assignment10 fundamentals of corporate finance, 4th edition brealey

ADMS3530 3.0 Assignment #2 AK/ADMS3530 Summer 2007 Assignment #2 -SOLUTIONS Instructions: (1) This assignment is to be done individually You must sign and submit the standard cover page supplied as the last page of this assignment (2) This assignment is due at the start of class, the week of July 23rd, 2007 (last class) This assignment can be typewritten or handwritten Work that is too difficult to read due to messiness and poor handwriting will receive zero credit You must show your work to receive full credit (3) This assignment is worth a total of 100 marks and represents 10% of your overall grade Page ADMS3530 3.0 Assignment #2 Question #1 (14 marks) (a) (5 marks) A capital investment requiring one initial cash outflow is forecast to operating profits (cash) as follows Year Year Year Year $74,000 $84,000 $96,000 $70,000 The investment has an NPV of $20,850 based on a required rate of return of 12% Calculate the payback period of the investment Solution (a)Since the investment's NPV is $20,850, the initial investment is the value of Inv satisfying $20,850 = $74,000 $84,000 $96,000 $70,000 + + + – Inv 1.12 1.12 1.12 1.12 = $66,071.4 + $66,964.3 + $68,330.9 + $44,486.3 – Inv Inv = $225,003 Full payback on the project occurs sometime between years and to recover our initial investment of $225,003 Cumulative profit after years = $74,000 + $84,000 = $158,000 Cumulative profit after years = $158,000 + 96,000 = $254,000 Payback period = + $225,003 − $158,000 = 2.7 yrs or yrs months $254,000 − $158,000 Page ADMS3530 3.0 Assignment #2 (b) (9 marks) The initial investment and expected profits (cash) from mutually exclusive capital investments being considered by a firm are as follows: Investment A Investment B Initial Investment 70,000 65,000 Year profit 30,000 50,000 Year profit 80,000 50,000 Calculate the internal rate of return for each investment Which one would be selected based on an IRR ranking? (3 marks) (i) Which investment should be chosen if the firm’s cost of capital is 14% (support your answer)? (3 marks) (ii) Which investment should be chosen if the firm’s cost of capital is 17% (support your answer)? (3 marks) Solution (b) (i) The IRR on Investment A is the value of i satisfying NPV = = $30,000 $80,000 + – $70,000 1+ i (1 + i )2 The solution is i = 30.5% = IRR on Investment A The IRR on Investment B is the value of i satisfying NPV = = $50,000 $50,000 + – $65,000 1+ i (1 + i )2 The solution is i = 34.2% = IRR on Investment B Investment B would be selected on the basis on an IRR ranking (ii) $80,000 $30,000 + – $70,000 = $17,873 1.14 1.14 $50,000 $50,000 + – $65,000 = $17,333 NPV(Investment B) = 1.14 1.14 NPV(Investment A) = With the cost of capital at 14%, Investment A has the larger NPV and should be chosen (iii) Similarly, if you repeat part (ii) with the cost of capital of 17%, you would derive the following answers NPV(Investment A) = $14,082 NPV(Investment B) = $14,261 Investment B now has the higher NPV and should be chosen Page ADMS3530 3.0 Assignment #2 Question #2 (14 marks) Allergy-free Corp is considering launching a “hay-fever” vaccine in Canada that will eliminate entirely the need for many Canadians to take seasonal allergy medication The vaccines will be sold to the medical community and government for $2.30 per vaccine Variable costs are $0.6440 per pill and fixed costs excluding depreciation are $3,500,000 per year The capital investment for the new manufacturing equipment will be $4,500,000 and will be depreciated straight-line over years to a final value of zero Allergy-free Corp.’s cost of capital is 14% annually and it currently pays no taxes (a) What is the accounting break-even level of sales for the new vaccine, in terms of number of vaccines that must be sold? Solution Variable cost = $0.644 / $2.30 = $0.28 per $1 of revenue Additional profit per $1 of additional sales is therefore $0.72 Depreciation per year = $4,500,000 / = $562,500 fares of common stocks outstanding, which just paid $0.75 dividend per share The firm’s common stocks have a beta of 1.5 The annual sustainable growth rate of the firm’s earnings and dividends is 3% The risk-free rate is 3.5% and