final 6 fundamentals of corporate finance, 4th edition brealey

AK/ADMS 3530.03 Finance Final Exam Winter 2007 Solutions Type A Exam Numerical questions (2 points each) (Q in B) What is the present value of the following payment stream, discounted at percent annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3? A) B) C) D) $5,022.11 $5,144.03 $5,423.87 $5,520.00 Answer A 1000 + 2000 (1.08 ) (1.08 ) + 3000 (1.08 ) PV = = $925.93 + $1,714.68 + $2,381.50 = $5,022.11 (Q in B) What is the present value of a four-year annuity of $100 per year that begins two years from today if the discount rate is percent? A) B) C) D) $297.22 $323.86 $356.85 $388.97 Answer A    09 − 09(1.09)4   PV1 = $100  = $100 [3.2397] PV1 = $323.97 323.97 PV0 = 1.09 = $297.22 (Q in B) $3,000 is deposited into an account paying 10 percent annually, to provide three annual withdrawals of $1,206.34 beginning in one year How much remains in the account after the second withdrawal? A) B) C) D) $587.32 $1,096.67 $1,206.34 $1,326.97 Answer B 1,206.34 1.1 = 1096.67 (Q in B) Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check (to be paid at the end of each month) that will last for 25 years, during which time the fund will earn percent interest with monthly compounding? A) B) C) D) $261,500 $323,800 $578,700 $690,000 Answer B The monthly interest rate is 8% / 12 = 0.667% PV = $2,500 × [1/0.00667 – 1/(0.00667(1.00667300))] = $2,500 [129.52] = $323,800 (Q in B) An investor buys a ten-year, percent coupon bond for $1,050, holds it for one year and then sells it for $1,040 What was the investor's rate of return over the 1-year holding period? Assume coupons are paid annually A) B) C) D) 5.71 percent 6.00 percent 6.67 percent 7.00 percent Answer A Return on bond = (Interest coupon + Capital gain) / Purchase price of bond In our example there was a capital loss of $10 given that the selling price of the bond ($1,040) was less than the purchase price of the bond ($1,050) Rate of return = ($70 - $10)/$1,050 = 5.71% (Q in B) A bond with 10 years until maturity, an percent coupon rate, and an percent original yield to maturity increased in price to $1,107.83 yesterday What appears to have happened to interest rates? Coupons are paid annually A) B) C) D) Rates increased by 2.00 percent Rates decreased by 2.00 percent Rates increased by 0.72 percent Rates decreased by 1.50 percent Answer D 1  1000 +  −  i i (1 + i )10  (1 + i ) 10 $1,107.83 = $80  i = 6.5%, yield to maturity was 8.0% prior to the price change Therefore the rates have decreased by 1.5% (Q in B) Which of the following statements is correct about a stock currently selling for $50 per share that has a 16 percent expected return and a 10 percent expected capital appreciation? A) B) C) D) Its expected dividend exceeds the actual dividend Its expected return will exceed the actual return It is expected to pay $3 in dividends for next year It is expected to pay $8 in dividends for next year Answer C Expected return = expected dividend yield + expected capital appreciation 16% = expected dividend yield + 10% 6% = expected dividend yield $50 share price × 6% = $3 expected dividend payment (Q in B) An investor receives a 15 percent total return by purchasing a stock for $40 and selling it after one year with a 10 percent capital gain How much was received in dividend income during the year? A) B) $2.00 $2.20 C) D) $4.00 $6.00 Answer A Percentage return = capital gain + dividend initial share price $40x10% + dividend $40 15% = Dividend = $2 (Q 13 in B) Because of its age, your car costs $4,000 annually in maintenance expense You could replace it with a newer vehicle costing $8,000 Both vehicles would be expected to last four more years If your opportunity cost is percent, what would be the maximum annual maintenance expense on the newer vehicle to still justify its purchase? A) B) C) D) $1,250 $1,585 $2,000 $2,415 Answer B  1  −  4 08 08(1.08)  $8,000 = Annuity  = Annuity [3.3121] = $2,415.39 When combined with the annuitized cost of the vehicle, any annual expense over $1,584.61 would place the total