assignment12 fundamentals of corporate finance, 4th edition brealey

AK/ADMS3530 3.0 Assignment #2 Solutions Winter 2007 Question (18 marks) Blooper Technology Inc is considering purchasing two machines, A and B, which are expected to generate $36,000 and $40,000 respectively in cash flows per year for years Although Machine B is more expensive than Machine A, its payback period (3.25 years) is shorter compared to that of Machine A (3.5 years) Blooper’s opportunity cost of capital is 10% (a) Which machine would you take if the machines were mutually exclusive and if shareholder maximization were your basis for decision? Explain (5 Marks) Answer COST OF MACHINE A= 3.50 × 36,000 = $126,000 COST OF MACHINE B= 3.25 × 40,000 = $130,000 NPV A = -126,000 + 36,000 (PVIFA 5, 10%) = $10,468.32 NPV B = -130,000 + 40,000 (PVIFA 5, 10%) = $21,631.47 MACHINE B SINCE IT HAS A GREATER NPV (b) If the company is willing to accept any project with a discounted payback period less than 4.25 years, would you recommend buying these machines? Explain (4 Marks) Answer (CASH FLOWS IN THOUSANDS OF DOLLARS) -126 36 36 36 36 36 $32.73 $29.75 $27.05 $24.59 $22.35 DISCOUNTED PAYBACK A=4.53 YEARS -130 REJECT BECAUSE DPB > 4.25 40 40 40 40 40 $36.36 $33.06 $30.05 $27.32 $24.84 DISCOUNTED PAYBACK B= 4.13 YEARS ACCEPT BECAUSE DPB < 4.25 ADMS3530 3.0 Assignment #2 solutions (c) Calculate the internal rate of return on each machine Would you buy these machines based on IRR? Explain (3 Marks) Answer IRR OF MACHINE A: 13.20 % (PV=-126, PMT=36, FV=0, N=5, I=?) IRR OF MACHINE B: 16.32 % (PV=-130, PMT=40, FV=0, N=5, I=?) YES BOTH IRRS ARE GREATER THAN THE COST OF CAPITAL (d) Machine A comes with an optional module which extends its useful life more years (with the same annual cash flows of $36,000) at an additional initial cost of $20,000 Which machine should you take after considering this option? ( Marks) Answer THE PV OF THE CF STREAM FROM MACHINE A = -146 +36 X (PVIFA 7, 10%) = -146 + 36 × 4.8684 = $29,263.08 EQUIVALENT ANNUAL CF FROM A= $29,263.08 / 4.8684 = $6,010.82 THE PV OF THE CF STREAM FROM MACHINE B= -130 + 40 × (PVIFA 5, 10%) = -130 + 40 × 3.7908 = $21,631.47 EQUIVALENT ANNUAL CF FROM B= $21,631.47 / 3.7908 = $5,707.31 CHOSE MACHINE A Question (10 marks) Calculate the NPV for the following capital budgeting proposal: $110,000 initial cost, to be depreciated straight-line over five years to an expected salvage value of $5,000, 35 percent tax rate, $35,000 additional annual revenues, $5,000 additional annual expense, $7,000 additional investment in working capital today to be recovered in year Project has a percent cost of capital Assume that the CCA is same as depreciation Answer (Cash flows are in dollars) Page ADMS3530 3.0 Assignment #2 solutions Year Year Year Year Year Year Cost (110,000) Change in Working Capital (7,000) 7,000 Revenues 35,000 35,000 35,000 35,000 35,000 5,000 5,000 5,000 5,000 5,000 21,000 21,000 21,000 21,000 21,000 9,000 9,000 9,000 9,000 16,000 3,150 3,150 3,150 3,150 5,600 5,850 5,850 5,850 5,850 10,400 less Expenses less Depreciation = Net Inc less Taxes (35%) = NI After Tax Salvage Value 5,000 Cash Flows (117,000) 26,850 26,850 26,850 26,850 36,400 NPV of Project = PV of Cash Flows - Initial Investment NPV = $26,850  1   − 4 .09 09(1.09)  $36,400 (1.09)5 + - $117,000 = -$6,356.02 Given that the NPV is negative, you reject the project Alternatively, (Cash flows are in dollars) Year Year Year