the rate of return on the market portfolio is 12% The firm pays taxes at a rate of 35% Compute Cocoa’s WACC Solution Bonds: The market price of bond today is: 1 Face Value − ]+ PB = C × [ t rdebt rdebt (1 + rdebt ) (1 + rdebt ) t 1 $1,000 − ]+ 30 0.03 0.03(1 + 0.03) (1 + 0.03) 30 = $1,098 The number of bonds issued = $45,000,000/$1,000 = 45,000 So the total market value of bonds is: D = 45,000 × $1,098 = $49,410,099.30 = $35 × [ Preferred stocks: The par value of each preferred stock = $7,500,000/250,000 = $30 The annual dividend paid on each preferred stock = $30 × 4.5% = $1.35 So the market price of preferred stock per share = $1.35/0.05 = $27, and the total market value of preferred stocks is: P = 250,000 × $27 = $6,750,000 Common stocks: Using the CAPM, we can calculate the cost of common stocks as: requity = r f + β (rm − r f ) = 3.5% + 1.5 × (12% − 3.5%) = 16.25% Using the DDM, we can compute today’s common stock price as: DIV1 $0.75 × (1 + 3%) P0 = = = $5.83 requity − g 16.25% − 3% Therefore, the total market value of common stocks is: E = 3,000,000 × $5.83 = $17,490,566.04 Page 12 ADMS3530 3.0 Assignment #2 Cocoa Corp.’s total market value is: V = D + P +E = $(49,410,099.30 + 6,750,000 + 17,490,566.04) = $73,650,665.34 The weights of each security are: D/V = 0.6709, P/V = 0.0916, and E/V = 0.2375 D P E × (1 − Tc )rdebt ] + [ × rpreferred ] + [ × requity ] V V V = [0.6709 × (1 − 0.35) × 0.06] + [0.0916 × 0.05] + [0.2375 × 0.1625] WACC = [ = 0.0693 So Cocoa Corp.’s WACC is about 6.93% Page 13 ADMS3530 3.0 Assignment #2 Question #7 (20 marks) To compete with Apple’s new i-Phone, Motorola is planning on unveiling its Mphone, a smart phone that include voice, internet access, unlimited data and a new feature that allows users to scroll through their voicemail in an inbox like email The Motorola marketing department estimates annual sales of 150,000, 250,000, 80,000 and 30,000 units for years one to four respectively and which time, the life cycle will end Pricing will be aggressive Motorola will sell the M-phone at a price of $490 in the first year and then reduce it by $70 a year to appeal to the mass markets Fixed costs are $3.2 million annually and variable costs are estimated at 35% of the selling price In addition, the Motorola accounting department will allocate general overhead of $2 million annually The manufacturing equipment will cost $30 million, $4 million to transport and another $1 million to install and falls into the class (CCA rate = 20%) pool along with other equipment After Year there will still be class assets remaining in the pool and the half-year rule applies At the end of the project, the equipment can be sold as salvage for $75,000 Initial net working capital (NWC) investment is forecast to be $1.5 million (today) and is expected to decrease by $200,000 in each year from year to year It is estimated that there will be a complete recovery of net working capital in year R&D for this machine has been steep costing $20 million over the past two years and expected additional $5 million in R&D is expected to be incurred in year one before launching the multi-language version outside of the USA The M-phone will be manufactured in China in a manufacturing plant already owned by Motorola and currently vacant The plant cost $4.0 million two years ago and has a current market value of $12.5 million Unfortunately, as consumers buy the Mphone, Motorola expects profits of existing products, will be reduced by $2.5 million annually during the M-phone product life cycle Motorola pays corporate taxes at the marginal rate of 36% and the CFO requires that all projects worldwide earn at least 7% above its weighted average cost of capital In addition you are given the following financial information: Motorola Balance Sheet ( Book Value in $millions) Assets Cash & short-term securities Accounts receivable Inventories Plant & Equipment Total Assets $10 30 70 110 $220 Liabilities & Net Worth Bonds 8% coupon (paid semi-annually), Maturity = 10 years, current YTM = 9% Preferred Stock (par value = $20/share) Common Stock Retained Earnings Total liabilities & net worth Page 14 $40 20 50 110 $220 ADMS3530 3.0 Assignment #2 Other Info: • Preferred stock