback period of the project? A) B) C) D) 1.20 years 1.29 years 1.50 years 1.67 years 11 At what discount rate would you be indifferent between accepting and rejecting a project which costs $6,000 today with annual cash flows of $1,200 for the next nine years? A) B) C) D) 13.50% 13.60% 13.70% 13.80% 12 A project requires an installed cost of a new machine of $412,670 The four year useful life of the machine is expected to generate annual cash inflows of $212,817, $153,408, $102,389, and $72,308, respectively The machine has no salvage value At what discount rate is the NPV of this project equal to zero? A) B) C) D) 14.57% 14.75% 15.25% 15.33% 13 What is the amount of the operating cash flow for a firm with $500,000 profit before tax, $100,000 depreciation expense, and a 35% corporate tax rate? A) B) C) D) $260,000 $325,000 $360,000 $425,000 14 What is the present value of the CCA tax shield at 10% discount rate for a firm in the 35% tax bracket that purchased a $50,000 asset, if the CCA rate is 15% and the half-year rule applies? Assume no salvage value A) B) C) D) $10,023 $10,866 $17,500 $37,908 15 What is the net effect on a firm’s working capital if a new project requires: $30,000 increase in inventory, $10,000 increase in accounts receivable, $25,000 increase in machinery, and $20,000 increase in accounts payable? A) B) C) D) -$5,000 $10,000 $20,000 $45,000 16 In capital budgeting analysis, an increase in working capital can be shown as: A) A cash inflow at the beginning of the project B) A cash outflow at the beginning and an equal cash inflow at the end of the project C) A cash inflow at the beginning and an equal cash outflow at the end of the project D) A decrease in the initial amount invested 17 New projects or products can have an indirect effect on the firm as well as direct effect Which of the following appears to be an indirect effect of a launching a new product? A) Additional working capital is required B) Sales force will need to be increased C) Sales of our similar product will decline D) Additional machinery must be purchased 18 What is the maximum percentage of variable costs in relation to sales that a firm could experience and still (accounting) break even with $5 million revenue, $1 million fixed costs and $500,000 depreciation? A) 30% B) 70% C) 80% D) 90% 19 Calculate the NPV break-even level of sales for a project requiring an investment of $3,000,000 and providing as annual cash flows: 0.15×sales less $250,000 Assume the project will last 10 years and that the discount rate is 10% A) $3,254,890 B) $3,504,890 C) $4,536,150 D) $4,921,504 20 Market demand allowed a firm to raise its price by 20% to $60 What is the new level of accounting break-even revenue if fixed charges including depreciation are $1 million and variable costs per product were 70% of the old price? A) $2,000,000 B) $2,400,000 C) $2,857,143 D) $3,333,333 21 A firm with $600,000 fixed costs and $200,000 depreciation is expected to produce $225,000 in pretax profits What is its DOL? A) B) C) D) 3.56 3.67 4.56 4.67 22 If a firm’s DOL is when its pretax profit is $2,000,000 and its depreciation is $500,000, how much fixed costs (excluding depreciation) does it have? A) B) C) D) $5,000,000 $5,500,000 $6,000,000 $7,500,000 23 A decision tree shows a 30% probability of $2 million in returns and a 70% chance of $1 million in returns occurring one year in the future What is the maximum amount you would invest today in this project if the discount rate is 10%? A) $818,182 B) $1,181,818 C) $1,300,000 D) $1,363,636 24 Which of the following variables would you suspect to be least significant in a sensitivity analysis of a fast-food establishment? A) Sales B) Labour cost C) Depreciation schedule D) Food cost 25 Which of the following offers the most plausible scenario for a firm that maintained a constant DOL when its level of fixed costs (excluding depreciation) doubled? A) B) C) D) Depreciation expense increased Variable cost percentage decreased Sales revenues declined Pretax profits decreased 26 The option for a firm to expand future productions has value because: A) B) C) D) the future holds uncertainty future production will be profitable production costs will be higher in the future the option requires