CH10

# 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 ¥44.00 B 2. Variable Cost 39.60 B 3. Fixed Cost 2.00 B 4. Depreciation 1.50 B 5. Pre-tax Profit ¥0.90 B 6. Tax @ 50% 0.45 B 7. Net Operating Profit ¥0.45 B 8. Operating Cash Flow ¥1.95 B 2. Following the calculations in Section 10.1 of the text, we find: NPV Pessimistic Expected Optimistic Market Size -1.2 3.4 8.0 Market Share -10.4 3.4 17.3 Unit Price -19.6 3.4 11.1 Unit Variable Cost -11.9 3.4 11.1 Fixed Cost -2.7 3.4 9.6 The principal uncertainties appear to be market share, unit price, and unit variable cost. 3. a. Year 0 Years 1-10 Investment ¥30 B 1. Revenue ¥37.5 B 2. Variable Cost 26.0 3. Fixed Cost 3.0 4. Depreciation 3.0 5. Pre-tax Profit (1-2-3-4) ¥5.5 6. Tax 2.75 7. Net Operating Profit (5-6) ¥2.75 8. Operating Cash Flow (4+7) 5.75 Net cash flow - ¥30 B + ¥5.33 B 90 ¥3.02B 1.10 ¥1.95B ¥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 -3.00 0.0 -30.0 -30.0 100 37.50 30.00 26.00 3.00 2.75 230.4 -225.1 5.3 200 75.00 60.00 52.00 3.00 7.00 460.8 -441.0 19.8 Note that the break-even point can be found algebraically as follows: NPV = -Investment + [PV × (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 ¥31.8 B 2. Variable Cost 22.1 3. Fixed Cost 3.0 4. Depreciation 3.0 5. Pre-tax Profit ¥3.7 B 6. Tax 1.85 7. Net Profit ¥1.85 8. Operating Cash Flow ¥4.85 V P F t) (1 V) (P ) (PVA t) D (PV I Q 10/10% - + - × - × × × - = 260,000 375,000 000 3,000,000, (0.5) 260,000) (375,000 (6.144567) 659 9,216,850, ,000 30,000,000 - + × - × - = 84,910.7 26,087.0 58,823.7 115,000 000 3,000,000, 353,313 ,342 20,783,149 = + = + =
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) × (0.5) 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 92 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) × (0.5)] + 1.5 VC = 31.12 This will yield NPV = 0, assuming the tax credits can be used elsewhere in the company. 4. If Rustic replaces now rather than in one year, several things happen: i. It incurs the equivalent annual cost of the \$10 million capital investment. ii. It reduces manufacturing costs. iii. It earns a return for 1 year on the \$1 million salvage value. For example, for the “Expected” case, analyzing “Sales” we have (all dollar figures in millions): i. The economic life of the new machine is expected to be 10 years, so the equivalent annual cost of the new machine is: 10/5.6502 = 1.77 ii. The reduction in manufacturing costs is: (0.5) × (4) = 2.00 iii. The return earned on the salvage value is: (0.12) × (1) = 0.12 Thus, the equivalent annual cost savings is: -1.77 + 2.0 + 0.12 = 0.35
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