Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

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Unformatted text preview: 0 194 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 = [$97,678.02 + $185,000(1 – 0.34) – $78,000(0.34)] / [($60 – 14) (1 – 0.34)] QF = 6,365.55 or about 6,366 units Intermediate 11. a. At the accounting breakeven, the IRR is zero percent since the project recovers the initial investment. The payback period is N years, the length of the project since the initial investment is exactly recovered over the project life. The NPV at the accounting breakeven is: NPV = I [(I/N)(PVIFAR%,N) – 1] b. c. At the cash breakeven level, the IRR is –100 percent, the payback period is negative, and the NPV is negative and equal to the initial cash outlay. The definition of the financial breakeven is where the NPV of the project is zero. If this is true, then the IRR of the project is equal to the required return. It is impossible to state the payback period, except to say that the payback period must be less than the length of the project. Since the discounted cash flows are equal to the initial investment, the undiscounted cash flows are greater than the initial investment, so the payback must be less than the project life. 12. Using the tax shield approach, the OCF at 90,000 units will be: OCF = [(P – v)Q – FC](1 – tC) + tC(D) OCF = [($54 – 42)(90,000) – 185,000](0.66) + 0.34($380,000/4) OCF = $623,000 We will calculate the OCF at 91,000 units. The choice of the second level of quantity sold is arbitrary and irrelevant. No matter what level of units sold we choose, we will still get the same sensitivity. So, the OCF at this level of sales is: OCF = [($54 – 42)(91,000) – 185,000](0.66) + 0.34($380,000/4) OCF = $630,920 The sensitivity of the OCF to changes in the quantity sold is: Sensitivity = ∆ OCF/∆ Q = ($623,000 – 630,920)/(90,000 – 91,000) ∆ OCF/∆ Q = +$7.92 OCF will increase by $7.92 for every additional unit sold. 13. a. The base-case, best-case, and worst-case values are shown below. Remember that in the bestcase, unit sales increase, while costs decrease. In the worst-case, unit sales, and costs increase. Scenario Base Best Worst Unit sales 240 264 216 Variable cost $19,500 $17,550 $21,450 Fixed costs $830,000 $747,000 $913,000 195 Using the tax shield approach, the OCF and NPV for the base case estimate are: OCFbase = [($25,000 – 19,500)(240) – $830,000](0.65) + 0.35($960,000/4) OCFbase = $402,500 NPVbase = –$960,000 + $402,500(PVIFA15%,4) NPVbase = $189,128.79 The OCF and NPV for the worst case estimate are: OCFworst = [($25,000 – 21,450)(216) – $913,000](0.65) + 0.35($960,000/4) OCFworst = –$11,030 NPVworst = –$960,000 – $11,030(PVIFA15%,4) NPVworst = –$991,490.41 And the OCF and NPV for the best case estimate are: OCFbest = [($25,000 – 17,550)(264) – $747,000](0.65) + 0.35($960,000/4) OCFbest = $876,870 NPVbest = –$960,000 + $876,870(PVIFA15%,4) NPVbest = $1,543,444.88 b. To calculate the sensitivity of the NPV to changes in fixed costs, we choose another level of fixed costs. We will use fixed costs of $840,000. The OCF using this level of fixed costs and the other base case values with the tax shield approach, we get: OCF = [($25,000 – 19,500)(240) – $840,000](0.65) + 0.35($960,000/4) OCF = $396,000 And the NPV is: NPV = –$960,000 + $396,000(PVIFA15%,4) NPV = $170,571.43 The sensitivity of NPV to changes in fixed costs is: ∆ NPV/∆ FC = ($189,128.79 – 170,571.43)/($830,000 – 840,000) ∆ NPV/∆ FC = –$1.856 For every dollar FC increase, NPV falls by $1.86. 196 c. The accounting breakeven is: QA = (FC + D)/(P – v) QA = [$830,000 + ($960,000/4)]/($25,000 – 19,500) QA = 194.55 or about 195 units 14. The marketing study and the research and development are both sunk costs and should be ignored. We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be: Sales New clubs Exp. clubs Cheap clubs $750 × 55,000 = $41,250,000 $1,100 × (–12,000) = –13,200,000 $400 × 15,000 = 6,000,000 $34,050,000 For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets any more, we will save these variable costs, which is an inflow. So: Var. costs New clubs Exp. clubs Cheap clubs –$390 × 55,000 = –$21,450,000 –$620 × (–12,000) = 7,440,000 –$210 × 15,000 = –3,150,000 –$17,160,000 The pro forma income statement will be: Sales Variable costs Fixed costs Depreciation EBT Taxes Net income $34,050,000 17,160,000 8,100,000 2,700,000 $6,090,000 2,436,000 $3,654,000 Using the bottom up OCF calculation, we get: OCF = NI + Depreciation = $3,654,000 + 2,700,000 OCF = $6,354,000 197 So, the payback period is: Payback period = 3 + $1,238,000/$6,345,000 Payback period = 3.195 years The NPV is: NPV = –$18,900,000 – 1...
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