currently sells for $15/share • Common stock sells for $20/share • There are million common shares outstanding • Preferred stock pays a $2 dividend per share • Beta of common stock is 0.8 • Market risk premium is 10% • Risk-free rate is 6% Should Motorola go ahead with the M-phone project? Solution: Break the problem down into parts: Part A and Part B Part A: Find Motorola’s WACC: WACC Step#1: Find market value of each of the firm’s securities: (i) Bonds (Debt) The bonds must be selling below par value, because the YTM is greater than the coupon rate The price (per $1000 par value) = PV (coupons) + PV (face value) Using your calculator: FV = $1000, PMT = $80/2=40, i = 9/2=4.5%, n = 20, COMP PV PV = -$934.96 The total market value of the bonds is $40 million par value × $935.96 market value per bond $1,000 par value per bond = $37,478,400 million (ii) Preferred Stock: There are $20 book value million/$20 book(par) value per share = 1,000,000 shares of preferred stock selling at $15 per share, for total market value of $15,000,000 million (iii) Common Stock There are million shares of common stock selling at $20/share, for a total market value $60 million WACC Step 2: Calculate proportion of firm’s total market value (V) that each security contributes: Page 15 ADMS3530 3.0 Assignment #2 The capital structure is: Dollars Bonds Preferred Stock Common Stock Total 37.4784 million 15.0 million 60.00 million 112.4784 million Percent 33.21% 13.34% 53.35% 100.0% Step 3: Determine the required rate of return on each security (i) The yield to maturity on debt is rdebt = 9% (ii) The rate on preferred stock is rpreferred = $2/$15 = 133 = 13.3% (iii) The rate on common stock is requity = rf + β(rm – rf) = 6% + × 10% = 14% Step 4: Calculate the weighted-average of these returns: Using the capital structure derived in the previous problem, we can calculate WACC as: WACC = Error!× rdebt + Error!× requity + Error! × rpreferred = 3321 × (1 – 36) × 9% + 5335 × 14% + 1334 × 13.3% = 01913 + 07469 + 01744 = 1116 = 11.16% Part B: Find Motorola’s discount rate = 7% + WACC = 7% + 11.16% = 18.16% use this rate to discount project’s cash flows to find project NPV Ỉ see spreadsheet below for details NPV Motorola Project = 11,487,272 Therefore, Motorola should go ahead with the M-Phone Project Motorola's M-Phone Page 16 ADMS3530 3.0 Assignment #2 Project CCA rate (d) Rate of Return (r) Tax Rate Variable Cost Percentage Initial capital investment (C) Salvage (S) Year 20% 18.16% 36% 35% $ 35,000,000.00 $ 75,000.00 All figures in blue are the given data calculated from Part A of Solution 150,000 $490 $172 250,000 $420 $147 80,000 $350 $123 30,000 $280 $98 $0 $0 Sales Variable costs New R&D expense Fixed costs Reduction in existing sales $73,500,000 -25,725,000 -5,000,000 -3,200,000 -2,500,000 $105,000,000 -36,750,000 $28,000,000 -9,800,000 $8,400,000 -2,940,000 $0 -3,200,000 -2,500,000 -3,200,000 -2,500,000 -3,200,000 -2,500,000 0 Before Tax CFop Taxes After Tax CFop (1) 37,075,000 -13,347,000 $23,728,000 62,550,000 -22,518,000 $40,032,000 12,500,000 -4,500,000 $8,000,000 -240,000 86,400 ($153,600) 0 $0 200,000 200,000 200,000 200,000 700,000 Units/year Price/unit Variable cost/unit Change in NWC (2) -1,500,000 Opp Cost of Land (3) Capital Investment (4) -12,500,000 -35,000,000 Total Cash Flow (1+2+3+4) Discounted Cash Flow PV excluding CCATS -49,000,000 -49,000,000 5,397,108 PV(CCATS) 6,090,163 NPV = 75,000 23,928,000 20,250,508 40,232,000 28,815,798 8,200,000 4,970,527 46,400 23,803   CdT   + r   SdT    r + d   + r  −  r + d   (1 + r ) t        =   11,487,272 Page 17 775,000 336,472 ... -2 5,725,000 -5 ,000,000 -3 ,200,000 -2 ,500,000 $105,000,000 -3 6,750,000 $28,000,000 -9 ,800,000 $8,400,000 -2 ,940,000 $0 -3 ,200,000 -2 ,500,000 -3 ,200,000 -2 ,500,000 -3 ,200,000 -2 ,500,000 0 Before Tax... depreciated straight-line over years to a final value of zero Allergy-free Corp.’s cost of capital is 14% annually and it currently pays no taxes (a) What is the accounting break-even level of sales for... Change in NWC (2) -1 ,500,000 Opp Cost of Land (3) Capital Investment (4) -1 2,500,000 -3 5,000,000 Total Cash Flow (1+2+3+4) Discounted Cash Flow PV excluding CCATS -4 9,000,000 -4 9,000,000 5,397,108