annual expense of the new vehicle over $4,000 10 (Q 14 in B) The profitability index for a project costing $40,000 and returning $15,000 annually for four years at an opportunity cost of capital of 12 percent is: A) B) C) D) 0.139 0.320 0.500 0.861 Answer A  1  −    12 12(1.12)  PV = $15,000 = $15,000 [3.0373] = $45,560 and NPV = $45,560 - $40,000 = $5,560 Profitability index = $5,560 / $40,000 = 0.139 11 (Q 15 in B) What is the minimum number of years that an investment costing $500,000 must return $65,000 per year at a discount rate of 13 percent in order to be an acceptable investment? A) B) C) D) 8.69 years 14.00 years 27.51 years An infinite number of years Answer D NPV = ($65,000 / 0.13) - $500,000 = 12 (Q 16 in B) You can continue to use your less efficient machine at a cost of $8,000 annually for the next five years Alternatively, you can purchase a more efficient machine for $12,000 plus $5,000 annual maintenance for the next five years At a cost of capital of 15 percent, you should: A) B) C) D) Buy the new machine and save $388 in equivalent annual costs Buy the new machine and save $600 in equivalent annual costs Keep the old machine and save $388 in equivalent annual costs Keep the old machine and save $580 in equivalent annual costs Answer D The PV of total cost of the more efficient machine is $28,760.78, which translates into an EAC of $8,579.79, which is $579.79 higher than the annual cost associated with the less efficient machine 13 (Q 17 in B) What is the approximate IRR for a project that costs $100,000 and provides annual cash inflows of $30,000 for six years? A) B) C) D) 19.9 percent 30.0 percent 32.3 percent 80.0 percent Answer A Use the following information to answer Questions 14 – 17 (Questions – 12 in Type B) Jensen Industries is considering purchasing a new Numerically Controlled Drilling Press The press costs $100,000, and belongs to a 15% CCA rate asset class (declining balance method) and the half-year rule applies The press is estimated to have cash flow savings of $34,000 per year for years and will require an immediate increase in Net Working Capital of $5,000, which will be recovered when the machine is sold at the end of year Initially assume there is zero salvage value The discount rate is 10% and the tax rate is 40% 14 (Q in B) What is Jensen’s CCA in Year and Year 2? A) B) C) D) $7,500; $12,750 $7,500; $13,875 $15,000; $12,750 $15,000; $13,875 Answer B CCA in year = $100,000 x ½ x 0.15 = $7,500 CCA in Year = $(100,000-7,500) x 0.15 = $13,875 15 (Q 10 in B) What is the present value of Jensen’s CCA tax shield? A) B) C) D) $5,367 $11,667 $19,419 $22,909 Answer D PVCCATS =  $100,0000 × 15% × 40%  1 + 0.5 × 10%     + 10%  = $22,909 10% + 15% 16 (Q 11 in B) Should Jensen accept the project? A) B) C) D) Yes, because the NPV is positive, and it exceeds $10,000 Yes, because the NPV is positive, although it is less than $10,000 No, because the NPV is negative, and it is between and -$10,000 No, because the NPV is negative, and it is between -$10,000 and $100,000 Answer B NPV=-$105,000 + $34,000(1-0.40)(PVIFA6yr,10%) + $5,000 (PVIF $22,909 = $9,578.69 Year Savings Tax @ 40% After-tax savings Capital Investment Change in NWC CFs Excluding CCATS Discounted CFs PV of CCATS NPV -100,000 -5,000 -105,000 -105,000 22,909 $ 9,578.69 34,000 13,600 20,400 20,400 18,545 34,000 13,600 20,400 20,400 16,860 34,000 13,600 20,400 20,400 15,327 34,000 13,600 20,400 20,400 13,933 6yr,10%) 34,000 13,600 20,400 34,000 13,600 20,400 20,400 12,667 5,000 25,400 14,338 + >0 17 (Q 12 in B) By how much will the NPV increase if Jensen is able to obtain a $10,000 salvage value at the end of Year 6? A) B) C) D) $1,824 $4,290 $5,645 $6,000 Answer B NPV increase = PV of salvage value – PV of lost CCATS due to salvage value   $10,000   $10,000 × 15% × 40%   −   = $4,290  6  10% 15 % +  (1 10 %) +  (1 + 10%)    NPV increase =  18 (Q 23 in B) What happens to the NPV of a one-year project if fixed costs are increased from $400 to $600, the firm is profitable, has a 15 percent tax rate and employs a 12 percent cost of