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Solutions to HW 2 #5-8 ( 1-4 are same as for HW2a) 5. L.J.'s Toys Inc. just purchased a $200,000 machine to produce toy cars. The machine will be fully depreciated by the straight-line method over its five-year economic life. Each toy sells for $25. The variable cost per toy is $5, and the firm incurs fixed costs of $350,000 each year. The corporate tax rate for the company is 25 percent. The appropriate discount rate is 12 percent. What is the financial break-even point for the project? When calculating the financial breakeven point, we express the initial investment as an equivalent annual cost (EAC). Dividing the initial investment by the seven-year annuity factor, discounted at 12 percent, the EAC of the initial investment is: EAC = Initial Investment / PVIFA12%,5 EAC = $200,000 / 3.60478 EAC = $55,481.95 Note that this calculation solves for the annuity payment with the initial investment as the present value of the annuity. In other words: PVA = C({1 – [1/(1 + R)]t } / R) $200,000 = C{[1 – (1/1.12)5 ] / .12} C = $55,481.95 The annual depreciation is the cost of the equipment divided by the economic life, or: Annual depreciation = $200,000 / 5 Annual depreciation = $40,000 Now we can calculate the financial breakeven point. The financial breakeven point for this project is: QF = [EAC + FC(1 – tC) – Depreciation(tC)] / [(P – VC)(1 – tC)] QF = [$55,481.95 + $350,000(.75) – $40,000(0.25)] / [($25 – 5) (.25)] QF = 20,532.13 or about 20,532 units 6. Ang Electronics, Inc., has developed a new DVDR. If the DVDR is successful, the present value of the payoff (at the time the product is brought to market) is $20 million. If the DVDR fails, the present value of the payoff is $5 million. If the product goes directly to market, there is a 50 percent chance of success. Alternatively, Ang can delay the launch by one year and spend $2 million to test market the DVDR. Test marketing would allow the firm to improve the product and increase the probability of success to 75 percent. The appropriate discount rate is 15 percent. Required: (a) Calculate the NPV We need to calculate the NPV of the two options, go directly to market now, or utilize test marketing first. The NPV of going directly to market now is: NPV = CSuccess (Prob. of Success) + CFailure (Prob. of Failure) NPV = $20,000,000(0.50) + $5,000,000(0.50) NPV = $12,500,000 Now we can calculate the NPV of test marketing first. Test marketing requires a $2 million cash outlay. Choosing the test marketing option will also delay the launch of the product by one year. Thus, the expected payoff is delayed by one year and must be discounted back to year 0. NPV= C0 + {[CSuccess (Prob. of Success)] + [CFailure (Prob. of Failure)]} / (1 + R)t NPV = –$2,000,000 + {[$20,000,000 (0.75)] + [$5,000,000 (0.25)]} / 1.15 NPV = $12,130,434.78 The company should go directly to market with the product since that option has the highest expected payoff. 7. We are examining a new project. We expect to sell 7,000 units per year at $60 net cash flow apiece for the next 10 years. In other words, the annual operating cash flow is projected to be $60 × 7,000 =$420,000. The relevant discount rate is 16 percent, and the initial investment required is $1,800,000. Suppose you think it is likely that expected sales will be revised upwards to 9,000 units if the first year is a success and revised downwards to 4,000 units if the first year is not a success, which means the project will be abandoned for $1,400,000. (Do not include the dollar sign ($). Round your answer to 2 decimal places. For example 3.16) Requirement 1: If success and failure are equally likely, what is the NPV of the project? Consider the possibility of abandonment in answering If we couldn't abandon the project, the present value of the future cash flows when the quantity is 4,000 will be: PV future CFs = $60(4,000)(PVIFA16%,9) PV future CFs = $1,105,570.53 The gain from the option to abandon is the abandonment value minus the present value of the cash flows if we cannot abandon the project, so: Gain from option to abandon = $1,400,000 – 1,105,570.53 Gain from option to abandon = $294,429.47 We need to find the value of the option to abandon times the likelihood of abandonment. So, the value of the option to abandon today is: Option value = (.50)($294,429.47)/1.16 Option value = $126,909.25 8. A firm is considering an investment in a new machine with a price of $32 million to replace its existing machine. The current machine has a book value of $8 million, and a market value of $9 million. The new machine is expected to have a four-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $5 million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of $500,000 in net working capital. The required return on the investment is 10 percent, and the tax rate is 39 percent. Replacement decision analysis is the same as the analysis of two competing projects, in this case, keep the current equipment, or purchase the new equipment. We will consider the purchase of the new machine first Purchase new machine: The initial cash outlay for the new machine is the cost of the new machine, plus the increased net working capital. So, the initial cash outlay will be: Purchase new machine -$ 32,000,000 Net working capital -500,000 Total -$ 32,500,000 Next, we can calculate the operating cash flow created if the company purchases the new machine. The saved operating expense is an incremental cash flow, so using the pro forma income statement, and adding depreciation to net income, the operating cash flow created by purchasing the new machine each year will be: Operating expense $ 5,000,000 Depreciation 8,000,000 EBT -$ 3,000,000 - Taxes 1,170,000 Net income -$ 1,830,000 OCF $ 6,170,000 So, the NPV of purchasing the new machine, including the recovery of the net working capital, is: NPV = -$32,500,000 + $6,170,000(PVIFA10%,4) + $500,000 / 1.104 NPV = -$12,600,423.47 And the IRR is: 0 = -$32,500,000 + $6,170,000(PVIFAIRR,4) + $500,000 / (1 + IRR)4 Using a spreadsheet or financial calculator, we find the IRR is: IRR = -9.38% Now we can calculate the decision to keep the old machine: Keep old machine: The initial cash outlay for the new machine is the market value of the old machine, including any potential tax. The decision to keep the old machine has an opportunity cost, namely, the company could sell the old machine. Also, if the company sells the old machine at its current value, it will incur taxes. Both of these cash flows need to be included in the analysis. So, the initial cash flow of keeping the old machine will be: Keep machine -$ 9,000,000 Taxes 390,000 Total -$ 8,610,000 Next, we can calculate the operating cash flow created if the company keeps the old machine. There are no incremental cash flows from keeping the old machine, but we need to account for the cash flow effects of depreciation. The income statement, adding depreciation to net income to calculate the operating cash flow will be: Depreciation $ 2,000,000 EBT -$ 2,000,000 Taxes -780,000 Net income -$ 1,220,000 OCF $ 780,000 So, the NPV of the decision to keep the old machine will be: NPV = -$8,610,000 + $780,000(PVIFA10%,4) NPV = -$6,137,504.95 And the IRR is: 0 = -$8,610,000 + $780,000(PVIFAIRR,4) Using a spreadsheet or financial calculator, we find the IRR is: IRR = 0% The company should purchase the new machine since it has a greater NPV.

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posted: | 4/24/2011 |

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