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Unformatted text preview: C)] / [(P – VC)(1 – tC)] QA = [($0 + 3,200) (1 – 0.30)] / [($10 – 7) (1 – 0.30)] QA = 1,066.67 or about 1,067 units b. When calculating the financial breakeven point, we express the initial investment as an equivalent annual cost (EAC). The initial investment is the $12,000 in licensing fees. Dividing the initial investment by the threeyear annuity factor, discounted at 12 percent, the EAC of the initial investment is: EAC = Initial Investment / PVIFA12%,3 EAC = $12,000 / 2.4018 EAC = $4,996.19 204 Note, 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) $12,000 = C{[1 – (1/1.12)3 ] / .12} C = $4,996.19 Now we can calculate the financial breakeven point. Notice that there are no fixed costs or depreciation. The financial breakeven point for this project is: QF = [EAC + FC(1 – tC) – Depreciation(tC)] / [(P – VC)(1 – tC)] QF = ($4,996.19 + 0 – 0) / [($10 – 7) (.70)] QF = 2,379.14 or about 2,379 units 21. The payoff from taking the lump sum is $12,000, so we need to compare this to the expected payoff from taking one percent of the profit. The decision tree for the movie project is: Big audience $20,000,000 30% Movie is good 10% Script is good Read script Script is bad 90% Don't make movie No profit Make movie Movie is bad 70% Small audience No profit The value of one percent of the profits as follows. There is a 30 percent probability the movie is good, and the audience is big, so the expected value of this outcome is: Value = $20,000,000 × .30 Value = $6,000,000 The value if the movie is good, and has a big audience, assuming the script is good is: Value = $6,000,000 × .10 Value = $600,000 205 This is the expected value for the studio, but the screenwriter will only receive one percent of this amount, so the payment to the screenwriter will be: Payment to screenwriter = $600,000 × .01 Payment to screenwriter = $6,000 The screenwriter should take the upfront offer of $12,000. 22. We can calculate the value of the option to wait as the difference between the NPV of opening the mine today and the NPV of waiting one year to open the mine. The remaining life of the mine is: 60,000 ounces / 7,500 ounces per year = 8 years This will be true no matter when you open the mine. The aftertax cash flow per year if opened today is: CF = 7,500($450) = $3,375,000 So, the NPV of opening the mine today is: NPV = –$14,000,000 + $3,375,000(PVIFA12%,8) NPV = $2,765,784.21 If you open the mine in one year, the cash flow will be either: CFUp = 7,500($500) = $3,750,000 per year CFDown = 7,500($410) = $3,075,000 per year The PV of these cash flows is: Price increase CF = $3,750,000(PVIFA12%,8) = $18,628,649.13 Price decrease CF = $3,075,000(PVIFA12%,8) = $15,275,492.28 So, the NPV is one year will be: NPV = –$14,000,000 + [.60($18,628,649.13) + .40($15,275,492.28)] NPV = $3,287,386.39 And the NPV today is: NPV today = $3,287,386.39 / 1.12 NPV today = $2,935,166.42 So, the value of the option to wait is: Option value = $2,935,166.42 – 2,765,784.21 Option value = $169,382.21 206 23. a. The NPV of the project is sum of the present value of the cash flows generated by the project. The cash flows from this project are an annuity, so the NPV is: NPV = –$84,000,000 + $22,000,000(PVIFA19%,10) NPV = $11,456,567.07 b. The company should abandon the project if the PV of the revised cash flows for the next nine years is less than the project’s aftertax salvage value. Since the option to abandon the project occurs in year 1, discount the revised cash flows to year 1 as well. To determine the level of expected cash flows below which the company should abandon the project, calculate the equivalent annual cash flows the project must earn to equal the aftertax salvage value. We will solve for C2, the revised cash flow beginning in year 2. So, the revised annual cash flow below which it makes sense to abandon the project is: Aftertax salvage value = C2(PVIFA19%,9) $30,000,000 = C2(PVIFA19%,9) C2 = $30,000,000 / PVIFA19%,9 C2 = $7,205,766.07 24. a. The NPV of the project is sum of the present value of the cash flows generated by the project. The annual cash flow for the project is the number of units sold times the cash flow per unit, which is: Annual cash flow = 15($410,000) Annual cash flow = $6,150,000 The cash flows from this project are an annuity, so the NPV is: NPV = –$17,000,000 + $6,150,000(PVIFA25%,5) NPV = –$460,928.00 b. The company will abandon the project if unit sales are not revised upward. If the unit sales are revised upward, the aftertax cash flows for the project over the last four years will be: New annual cash flow = 20($410,000) New annual cash flow = $8,200,000 The NPV of the project will be the initial cost, plus the expected cash flow in year one based on 15 unit sales projection, plus the expected value of abandonment, plus the expected value of expansion. We need to remember that the abandonment value occurs in year 1, and the present value of the expansion cash flows are in year one, so each of these must be discounted back to today. So, the project NPV under the abandonment or expansion scenario is: NPV = –$17,000,000 + $6,150,000 / 1.25 + .50($11,000,000) / 1.25 + [.50($8,200,000)(PVIFA25%,4)] / 1.25 NPV = $66,048.00 207 25. To calculate the unit sales for each scenario, we multiply the market sales times the company’s market share. We can then use the q...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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