capital? A) B) C) D) NPV decreases by $200.00 NPV decreases by $170.00 NPV decreases by $151.79 NPV decreases by $116.07 Answer C Fixed costs +$200 Profit before tax -$200 Taxes -$30 change in cash flow= -$200 + $30 = -$170, which discounts to -$151.79 19 (Q 24 in B) Fixed costs including depreciation have increased at Leverage, Inc from $4 million to $6 million in an effort to reduce variable costs What must the new variable-cost percentage be to leave accounting break-even at $20 million? A) B) C) D) 60 percent 65 percent 70 percent 75 percent Answer C $4 million - variable costs = $20 million Old: variable costs = 80% $6 million x = $20 million New: x = 30% Therefore, variable-cost percentage must reduce from 80 percent to 70 percent to leave the accounting break-even revenues unaffected 20 (Q 25 in B) Approximately how much was paid to invest in a project that has an NPV break-even level of sales of $5 million, annual cash flows determined by: 0.1 × sales – $300,000, a six-year life, and an percent discount rate? A) B) C) D) $416,667 $924,576 $1,016,678 $2,311,450 Answer B PV (cash flows) = investment    08 − 08(1.08)6    (0.1 x $5 million – $300,000) 4.6229 ($200,000) = $924,576 21 (Q 26 in B) What percentage change in sales occurs if profits increase by percent when the firm's degree of operating leverage is 4.5? A) B) C) D) 0.33 percent 0.67 percent 1.50 percent 3.33 percent Answer B % change in profits DOL = % change in sales 3% = % change in sales % change in sales = 0.67% 22 (Q 18 in B) If an asset's expected return is 10 percent, which represents a 20 percent return in a good economy and a percent loss in a bad economy, what is the probability of a good economy? A) B) C) D) 60.00 percent 40.00 percent 33.33 percent 18.33 percent Answer A p: probability of a good economy; 1-p: probability of a bad economy It follows that: 10% = 20% × p + (-5%) × (1- p) ⇒ p = 60% 23 (Q 19 in B) What is the approximate standard deviation of returns for a oneyear project that is equally likely to return 100 percent as it is to provide a 100 percent loss? A) B) C) D) percent 50 percent 71 percent 100 percent Answer D Mean = (0.5 × 100%) + (0.5 × (–100%)) = 50% – 50% = 0% (100 − )2 + (− 100 − )2 10,000 + 10,000 = Variance = = 10,000 Standard deviation = 10,000 = 100% 24 (Q 20 in B) What is the approximate variance of returns (in percentages squared) if over the past three years an investment returned 8.0 percent, -12.0 percent, and 15.0 percent? A) B) C) D) 31 131 182 961 Answer B − 12 + 15 Mean = = 3.67% (8 − 3.67 )2 + (− 12 − 3.67 )2 + (15 − 3.67 )2 Variance = 18.75 + 245.55 + 128.37 = = 130.89 percentages squared 25 (Q 21 in B) What is the standard deviation of a five-stock portfolio that produced portfolio returns of -4%, 2% and 5% with equal probability? A) B) C) D) 2.90% 3.24% 3.74% 4.58% Answer C The equal probability is 1/3 The portfolio expected return = (1/3)(-4% + 2% + 5%) = 1% The portfolio variance = (1/3)[(-4%-1%)2 + (2%-1%)2 + (5%-1%)2] = 14 percentages squared = 0.0014 10 Taking the square root of the portfolio variance, we find that the portfolio standard deviation is 3.74% 26 (Q 22 in B) What is the expected rate of return on a portfolio that will decline in value by 13 percent in a recession, will increase by 16 percent in normal times, and will increase by 23 percent during boom times if each scenario has equal likelihood? A) B) C) D) 8.67 percent 13.00 percent 13.43 percent 17.33 percent Answer A (- 13 + 16 + 23 ) (26 ) = Expected return = = 8.67% 27 (Q 31 in B) If a stock consistently goes up (down) by 1.6 percent when the market portfolio goes down (up) by 1.2 percent then the stock’s beta: A) B) C) D) equals 0.75 equals 1.33 equals -0.75 equals -1.33 Answer D It is obvious that the stock’s beta should be negative Also the stock is an aggressive stock The beta of the stock is – 1.6% / 1.2% = -1.33 28 (Q 32 in B) Which of the following statements is correct when Treasury bills yield 7.5 percent and the market risk premium is 9.5 percent? A) B) C) D) The S&P 500 would be expected to yield about 8.50 percent The