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Unformatted text preview: roject using nominal cash flows or real cash flows. Either method will result in the same NPV. For this problem, we will calculate the NPV using both nominal and real cash flows. The initial investment in either case is $150,000 since it will be spent today. We will begin with the nominal cash flows. The revenues and production costs increase at different rates, so we must be careful to increase each at the appropriate growth rate. The nominal cash flows for each year will be: Year 0 Revenues Costs Depreciation EBT Taxes Net income OCF Capital spending Total cash flow –$150,000 –$150,000 Year 4 $81,033.75 23,820.32 21,428.57 $35,784.86 12,166.85 $23,618.01 $45,046.58 $40,285.71 Year 5 $85,085.44 25,249.54 21,428.57 $38,407.33 13,058.49 $25,348.84 $46,777.41 $41,803.71 Year 6 $89,339.71 26,764.51 21,428.57 $41,146.63 13,989.85 $27,156.77 $48,585.34 $43,389.69 Year 7 $93,806.69 28,370.38 21,428.57 $44,007.74 14,962.63 $29,045.11 $50,473.68 Year 1 $70,000.00 $20,000.00 21,428.57 $28,571.43 9,714.29 $18,857.14 $40,285.71 Year 2 $73,500.00 21,200.00 21,428.57 $30,871.43 10,496.29 $20,375.14 $41,803.71 Year 3 $77,175.00 22,472.00 21,428.57 $33,274.43 11,313.31 $21,961.12 $43,389.69 Revenues Costs Depreciation EBT Taxes Net income OCF Capital spending Total cash flow $45,046.58 $46,777.41 $48,585.34 $50,473.68 Now that we have the nominal cash flows, we can find the NPV. We must use the nominal required return with nominal cash flows. Using the Fisher equation to find the nominal required return, we get: (1 + R) = (1 + r)(1 + h) (1 + R) = (1 + .08)(1 + .05) R = .1340 or 13.40% 160 So, the NPV of the project using nominal cash flows is: NPV = –$150,000 + $40,285.71 / 1.1340 + $41,803.71 / 1.13402 + $43,389.69 / 1.13403 + $45,046.58 / 1.13404 + $46,777.41 / 1.13405 + $48,585.34 / 1.13406 + $50,473.68 / 1.13407 NPV = $43,748.88 We can also find the NPV using real cash flows and the real required return. This will allow us to find the operating cash flow using the tax shield approach. Both the revenues and expenses are growing annuities, but growing at different rates. This means we must find the present value of each separately. We also need to account for the effect of taxes, so we will multiply by one minus the tax rate. So, the present value of the aftertax revenues using the growing annuity equation is: PV of aftertax revenues = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}(1 – tC) PV of aftertax revenues = $70,000{[1/(.134 – .05)] – [1/(.134 –.05)] × [(1 + .05)/(1 + .134)]7}(1–.34) PV of aftertax revenues = $229,080.28 And the present value of the aftertax costs will be: PV of aftertax costs = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}(1 – tC) PV of aftertax costs = $20,000{[1/(.134 – .06)] – [1/(.134 – .06)] × [(1 + .06)/(1 + .134)]7}(1 – .34) PV of aftertax costs = $67,156.07 Now we need to find the present value of the depreciation tax shield. The depreciation amount in the first year is a real value, so we can find the present value of the depreciation tax shield as an ordinary annuity using the real required return. So, the present value of the depreciation tax shield will be: PV of depreciation tax shield = ($150,000/7)(.34)(PVIFA13.40%,7) PV of depreciation tax shield = $31,824.67 Using the present value of the real cash flows to find the NPV, we get: NPV = Initial cost + PV of revenues – PV of costs + PV of depreciation tax shield NPV = –$150,000 + $229,080.28 – 67,156.07 + 31,824.67 NPV = $43,748.88 Notice, the NPV using nominal cash flows or real cash flows is identical, which is what we would expect. 23. Here we have a project in which the quantity sold each year increases. First, we need to calculate the quantity sold each year by increasing the current year’s quantity by the growth rate. So, the quantity sold each year will be: Year 1 quantity = 6,000 Year 2 quantity = 6,000(1 + .08) = 6,480 Year 3 quantity = 6,480(1 + .08) = 6,998 Year 4 quantity = 6,998(1 + .08) = 7,558 Year 5 quantity = 7,558(1 + .08) = 8,163 161 Now we can calculate the sales revenue and variable costs each year. The pro forma income statements and operating cash flow each year will be: Year 0 Revenues Fixed costs Variable costs Depreciation EBT Taxes Net income OCF Capital spending NWC –$145,000 –28,000 Year 1 $288,000.0 0 80,000.00 120,000.00 29,000.00 $59,000.00 20,060.00 $38,940.00 $67,940.00 Year 2 $311,040.0 0 80,000.00 129,600.00 29,000.00 $72,440.00 24,629.60 $47,810.40 $76,810.40 Year 3 $335,923.2 0 80,000.00 139,968.00 29,000.00 $86,955.20 29,564.77 $57,390.43 $86,390.43 Year 4 $362,797.0 6 80,000.00 151,165.44 29,000.00 $102,631.6 2 34,894.75 $67,736.87 $96,736.87 Year 5 $391,820.8 2 80,000.00 163,258.68 29,000.00 $119,562.1 5 40,651.13 $78,911.02 $107,911.0 2 28,000 $135,911.0 2 Total cash flow –$173,000.00 $67,940.00 $76,810.40 $86,390.43 $96,736.87 So, the NPV of the project is: NPV = –$173,000 + 67,940 / 1.25 + $76,810.40 / 1.252 + $86,390.43 / 1.253 + $96,736.87 / 1.254 + $135,911.02 / 1.255 NPV = $58,901.30 We could also have calculated the cash flows using the tax shield app...
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 Spring '10
 eshmalwi
 Finance, Corporate Finance

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