no investment today 27 In a year in which common stocks offered an average return of 18%, Treasury bonds offered 10% and Treasury bills offered 7%, the risk premium for common stocks was: A) B) C) D) 1% 3% 8% 11% 28 What is the standard deviation of returns for a one-year project with (only) two equally likely outcomes: a 100% gain and a 100% loss? A) B) C) D) 0% 50% 71% 100% 29 If when a coin is tossed the observance of a head rewards you with a dollar and the observance of a tail costs you fifty cents, how much would you expect to gain after twenty tosses? Assume that a head and a tail are equally likely to occur in a toss A) $5.00 B) $7.50 C) $10.00 D) $15.00 30 A portfolio consists of 75% of stock L and 25% of stock S The standard deviations of stocks L and S are 16% and 20%, respectively The covariance of stocks L and S is -160 percentages squared Compute the standard deviation of this portfolio A) 10.44% B) 12.50% C) 15.13% D) 17.00% 31 Industries that generally perform well when other industries are performing well are referred to as: A) B) C) D) diversified industries systematic risk industries cyclical industries countercyclical industries 32 Although unique risk is present in differing amounts, individual stocks are: A) B) C) D) exposed to the same amount of market risk exposed to differing amounts of market risk also not exposed to market risk; only the general economy is subject to market risk able to diversify away their market risk 33 Which statement is correct concerning macro risk exposure? A) All firms face equal macro risk exposure B) Only portfolios of stocks face macro risk exposure C) Macro risk exposure affects the cost of capital D) Macro risk exposure is less important to diversified investors than micro (specific) risk exposure 34 What should be the beta of stock C if an investor wishes to achieve a portfolio beta of in the following equally weighted portfolio: stock A (beta = 0.9), stock B (beta = 1.1), and stock C? A) B) C) D) 0.93 1.00 1.08 1.15 35 Calculate the risk premium on a stock given the following information: risk-free rate = 5%, market portfolio return = 13% and beta of the stock = 1.3 A) B) C) D) 8.0% 10.4% 15.4% 16.9% 36 What portfolio return would be expected by an investor whose portfolio was 25% market portfolio, 25% of a stock with beta of 0.8, and 50% Treasury bills if the risk-free rate was 7% and the market risk premium was 8%? A) B) C) D) 8.85% 9.50% 10.60% 12.00% 37 What is the beta of a portfolio with an expected return of 12% if the expected return on the market portfolio is 14% and Treasury bills yield 6%? A) B) C) D) 0.43 0.50 0.60 0.75 38 What happens to the expected portfolio return if the portfolio beta increases from to 1.2, the risk-free rate decreases from 5% to 2.2%, and the market risk premium increases from 8% to 9%? A) B) C) D) It increases from 13% to 14% It increases from 13% to 15.64% It decreases from 18% to 15.64% It remains unchanged 39 Where will the following two projects plot in relation to the security market line (SML) if the risk-free rate is 6% and the market risk premium is 9%? Which project should be undertaken? Project I II Beta 2.0 1.1 IRR 25% 15% A) Project I plots above the SML and should be accepted; Project II plots below the SML and should be rejected B) Project I plots above the SML and should be rejected; Project II plots below the SML and should be accepted C) Project I plots below the SML and should be accepted; Project II plots above the SML and should be rejected D) Project I plots below the SML and should be rejected; Project II plots above the SML and should be accepted 40 When the overall market experiences a decline of 8%, an investor with a portfolio of aggressive stocks will probably experience: A) B) C) D) negative portfolio returns of less than 8% negative portfolio returns of more than 8% positive portfolio returns of less than 8% positive portfolio returns of more than 8% 41 Decreases in the risk-free rate will reduce, other things being equal: A) B) C) D) the market risk premium the stock’s risk premium the stock’s beta the stock’s expected return 10 42 The WACC for a firm with only debt and equity in its capital structure, a debt-to-equityratio of 3/2, 8% cost of debt, 15% cost of