Chapter_9 - Chapter 9:Risk Analysis Real Options and...

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Answers to End–of–Chapter Problems 9-1 Chapter 9 :Risk Analysis, Real Options, and Capital Budgeting 9.1 a . To calculate the accounting breakeven, we first need to find the depreciation for each year. The depreciation is: Depreciation = $724,000 / 8 Depreciation = $90,500 per year And the accounting breakeven is: Q A = ($850,000 + $90,500) / ($39 – $23) Q A = 58,781 units b. We will use the tax shield approach to calculate the Operating Cash Flow, OCF. The OCF is: OCF base = [(Price – Variable cost) × Sales units – Fixed cost] × (1 – T c ) + T c × Depreciation OCF base = [($39 – $23) × 75,000 – $850,000] × (0.65) + 0.35 × ($90,500) OCF base = $259,175 Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so the NPV is: NPV base = –$724,000 + $259,175 × 8 % 15 Α NPV base = $439,001.55 To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 80,000 units. The NPV at this sales level is: OCF new = [($39 – $23) × (80,000) – $850,000] × (0.65) + 0.35 × ($90,500) OCF new = $311,175 And the NPV is: NPV new = – $724,000 + $311,175 × 8 % 15 Α NPV new = $672,342.27 So, the change in NPV for every unit change in sales is: Δ NPV/ Δ S = ($439,001.55 – $672,342.27) / (75,000 – 80,000) Δ NPV/ Δ S = $46.668 If sales were to drop by 500 units, then NPV would drop by: NPV drop = $46.668 × (500) = $23,334.07 You may wonder why we chose 80,000 units. It doesn’t matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same.
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Answers to End–of–Chapter Problems 9-2 c. To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a variable cost of $24. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use. So, using the tax shield approach, the OCF at a variable cost of $24 is: OCF new = [($39 – $24) × (75,000) – $850,000] × (0.65) + 0.35 × ($90,500) OCF new = $210,425 So, the decrease in OCF for a $1 increase in variable costs is: Δ OCF/ Δ v = ($259,175 – $210,425) / ($23 – $24) Δ OCF/ Δ v = –$48,750 If variable costs decrease by $1 then, OCF would increase by $48,750. 9.2 We will use the tax shield approach to calculate the OCF for the best- and worst-case scenarios. For the best- case scenario, the price and quantity increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. Doing so, we get: OCF best = {[($39) × (1.1) – ($23) × (0.9)] × (75,000) × (1.1) – $850,000 × (0.9)} × (0.65) + 0.35 × ($90,500) OCF best = $724,900.00 The best-case NPV is: NPV best = –$724,000 + $724,900 × 8 % 15 Α NPV best = $2,528,859.36 For the worst-case scenario, the price and quantity decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. The variable and fixed costs both increase by 10 percent, so we will
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