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Unformatted text preview: $724,000/8 Depreciation = $90,500 per year And the accounting breakeven is: QA = ($850,000 + 90,500)/($39 – 23) QA = 58,781 units b. We will use the tax shield approach to calculate the OCF. The OCF is: OCFbase = [(P – v)Q – FC](1 – tc) + tcD OCFbase = [($39 – 23)(75,000) – $850,000](0.65) + 0.35($90,500) OCFbase = $259,175 Now we can calculate the NPV using our basecase projections. There is no salvage value or NWC, so the NPV is: NPVbase = –$724,000 + $259,175(PVIFA15%,8) NPVbase = $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: OCFnew = [($39 – 23)(80,000) – $850,000](0.65) + 0.35($90,500) OCFnew = $311,175 And the NPV is: NPVnew = –$724,000 + $311,175(PVIFA15%,8) NPVnew = $672,342.27 189 So, the change in NPV for every unit change in sales is: ∆ NPV/∆ S = ($439,001.55 – 672,342.27)/(75,000 – 80,000) ∆ NPV/∆ 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. Because 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. 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: OCFnew = [($39 – 24)(75,000) – 850,000](0.65) + 0.35($90,500) OCFnew = $210,425 So, the change in OCF for a $1 change in variable costs is: ∆ OCF/∆ v = ($259,175 – 210,425)/($23 – 24) ∆ OCF/∆ v = –$48,750 If variable costs decrease by $1 then, OCF would increase by $48,750 2. We will use the tax shield approach to calculate the OCF for the best and worstcase scenarios. For the bestcase 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: OCFbest = {[($39)(1.1) – ($23)(0.9)](75,000)(1.1) – $850,000(0.9)}(0.65) + 0.35($90,500) OCFbest = $724,900.00 The bestcase NPV is: NPVbest = –$724,000 + $724,900(PVIFA15%,8) NPVbest = $2,528,859.36 For the worstcase 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 multiply the base case numbers by 1.1, a 10 percent increase. Doing so, we get: OCFworst = {[($39)(0.9) – ($23)(1.1)](75,000)(0.9) – $850,000(1.1)}(0.65) + 0.35($90,500) OCFworst = –$146,100 190 The worstcase NPV is: NPVworst = –$724,000 – $146,100(PVIFA15%,8) NPVworst = –$1,379,597.67 3. We can use the accounting breakeven equation: QA = (FC + D)/(P – v) to solve for the unknown variable in each case. Doing so, we find: (1): QA = 110,500 = ($820,000 + D)/($41 – 30) D = $395,500 (2): QA = 143,806 = ($3.2M + 1.15M)/(P – $56) P = $86.25 (3): QA = 7,835 = ($160,000 + 105,000)/($105 – v) v = $71.18 4. When calculating the financial breakeven point, we express the initial investment as an equivalent annual cost (EAC). Dividing the initial investment by the fiveyear annuity factor, discounted at 12 percent, the EAC of the initial investment is: EAC = Initial Investment / PVIFA12%,5 EAC = $250,000 / 3.60478 EAC = $69,352.43 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) $250,000 = C{[1 – (1/1.12)5 ] / .12} C = $69,352.43 The annual depreciation is the cost of the equipment divided by the economic life, or: Annual depreciation = $250,000 / 5 Annual depreciation = $50,000 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 = [$69,352.43 + $360,000(1 – 0.34) – $50,000(0.34)] / [($25 – 6)(1 – 0.34)] QF = 23,122.20 or about 23,122 units 5. If we purchase the machine today, the NPV is the cost plus the present value of the increased cash flows, so: NPV0 = –$1,800,000 + $340,000(PVIFA12%,10) NPV0 = $121,075.83 191 We should not necessarily purchase the machine today. We would want to purchase the machine when the NPV is the highest. So, we need to calculate the NPV each year. The NPV each year will be the cost plus the present value of the increased cash savings. We must be careful, however. In order to make the correct decision, the NPV for each year must be taken to a common date. We will discount all of the NPVs to today. Doing so, we get: Year 1: NPV1 = [–$1,670,000...
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 Spring '10
 eshmalwi
 Finance, Corporate Finance

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