equity, and a 35% tax rate is: A) B) C) D) 7.02% 9.12% 10.80% 13.80% 43 What is the WACC for a firm using 55% equity with a required return of 15%, 35% debt with a required return of 8%, 10% preferred stock with a required return of 10%, and a tax rate of 35%? A) B) C) D) 10.50% 10.72% 11.07% 12.05% 44 Should a project be accepted if it offers an annual after-tax cash flow of $1,250,000 infinitely, costs $10 million today, is riskier than the firm’s average projects, and the firm uses a 12.5% WACC? A) B) C) D) Yes, since NPV is positive Yes, since a zero NPV indicates marginal acceptability No, since NPV is zero No, since NPV is negative 45 What is the after-tax cost of preferred stock that sells for $10 per share in the market, has a book value of $8 per share, and offers a $1.2 dividend per share when the tax rate is 35%? A) B) C) D) 7.80% 9.75% 12.00% 15.00% 11 46 What proportion of a firm is equity financed if the WACC is 14%, the after-tax cost of debt is 7%, the tax rate is 35%, and the required return on equity is 18%? Assume the firm only uses debt and equity in its financing A) B) C) D) 36.36% 63.64% 70.26% 77.78% 47 A firm is financed 60% with equity and 40% with debt Currently, its before-tax cost of debt is 12% The firm’s common stock trades at $15 per share and its most recent dividend was $1 Future dividends are expected to grow by 4% infinitely If the tax rate is 34%, what is the firm’s WACC? A) B) C) D) 9.57% 9.73% 11.20% 11.36% 48 As more debt is added to the capital structure, the: A) B) C) D) cost of debt is expected to rise WACC will continually decline WACC will continually increase WACC will be unaffected 49 If a company’s WACC is less than the required return on equity, then the firm: A) B) C) D) is financed with more than 50% of debt is perceived to be safe has debt in its capital structure cannot be using any debt 12 50 Which of the following statements is false regarding flotation costs? A) It is easier to account for flotation costs by treating them as negative cash flows B) They increase the required rate of return C) They are the costs of issuing new securities D) They involve real money 13 Solutions D PV  payment  [ rmonth   $20,000  $1,883.33  [ ] rmonth (1  rmonth ) n rmonth  ] rmonth (1  rmonth )12 S olve for rmonth  1.9322% EAR  (1  rmonth )12   (1  0.019322)12   0.2582  25.82% B EAR  (1  APR / 2)   (1  0.06 / 2)   6.09% rmonth  (1  EAR )1 / 12   (1  0.0609)1 / 12   0.4939% $105,000  Payment  [ 1  ] 0.004939 0.004939(1.004939 2512 )  Payment  156.29, $105,000  Payment   $671.83 156.29 B Use your financial calculator, the YTM on the bond is found to be 9.212% (If you use the approximate formula, the YTM is found to be 9.243% Here we use the YTM obtained using the financial calculator.) The YTM is an APR assuming semi-annual compounding, so the effective annual yield (i.e EAR) = (1+0.09212/2) 2-1 = 9.4242% C Current yield  P 0.07875  $1,000 $78.75   0.094 P P $78.75  $837.77  83.77% of par  83.75 0.094 Since the price closed down 0.5 yesterday, the price the-day-before-yesterday was 83.75 + 0.5 = 84.25 14 D DIV5 $2(1  0.05)   $19.09 rg 0.16  0.05 DIV3 DIV1 DIV2 DIV4 P4 P0       r (1  r ) (1  r ) (1  r ) (1  r ) $6.5 $5 $3 $2 $19.09       $22.89 1.16 1.16 1.16 1.16 1.16 P4  D DIV1  DIV0 (1.25); DIV2  DIV0 (1.25) ; DIV3  DIV0 (1.25) ; DIV4  DIV0 (1.25) (1.18) DIV5 DIV4 (1  g ) DIV0 (1.25 )(1.18)(1  0.08)   rg rg 0.15  0.08 2.489DIV0   35.56DIV0 0.07 DIV0 (1.25) DIV0 (1.25) DIV0 (1.25) DIV0 (1.25) (1.18) 35.56DIV0 P0  $60      1.15 1.15 1.15 1.15 1.15  DIV0 ( 25.2) P4   DIV0  $60  $2.38  DIV1  $2.38  1.25  $2.975  $2.98 25.2 A B D NPVI  $10,000[ 1  ]  $20,000  $5,312.95, 0.09 0.09(1.09 ) $5,312.95  0.266 $20,000 1 NPVII  $2,500[  ]  $3,000  $3,328.24, 0.09 0.09(1.09 ) $3,328.24 PI II   1.109 $3,000 PI I  So choose Project II since PI is higher 15 10 B $7,000 $7,500  $6,250;  $5,798.95; 1.12 1.12 $8,000 $8,500  $5,694.24;  $5,401.90 1.12 1.12 Cost  $8,000  Discounted payback   $(8,000  6,250)  1.29 years $5,798.95 11 C IRR = 13.70% 12 A IRR = 14.57% 13 D Profit before tax -Taxes @ 35% Net profit + depreciation Cash flow from operations $500,000 -$175,000 $325,000 +$100,000 $425,000 14 A CdTC  0.5r ][ ] rd 1 r $50,000  0.15  0.35  0.5  0.1 [ ][ ]  $10,022.72  $10,023 0.1  0.15  0.1 PV of CCA tax shield  [ 15 C Change in working capital = increase in accounts receivable + increase in inventory – increase in accounts payable = $10,000 + $30,000 - $20,000 = $20,000 16 B 17 C 16 18 B Accounting break-even revenue = fixed costs (including depreciation) / profit margin So $5 million revenue = ($1 million + $500,000) / profit margin  profit margin = $1.5 million / $5 million = 0.3  The percentage of variable costs = – 0.3 = 0.7 = 70% 19 D NPV  PV (cash flows )  investment  1  (0.15sales  $250,000)[  ]  $3,000,000  0.1 0.1(1.110 )  (0.15sales  $250,000)  6.1446  $3,000,000 $4,536,150  0.9217sales  $4,536,150  sales   $4,921,504 0.9217 20 B Old price = $60/1.2 = $50 Therefore, variable costs per product = $50 × 0.7 = $35, which equals 58.33% of the new price So the new accounting break-even revenue = $1 million / (1-0.5833)  $2,400,000 21 C Accounting break-even revenue = + [fixed costs (including depreciation)/pretax profits] = + $(600,000 + 200,000)/$225,000 = 4.56 22 B Accounting break-even revenue = + (fixed costs + depreciation)/pretax profit = + (fixed costs + $500,000)/$2,000,000 = Fixed costs = $5,500,000 17 23 B 0.3  $2M  0.7  $1M  investment  1.1 0.3  $2M  0.7  $1M  Investment   $1,181,818 1.1 NPV  24 C 25 B 26 A 27 D The risk premium for common stocks = 18% - 7% = 11% 28 D Mean return  0.5  100%  0.5  100%  Variance  0.5  (100%  0)  0.5  ( 100%  0)  10,000 percentages squared S tan dard deviation  10,000 percentages squared  100% 29 A Expected gain  20  [$1  0.5  $0.5  0.5]  $5 30 A Co var iance  160 percentage s squared  0.016, Co var iance  0.016  Correlatio n (  )    0.5  L S 0.16  0.2  P  0.75  0.16  0.25  0.2  2(0.75)(0.25)(0.5)(0.16)(0.2)  0.1044  10.44% 31 C 32 B 33 C 18 34 B 1  0.9   1.1    C  3 1   C  (1   0.9   1.1)   3 Portfolio beta  35 B Stock risk premium = beta × market risk premium = 1.3 × (13% - 5%) = 10.4% 36 C S tock return  0.07  0.8  0.08  0.134 Market portfolio return  0.07  0.08  0.15  Portfolio return  0.25  0.15  0.25  0.134  0.5  0.07  0.106  10.6% 37 D Market risk premium  0.14  0.06  0.08 By the CAPM , 0.12  0.06    0.08    0.75 38 D By the CAPM, the old level of portfolio return = 0.05 + × 0.08 = 13% Again by the CAPM, the new level of portfolio return = 0.022 + 1.2 × 0.09 = 13% So the portfolio return is unchanged 39 A Project I: expected return = 0.06 + × 0.09 = 24 < IRR of 0.25  Project I plots above the SML and should be accepted Project II: expected return = 0.06 + 1.1 × 0.09 = 159 > IRR of 0.15  Project II plots below the SML and should be rejected 40 B 41 D 42 B It is straightforward to find that the weights of debt and equity in the firm’s capital structure are 60% and 40%, respectively  WACC  0.6  (1  0.35)  0.08  0.4  0.15  0.0912 19 43 C WACC  0.35  (1  0.35)  0.08  0.1  0.1  0.55  0.15  0.1107 44 D The NPV at the WACC = -$10 million + $1.25 million/0.125 = However, the WACC is the company cost of capital To determine the acceptance of an individual project, we need to use the project cost of capital Since the project in question is riskier than the firm’s average projects, the project cost of capital should be higher than the WACC of 12.5% So the NPV at the project cost of capital would be negative Therefore, reject the project 45 C Cost of preferred stock = $1.2/$10 = 12% Taxes have no impact on the cost of preferred stock 46 B WACC  (1  x)  7%  x  18%  14% ( Note : 7% is the after  tax cos t of debt )  0.14  0.07  0.07 x  0.18x  0.07  0.11x  0.14  0.07  0.11x  0.07  0.11x  x  63.64% 47 B requity  DIV1 $1(1  0.04) g  0.04  0.1093 P0 $15 WACC  0.4  (1  0.34)  0.12  0.6  0.1093  0.09726  0.0973 48 A 49 C 50 B 20 ... 30 A portfolio consists of 75% of stock L and 25% of stock S The standard deviations of stocks L and S are 16% and 20%, respectively The covariance of stocks L and S is -1 60 percentages squared... WACC for a firm with only debt and equity in its capital structure, a debt-to-equityratio of 3/2, 8% cost of debt, 15% cost of equity, and a 35% tax rate is: A) B) C) D) 7.02% 9.12% 10.80% 13.80%... 58.33% of the new price So the new accounting break-even revenue = $1 million / ( 1-0 .5833)  $2,400,000 21 C Accounting break-even revenue = + [fixed costs (including depreciation)/pretax profits]