chap010_sm

# Fundamentals of Corporate Finance + Standard & Poor's Educational Version of Market Insight

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CHAPTER 10 A Project is Not a Black Box Answers to Practice Questions 1. Year 0 Years 1-10 Investment ¥15 B 1. Revenue ¥44.000 B 2. Variable Cost 39.600 B 3. Fixed Cost 2.000 B 4. Depreciation 1.500 B 5. Pre-tax Profit ¥0.900 B 6. Tax @ 35% 0.315 B 7. Net Operating Profit ¥0.585 B 8. Operating Cash Flow ¥2.085 B 2. The spreadsheets show the following results: NPV Pessimistic Expected Optimistic Market Size 0.2 6.2 12.2 Market Share -11.8 6.2 24.2 Unit Price -23.8 6.2 16.2 Unit Variable Cost -13.8 6.2 16.2 Fixed Cost -1.8 6.2 14.2 The principal uncertainties are market share, unit price, and unit variable cost. 3. a. Year 0 Years 1-10 Investment ¥30 B 1. Revenue ¥37.500 B 2. Variable Cost 26.000 3. Fixed Cost 3.000 4. Depreciation 3.000 5. Pre-tax Profit (1-2-3-4) ¥5.500 6. Tax 1.925 7. Net Operating Profit (5-6) ¥3.575 8. Operating Cash Flow (4+7) 6.575 NPV = + ¥10.40 B 80 ¥2.19B 1.10 ¥2.085B ¥15B NPV 10 1 t t - = + - = =

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b. (See chart on next page.) Inflows Outflows Unit Sales Revenues Investment V. Costs F. Cost Taxes PV PV NPV (000’s) Yrs 1-10 Yr 0 Yr 1-10 Yr 1-10 Yr 1-10 Inflows Outflows 0 0.00 30.00 0.00 3.00 -2.10 0.0 -35.5 -35.5 100 37.50 30.00 26.00 3.00 1.93 230.4 -220.0 10.4 200 75.00 30.00 52.00 3.00 5.95 460.8 -404.5 56.3 Note that the break-even point can be found algebraically as follows: NPV = -Investment + [(PVA 10/10% ) × (t × Depreciation)] + [Quantity × (Price – V.Cost) – F.Cost] × (1 – t) × (PVA 10/10% ) Set NPV equal to zero and solve for Q: Proof: 1. Revenue ¥29.00 B 2. Variable Cost 20.11 3. Fixed Cost 3.00 4. Depreciation 3.00 5. Pre-tax Profit ¥2.89 B 6. Tax 1.01 7. Net Profit ¥1.88 8. Operating Cash Flow ¥4.88 0.01 30 29.99 30 (1.10) 4.88 NPV 10 1 t t - = - = - = = 81 V P F t) (1 V) (P ) (PVA t) D (PVA I Q 10/10% 10/10% - + - × - × × × - = 260,000 375,000 000 3,000,000, (0.65) 260,000) (375,000 (6.144567) 461 6,451,795, ,000 30,000,000 - + × - × - = 77,356 26,087 51,269 115,000 000 3,000,000, 459,306 ,539 23,548,204 = + = + = ) rounding to due difference (
c. The break-even point is the point where the present value of the cash flows, including the opportunity cost of capital, yields a zero NPV. d. To find the level of costs at which the project would earn zero profit, write the equation for net profit, set net profit equal to zero, and solve for variable costs: Net Profit = (R – VC – FC - D) × (1 – t) 0 = (37.5 – VC – 3.0 – 1.5) × (0.65) VC = 33.0 This will yield zero profit. Next, find the level of costs at which the project would have zero NPV. Using the data in Table 10.1, the equivalent annual cash flow yielding a zero NPV would be: ¥15 B/PVA 10/10% = ¥2.4412 B 82 0 50 100 150 200 250 300 350 400 450 500 0 100 200 Units (000's) Break-Even Break-Even NPV = 0 PV Inflows PV Outflows

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If we rewrite the cash flow equation and solve for the variable cost: NCF = [(R – VC – FC – D) × (1 – t)] + D 2.4412 = [(37.5 – VC – 3.0 – 1.5) × (0.65)] + 1.5 VC = 31.55 This will yield NPV = 0, assuming the tax credits can be used elsewhere in
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chap010_sm - CHAPTER 10 A Project is Not a Black Box...

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