Year Year Year Cost (110,000) Change in Working Capital (7,000) 7,000 Revenues 35,000 35,000 35,000 35,000 35,000 5,000 5,000 5,000 5,000 5,000 21,000 21,000 21,000 21,000 21,000 9,000 9,000 9,000 9,000 9,000 less Expenses less Depreciation = Net Inc Page ADMS3530 3.0 Assignment #2 solutions less Taxes (35%) = NI After Tax 3,150 3,150 3,150 3,150 3,150 5,850 5,850 5,850 5,850 5,850 Salvage Value 5,000 Cash Flows (117,000) 26,850 26,850 26,850 26,850 38,850 NPV of Project = PV of Cash Flows - Initial Investment NPV = $26,850  1   − 4 .09 09(1.09)  $38,850 (1.09)5 + - $117,000 = -$4,763.68 Given that the NPV is negative, you reject the project Both answers will be considered as valid Question (14 marks) The Atkinson College Entrepreneurship Team (ACET) is consulting to New Venture Skis Inc (NVS) who has designed a new top of the line ski The skis are expected to retail at $600 with a profit margin (PM) of 60% The first round of consulting to NVS, concluded earlier in the year, had been billed to NVS for $150,000 The research indicated that NVS would sell 50,000 sets of the new skis per year for years which will reduce 12,000 sets of projected sales per year from the current high end line of skis These high end skis sell for $1,000 with a variable cost of $550 However sales of the firm’s least expensive $300 skis will increase annually by 10,000 sets at a 33.3% PM Fixed costs are $7 million annually One million dollars has been spent on research and development of the new $600 skis New plant and equipment will cost $15,400,000 and has a 30% CCA rate and an expected salvage of $2 million Net working capital will increase by $900,000 annually that will be returned at the end of the project NVS has a 40% tax rate and a 14% cost of capital The half-year rule applies Compute the following for NVS: (a) Payback period (3 marks) Answer The marketing study and the research and development are both sunk costs and should be ignored Page ADMS3530 3.0 Sales New skis Expensive skis Cheap skis Total Var costs New skis Expensive skis Cheap skis Total Assignment #2 solutions $600 × 50,000 = $30,000,000 $1,000 × (– 12,000) = –$12,000,000 $300 × 10,000 = $21,000,000 $3,000,000 $240 × 50,000 = $12,000,000 $550 × (–12,000) = –$6,600,000 $200 × 10,000 = $7,400,000 $2,000,000 For the next years: Sales Variable costs Fixed costs CCA EBIT Taxes Net income Year $21,000,000 7,400,000 7,000,000 2,310,000 4,290,000 1,716,000 $ 2,574,000 Year $21,000,000 7,400,000 7,000,000 3,927,000 2,673,000 1,069,200 $1,603,800 Year $21,000,000 7,400,000 7,000,000 2,748,900 3,851,100 1,540,440 $2,310,660 Year $21,000,000 7,400,000 7,000,000 1,924,230 4,675,770 1,805,462 2,805,462 The half-year rule has been incorporated into the calculation of the annual CCA To accurately calculate the payback period, we need to estimate the operating cash flows in the first four years These can be determined from the following relationship (for this part depreciation is assumed to be the same as the CCA) : OCF1 = NI + D = $(2,574,000 + 2,310,000) = $4,884,000 OCF2 = NI + D = $(1,603,800 + 3,927,000) = $5,530,800 OCF3 = NI + D = $(2,310,660 + 2,748,900) = $5,059,560 OCF4 = NI + D = $(2,805,462 + 1,924,230) = $4,729,692 The initial cost is made up of the cost of the plant and equipment plus the increase in net working capital in Year 0: = $15.4M + 0.9M = $16.3M The sum of the OCFs in the first years is: $ $15,474,360 So the payback period = years + $(16,300,000 – 15,474,360) / $4,729,692 = 3.175 years (b) NPV (6 marks) Answer To find the NPV and IRR we need the after-tax net revenue each year as Page ADMS3530 3.0 Assignment #2 solutions well as the present value of the CCA tax shield and the initial and ending cash flows Initial cash flow = -$(15,400,000 + 900,000) = -$16,300,000 After-tax net revenue in Years 1-7 = (S – C)(1 – Tc) = $(21,000,000 – 14,400,000)(1 – 0.4) = $3,960,000 Ending cash flows (Year 7) = recovery of NWC + salvage value = $900,000 + 2,000,000 = $2,900,000 PV of CCATS = 15,400,000(0.3)(0.4) x (1 + 0.5(0.14)) 0.14 +0.3 +0.14 -2,000,000(0.3)(0.4) x 0.14 + 0.3 (1.14)7 = $3,724,121 NPV = –$16.3M + $3.96M (PVIFA14%,7) + $3,724,121 + $2.9M/1.147 = $5,307,458 Alternatively, the after-tax net revenue in Years 1-7 = $3,960,000 – $900,000 (change in NWC annually) = $3,060,000 NPV = –$16.3M + $3.06M (PVIFA14%,7) + $3,724,121 + $2.9M/1.147 = $1,705,282 Both NPV figures are acceptable for this question (c) IRR (5 marks) Answer To simplify the IRR calculation, it is assumed that CCA tax shield cash flows are as risky as the cash flows for the company’s overall operations Accordingly, the appropriate discount rate for the CCA tax shield is the company’s cost of capital The PV of CCATS is thus the same as for the NPV calculation NPV = = –$16.3M + $3.96M (PVIFAIRR%,7) + $3,724,121 + $2.9M/(1 + IRR)7 ⇒ IRR ≅ 26.6% Alternatively, NPV = = –$16.3M + $3.06M (PVIFAIRR%,7) + $3,724,121 + $2.9M/(1 + IRR)7 ⇒ IRR ≅ 18% Again both values of IRR are considered correct Page ADMS3530 3.0 Assignment #2 solutions Question (17 marks) Another consulting assignment on which the ACET is working is with Keep You Warm Corp (KYC), who has asked ACET for an evaluation of a six year $924,000 project to sell hi-tech ski glove warmers There is a zero salvage value on the project assets which use straight-line depreciation (to zero) Assume that the CCA is the same as depreciation The new hi-tech glove warmers will sell for $34 with a variable cost of $19 Sales are expected to be 130,000 pairs of gloves per year Fixed costs are $800,000 per year KYC has a 35% tax rate and a 15% cost of capital Consider this as the base case scenario (a) Calculate the accounting breakeven and the degree of operating leverage at that point (4 marks) Answer Depreciation = $924,000/6 = $154,000 per year The profit margin = $(34-19)/$34 = $0.4412 Accounting break even sales = ($800,000 + $154,000)/($0.4412) = $2,162,285 The following two answers are both acceptable for the DOL: 1) at the accounting break even sales level, the net income is 0, so the operating cash flow (OCF) = + depreciation (D) = $154,000 So DOL = + FC/OCF = + FC/D = + [$800,000+$154,000]/$154,000 = 7.195 Alternatively, 2) DOL = + FC/profits = ∞ since profits are zero (b) What is the sensitivity of Operating Cash Flows to change in the variable cost figure? What does your answer suggest about a $1 reduction in the variable costs? (5 marks) Answer VCnew = $18 (i.e $1 reduction) OCFnew = [($34 – $18)(130,000) – $800,000](0.65) + 0.35($154,000) = $885,900 OCFbase = [($34 – $19)(130,000) – $800,000](0.65) + 0.35($154,000) = $801,400 ∆OCF/∆VC = ($885,900 – $801,400) / ($18 – 19) = –$84,500 So if variable costs fell by $1, then the OCF would rise by $84,500 (c) Calculate the NPV for the base case (most likely scenario) and a sensitivity analysis by identifying the best case and worst case scenarios by changes to the