S&P 500 would be expected to yield about 9.50 percent The S&P 500 would be expected to yield about 12.68 percent The S&P 500 would be expected to yield about 17.00 percent Answer D The market portfolio (S&P 500) would yield 7.5% + 9.5% = 17% 11 29 (Q 27 in B) When Treasury bills yield percent and the expected return on the market is 16 percent, then the risk premium on a stock is equal to: A) B) C) D) percent 16 percent percent times the stock's beta percent plus the risk-free rate Answer C According to the CAPM, the risk premium on a stock = the market risk premium × β = (16% - 7%) × β = 9% × β 30 (Q 28 in B) An investor was expecting an 18 percent return on her portfolio with beta of 1.25 before the market risk premium increased from percent to 10 percent Based on this change, what return will now be expected on the portfolio? A) B) C) D) 20.0 percent 20.5 percent 22.5 percent 26.0 percent Answer B Old: 18% = rf + 1.25(8%) = rf + 10.0% 8.0% = rf New: Expected return = 8.0% + 1.25(10%) = 8.0% + 12.5% = 20.5% 31 (Q 29 in B) What happens to the expected return on an asset if the asset beta decreases from 1.5 to 1.2, the risk-free rate increases from percent to percent, and the market expected return decreases from percent to percent? A) B) C) D) It increases from 7.4 percent to 11.5 percent It increases from 13.4 percent to 17.5 percent It decreases from 11.5 percent to 7.4 percent It decreases from 17.5 percent to 13.4 percent Answer C 12 Before the change: rj = 4% + 1.5 (9% - 4%) = 11.5% After the change: rj = 5% +1.2 (7% - 5%) = 7.4% 32 (Q 30 in B) A project will generate $750,000 of cash flows annually for four years The initial outlay is $2 million The expected return on Treasury bills is percent and the market risk premium is percent What is the highest project beta that will justify acceptance of the project? A) B) C) D) 0.00 1.00 1.56 2.31 Answer C $2 million = $750,000 × (PVIFA4 yr, IRR) IRR = 18.45% This suggests a risk premium of 12.45 percent on the project, which corresponds to a beta of 1.56 33 (Q 37 in B) If a firm is 42% debt-financed and the value of equity equals $47 million, which of the following is correct about firm value and the value of debt? There are only debt and equity in the firm’s capital structure Firm value A) $81 million B) $47 million C) $42 million D) $81 million Value of debt $34 million $81 million $20 million $42 million Answer A Firm Value = $47M / (1-0.42) = $81M Debt = $(81M – 47M) = $34M Use the following information to answer Questions 34 – 37 (Questions 3336 in Type B) Eastman Chemical has 38 million shares of common stock outstanding The book value per share is $42 but the stock sells for $58 It also has 700,000, percent semiannual coupon bonds outstanding, par value $1,000 each The bonds have 10 years to maturity and sell for 86 percent of par Eastman’s common stock is twice as risky as the market portfolio The firm has 14 million shares of percent preferred stock outstanding which currently sell for $63 per 13 share The face value per preferred share is $100 The T-bills yield 5.25%, and the market risk premium is assumed to be 4.15% Eastman is in the 35% corporate income tax bracket 34 (Q 33 in B) Eastman’s after-tax cost of debt is: A) B) C) D) 4.53% 6.45% 6.96% 7.40% Answer D On your financial calculator: FV=1000, PV=-860, N=20, PMT=45; I=? 5.69% ẻ YTM=5.69 ì =11.38% After-tax cost of debt = 11.38% × (1-35%) = 7.40% 35 (Q 34 in B) Eastman’s cost of equity is: A) B) C) D) 9.40% 13.55% 14.65% 24.05% Answer B By the CAPM: requity = 5.25% + × 4.15% = 13.55% 36 (Q 35 in B) Eastman’s cost of preferred stock is: A) B) C) D) 4.85% 5.00% 6.22% 7.94% Answer D The annual dividend paid on per preferred share is $100 × 5% = $5 So rpreferred = $5 / $63 = 7.94% 37 (Q 36 in B) What is the discount rate that Eastman should use to evaluate a project which is very similar to the firm’s existing business? A) 8.56% B) 9.25% 14 C) 11.22% D) 13.55% Answer C Price Shares (million) Market Value ($ million) Weights Costs WACC Equity 58 38 2,204 0.60 13.55% 11.22% Preferred Debt 63 860 14 0.7 