Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

# Equipment the npv is npv 11300000 4019000pvifa164

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Unformatted text preview: uantity sold to find the revenue each year, and the variable costs each year. After doing these calculations, we will construct the pro forma income statement for each scenario. We can then find the operating cash flow using the bottom up approach, which is net income plus depreciation. Doing so, we find: Pessimistic 27,300 \$3,822,000.0 0 2,784,600.00 1,015,000.00 366,666.67 –\$344,266.67 –137,706.67 –\$206,560.00 \$160,106.67 Expected 37,500 \$5,437,500.0 0 3,675,000.00 950,000.00 350,000.00 \$462,500.00 185,000.00 \$277,500.00 \$627,500.00 Optimistic 46,200 \$6,930,000.0 0 4,342,800.00 900,000.00 333,333.33 \$1,353,866.6 7 541,546.67 \$812,320.00 \$1,145,653.3 3 Units per year Revenue Variable costs Fixed costs Depreciation EBT Tax Net income OCF Note that under the pessimistic scenario, the taxable income is negative. We assumed a tax credit in the case. Now we can calculate the NPV under each scenario, which will be: NPVPessimistic = –\$1,600,000 + \$160,106.67(PVIFA13%,6) NPV = –\$1,559,965.63 NPVExpected = –\$2,100,000 +\$627,500(PVIFA13%,6) NPV = \$408,462.49 NPVOptimistic = –\$2,000,000 +\$1,145,653.33(PVIFA13%,6) NPV = \$2,579,806.24 The NPV under the pessimistic scenario is negative, but the company should probably accept the project. Challenge 26. a. Using the tax shield approach, the OCF is: OCF = [(\$245 – 220)(55,000) – \$520,000](0.62) + 0.38(\$1,700,000/5) OCF = \$659,300.00 And the NPV is: NPV = –\$1,700,000 – 600,000 + \$659,300(PVIFA13%,5) + [\$600,000 + 300,000(1 – .38)]/1.135 NPV = \$445,519.88 208 209 b. In the worst-case, the OCF is: OCFworst = {[(\$245)(0.9) – 220](55,000) – \$520,000}(0.62) + 0.38(\$1,955,000/5) OCFworst = –\$156,770 And the worst-case NPV is: NPVworst = –\$1,955,000 – 600,000(1.05) –\$156,770(PVIFA13%,5) + [\$600,000(1.05) + 300,000(0.85)(1 – .38)]/1.135 NPVworst = –\$2,708,647.24 The best-case OCF is: OCFbest = {[\$245(1.1) – 220](55,000) – \$520,000}(0.62) + 0.38(\$1,445,000/5) OCFbest = \$1,475,370 And the best-case NPV is: NPVbest = – \$1,445,000 – \$600,000(0.95) + \$1,475,370(PVIFA13%,5) + [\$600,000(0.95) + 300,000(1.15)(1 – .38)]/1.135 NPVbest = \$3,599,687.00 27. To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 56,000. The OCF at this level of sales is: OCF = [(\$245 – 220)(56,000) – \$520,000](0.62) + 0.38(\$1,700,000/5) OCF = \$674,800 The sensitivity of changes in the OCF to quantity sold is: ∆ OCF/∆ Q = (\$659,300 – 674,800)/(55,000 – 56,000) ∆ OCF/∆ Q = +\$15.50 The NPV at this level of sales is: NPV = –\$1,700,000 – 600,000 + \$674,800(PVIFA13%,5) + [\$600,000 + 300,000(1 – .38)]/1.135 NPV = \$500,036.96 And the sensitivity of NPV to changes in the quantity sold is: ∆ NPV/∆ Q = (\$445,519.88 – 500,036.96))/(55,000 – 56,000) ∆ NPV/∆ Q = +\$54.52 You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV changes \$54.52 for every unit sale, so we can divide the NPV for 55,000 units by the sensitivity to get a change in quantity. Doing so, we get: \$445,519.88 = \$54.52 (∆ Q) ∆ Q = 8,172 210 For a zero NPV, sales would have to decrease 8,172 units, so the minimum quantity is: QMin = 55,000 – 8,172 QMin = 46,828 28. We will use the bottom up approach to calculate the operating cash flow. Assuming we operate the project for all four years, the cash flows are: Year Sales Operating costs Depreciation EBT Tax Net income +Depreciation Operating CF Change in NWC Capital spending Total cash flow 0 1 \$7,350,000 2,400,000 2,500,000 \$2,450,000 931,000 \$1,519,000 2,500,000 \$4,019,000 0 0 \$4,019,000 2 \$7,350,000 2,400,000 2,500,000 \$2,450,000 931,000 \$1,519,000 2,500,000 \$4,019,000 0 0 \$4,019,000 3 \$7,350,000 2,400,000 2,500,000 \$2,450,000 931,000 \$1,519,000 2,500,000 \$4,019,000 0 0 \$4,019,000 4 \$7,350,000 2,400,000 2,500,000 \$2,450,000 931,000 \$1,519,000 2,500,000 \$4,019,000 \$1,300,000 0 \$5,319,000 –\$1,300,000 –10,000,000 –\$11,300,000 There is no salvage value for the equipment. The NPV is: NPV = –\$11,300,000 + \$4,019,000(PVIFA16%,4) + \$1,300,000/1.164 NPV = \$663,866.41 The cash flows if we abandon the project after one year are: Year Sales Operating costs Depreciation EBT Tax Net income +Depreciation Operating CF Change in NWC Capital spending Total cash flow 0 1 \$7,350,000 2,400,000 2,500,000 \$2,450,000 931,000 \$1,519,000 2,500,000 \$4,019,000 \$1,300,000 7,066,000 \$12,385,000 –\$1,300,000 –10,000,000 –\$11,300,000 211 The book value of the equipment is: Book value = \$10,000,000 – (1)(\$10,000,000/4) Book value = \$7,500,000 So the taxes on the salvage value will be: Taxes = (\$7,500,000 – 6,800,000)(.38) Taxes = \$266,000 This makes the aftertax salvage value: Aftertax salvage value = \$6,800,000 + 266,000 Aftertax salvage value = \$7,066,000 The NPV if we abandon the project after one year is: NPV = –\$11,300,000 + \$12,385,000/1.16 NPV = –\$623,275.86 If we abandon the project after two years, the cash flows are: Year Sales Operating costs Depreciation EBT Tax Net income +Depreciation Operating CF Change in NWC Capital spending Total cash flow 0 1 \$7,350,000...
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## This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of Texas-Tyler.

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