sales numbers Explain why you selected these Page ADMS3530 3.0 Assignment #2 solutions numbers and what the impacts may be on your decision as to whether or not to move forward with the project (8 marks) Answer NPVbase = –$924,000 + $801,400(PVIFA15%,6) = $2,108,884.43 Answers to the sensitivity analysis will vary For example if sales rise by 5,000 units to 135,000 units: OCFnew = [$(34 – 19)(135,000) – $800,000](0.65) + 0.35($154,000) = $850,150 NPVnew = –$924,000 + $850,150(PVIFA15%,6) = $2,293,377.96 ∆NPV/∆S = ($2,293,377.96 – $2,108,884.43)/($34 × (135,000 – 130,000)) = 1.0853% In contrast, if sales were to drop by 5,000 units, then the OCF would drop to: [$(34 – 19)(125,000) – $800,000](0.65) + 0.35($154,000) = $752,650 NPVnew = –$924,000 + $752,650(PVIFA15%,6) = $1,924,390.90 ∆NPV/∆S = ($1,924,390.90 – $2,108,884.43)/($34 × (125,000 – 130,000)) = 1.0853% Question (10 marks) Calculate the expected returns, variances, and standard deviations for stock C, for stock E, and for a portfolio of both stocks C (2/3 weight) and E (1/3 weight) Scenario Probability Happiness 30% Indifference 50% Unhappiness 20% Return on C 15% 8% -4% Return on E -5% 4% 10% Answer Stock C : Expected return = 0.3 × % + 0.5 × 8% + 0.2 × ( − 4%) = 7.7% Variance = 0.3 × (15% - 7.7%) + 0.5 × (8% − 7.7%) + 0.2 × ( − 4% − 7.7%) = 41 percentage s squared, or 0.004341 Standard deviation = 43.41 = 59 , or 6.59% Stock E : Page ADMS3530 3.0 Assignment #2 solutions Expected return = 0.3 × ( − %) + 0.5 × 4% + 0.2 × 10 % = 2.5% Variance = 0.3 × (-5% - 2.5%) + 0.5 × (4% − 2.5%) + 0.2 × (1 0% − 2.5%) = 29 25 percentage s squared, or 0.002925 Standard deviation = 29.25 = 41 , or 5.41% Portfolio : Expected return = / × ( 7 %) + / × ( %) = 97 % Variance = 0.3 × (8.33% - 5.97%) + 0.5 × (6.67% − 5.97%) + 0.2 × ( 67% − 5.97%) = 5339 percentage s squared, or 0.00075339 Standard deviation = 7.5339 = 74 , or 2.74% Note that the standard deviation of the portfolio is less than that of either stock C or stock E because of diversification Question (12 marks) Use the following to answer the questions below: A market portfolio contains two stocks with the following returns: Aggressive Stock A, and Defensive Stock D: Scenario Bust Boom (a) Market -8% 32 Rate of Return Aggressive Stock A -10% 38 Defensive Stock D -6% 24 Find the beta of each stock In what way is stock D defensive? (5 marks) Answer Beta is the responsiveness of each stock's return to changes in the market return D is considered to be a more defensive stock than A because its return is less sensitive to the return of the overall market In a recession, D will usually outperform both stock A and the market portfolio Page ADMS3530 3.0 (b) Assignment #2 solutions If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock (4 marks) Answer We take an average of returns in each scenario to obtain the expected return rm = (32% – 8%)/2 = 12% rA = (38% – 10%)/2 = 14% rD = (24% – 6%)/2 = 9% (c) If the Treasury bill rate is percent, what does the CAPM say about the fair expected rates of return on the two stocks? (3 marks) Answer According to the CAPM, the expected returns that investors will demand of each stock, given the stock betas and given the expected return on the market, are: r = rf + β(rm – rf) rA = 4% + 1.2(12% – 4%) = 13.6% rD = 4% + 0.75(12% – 4%) = 10.0% Question (6 marks) Calculate the nominal return, real return, and risk premium for the following common stock investment: Purchase price $60.00 per share Dividend $3.50 per year Sales price $73.00 per share Treasury bill yield 8.5% Inflation rate 7.5% ANSWER NOMINAL RETURN = (CAPITAL GAIN + DIVIDEND) / INITIAL SHARE PRICE = (73-60 + 3.50) / 60 =27.5 % REAL RETURN = (1+ NOMINAL RATE) / (1+INFLATION RATE) - = (1.275/1.075) -1 = 18.6% RISK PREMIUM = NOMINAL RETURN LESS NOMINAL RETURN ON TREASURY BILLS = 27.5 – 8.5 Page 10 ADMS3530 3.0 Assignment #2 solutions = 19% IN NOMINAL TERMS Question (13 marks) A company issued $35,000,000 of 15-year, 7.5%, $1,000 par value debt at par three years ago Assume semi-annual coupon payments The yield to maturity on comparable debt today is 9% The firm also has 6,000,000 common shares outstanding, which currently trade at $26.00 per share The firm’s β is 1.26, the T-bill rate is 3.5% and the market risk premium is 6.7% Due to the early stage in its corporate life cycle, the firm has significant tax-loss carry forwards, resulting in the firm not expecting to have to pay taxes in the foreseeable future (a) Compute the firm’s weighted average cost of capital (WACC) (6 marks) Answer The bond price today is: 1 $1,000 − ]+ 24 0.045 0.045 × (1.045) (1.045) 24 = $37.5 × 14.4955 + $347.70 = $891.28 $37 × [ The market value of debts (D) = ($35,000,000/$1,000) × $891.28 = $31,194,800 The market value of equity (E) = $26 × 6,000,000 = $156,000,000 The market value of the firm (V) = D + E = $31,194,800 + $156,000,000 = = $187,194,800 The cost of equity (requity) is computed using the CAPM as: requity = 3.5% + 1.26 × 6.7% = 11.94% The cost of debt (rdebt) is the YTM on bond, which is 9% So the WACC with no taxes is calculated as: D E × rdebt + × requity V V $31,194,800 $156,000,000 = × 9% + × 11.94% = 11.45% $187,194,800 $187,194,800 WACC = (b) If the firm were able to issue an additional $26,000,000 in debt ($1,000 par value) at an 8.5% coupon rate (paid semi-annually) and use the proceeds to retire 1,000,000 shares, what would be the firm’s WACC? (4 marks) Answer Page 11 ADMS3530 3.0 Assignment #2 solutions D E × rdebt + × requity V V $( 31,194,800 + 26,000,000) $(156,000,000 − 26,000,000) = × 9% + × 11.94% $187,194,800 $187,194,800 = 11.04% Alternatively, D E WACC = × rdebt + × requity V V $31,194,800 $26,000,000 $(156,000,000 − 26,000,000) = × 9% + × 8.5% + × 11.94% $187,194,800 $187,194,800 $187,194,800 = 10.97% Both answers will be considered correct for this question WACC = Note that since debts are typically issued at par, the market value of the additional debt issue is equal to its par value (book value), which is $26,000,000 (c) How would your answer in part (a) change if the firm were taxable at 35%? (3 marks) Answer The WACC with taxes (35%) is calculated as: D E × (1 − TC ) × rdebt + × requity V V $31,194,800 $156,000,000 = × (1 − 0.35) × 9% + × 11.94% $187,194,800 $187,194,800 = 10.93% WACC = Page 12 ... Market -8 % 32 Rate of Return Aggressive Stock A -1 0% 38 Defensive Stock D -6 % 24 Find the beta of each stock In what way is stock D defensive? (5 marks) Answer Beta is the responsiveness of each... 26,850 26,850 26,850 26,850 36,400 NPV of Project = PV of Cash Flows - Initial Investment NPV = $26,850  1   − 4 .09 09(1.09)  $36,400 (1.09)5 + - $117,000 = -$ 6,356.02 Given that the NPV is... 26,850 26,850 26,850 26,850 38,850 NPV of Project = PV of Cash Flows - Initial Investment NPV = $26,850  1   − 4 .09 09(1.09)  $38,850 (1.09)5 + - $117,000 = -$ 4,763.68 Given that the NPV is