882 0.24 7.94% 602 0.16 7.40% Value 3,688 Conceptual questions (2 points each) 38 (Q 43 in B) When a manager does not accept a positive-NPV project, shareholders face an opportunity cost in the amount of the: A) B) C) D) project's initial cost project's NPV project's discounted cash flows soft capital rationing budget Answer B 39 (Q 44 in B) When mutually exclusive projects have different lives, the project which should be selected will have the: A) B) C) D) highest IRR longest life highest NPV, discounted at the opportunity cost of capital lowest equivalent annual cost Answer D 40 (Q 45 in B) When should the net working capital investments be included in the estimation of cash flows? A) Never B) At the beginning of the project C) At the end of a project D) Any time during the life of a project Answer D 15 41 (Q 46 in B) Capital budgeting investments are evaluated with the assumption that projects are: A) 100 percent -debt financed B) 100 percent -equity financed C) 50 percent -equity and 50 percent -debt financed D) 25 percent -equity and 75 percent -debt financed Answer B 42 (Q 38 in B) If sensitivity analysis indicates none of the individual variables will cause a negative NPV under pessimistic conditions, then the: A) B) C) D) project is assured to be successful project's discount rate should be reduced economic forecasts are possibly overly optimistic interaction of the variables should be considered Answer D 43 (Q 39 in B) The opportunity to alter production technology gives managers: A) B) C) D) the flexibility to adapt to changing situations increased cash flow from operations the opportunity to expand production the ability to expand product lines Answer A 44 (Q 40 in B) Which of the following concerns is likely to be most important to portfolio investors seeking diversification? A) B) C) D) Total volatility of each individual securities Standard deviation of individual securities Correlation of returns between securities Achieving the risk-free rate of return Answer C 16 45 (Q 41 in B) The risk premium that is offered on common stock is equal to the: A) B) C) D) expected return on the stock real rate of return on the stock excess of expected return over a risk-free return expected return on the S&P 500 index Answer C 46 (Q 42 in B) The standard deviations of individual stocks are generally higher than the standard deviation of the market portfolio because individual stocks: A) B) C) D) offer higher returns have more systematic risk not have unique risk have no diversification of risk Answer D 47 (Q 49 in B) Stock returns can be explained by the stock's _ and the stock's A) B) C) D) beta; unique risk beta; market risk unique risk; firm-specific risk aggressive risk; defensive risk Answer A 48 (Q 50 in B) What will happen to a stock that offers a lower risk premium than predicted by the CAPM? A) B) C) D) Its beta will increase Its beta will decrease Its price will decrease until yield is increased Its price will increase until yield is reduced Answer C 49 (Q 47 in B) Generally speaking, the optimal capital mix that minimizes the weighted average cost of capital also: A) maximizes EPS B) maximizes share price C) minimizes the required rate of return on equity 17 D) minimizes bankruptcy costs Answer B 50 (Q 48 in B) Firms have various sources of financing Which one of the following does not incur flotation costs? A) Long-term debt B) Preferred stock C) Common stock D) Retained earnings Answer D 18 ... price of bond In our example there was a capital loss of $10 given that the selling price of the bond ($1,040) was less than the purchase price of the bond ($1,050) Rate of return = ($70 - $10)/$1,050... $9,578.69 Year Savings Tax @ 40% After-tax savings Capital Investment Change in NWC CFs Excluding CCATS Discounted CFs PV of CCATS NPV -1 00,000 -5 ,000 -1 05,000 -1 05,000 22,909 $ 9,578.69 34,000 13,600... decreases by $116.07 Answer C Fixed costs +$200 Profit before tax -$ 200 Taxes -$ 30 change in cash flow= -$ 200 + $30 = -$ 170, which discounts to -$ 151.79 19 (Q 24 in B) Fixed costs including depreciation