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Unformatted text preview: lation. This means the cash flows each year are equal to net income. There is also no initial cash outlay, so the NPV is the present value of the future aftertax cash flows. The NPV of the project is: NPV = (PVRevenue – PVLabor costs – PVOther costs – PVLease payments)(1 – tC) NPV = ($4,245,283.02 – 2,358,490.57 – 471,698.11 – 147,405.66)(1 – .34) NPV = $836,674.53 Alternatively, we could have solved this problem by expressing everything in nominal terms. This approach yields the same answer as given above. However, in this case, the computation would have been impossible. The reason is that we are dealing with growing perpetuities. In other problems, when calculating the NPV of nominal cash flows, we could simply calculate the nominal cash flow each year since the cash flows were finite. Because of the perpetual nature of the cash flows in this problem, we cannot calculate the nominal cash flows each year until the end of the project. When faced with two alternative approaches, where both are equally correct, always choose the simplest one. 181 36. We are given the real revenue and costs, and the real growth rates, so the simplest way to solve this problem is to calculate the NPV with real values. While we could calculate the NPV using nominal values, we would need to find the nominal growth rates, and convert all values to nominal terms. The real labor costs will increase at a real rate of two percent per year, and the real energy costs will increase at a real rate of three percent per year, so the real costs each year will be: Year 1 $16.75 $4.35 Year 2 $17.09 $4.48 Year 3 $17.43 $4.61 Year 4 $17.78 $4.75 Real labor cost each year Real energy cost each year Remember that the depreciation tax shield also affects a firm’s aftertax cash flows. The present value of the depreciation tax shield must be added to the present value of a firm’s revenues and expenses to find the present value of the cash flows related to the project. The depreciation the firm will recognize each year is: Annual depreciation = Investment / Economic Life Annual depreciation = $175,000,000 / 4 Annual depreciation = $43,750,000 Depreciation is a nominal cash flow, so to find the real value of depreciation each year, we discount the real depreciation amount by the inflation rate. Doing so, we find the real depreciation each year is: Year 1 real depreciation = $43,750,000 / 1.05 = $41,666,666.67 Year 2 real depreciation = $43,750,000 / 1.052 = $39,682,539.68 Year 3 real depreciation = $43,750,000 / 1.053 = $37,792,894.94 Year 4 real depreciation = $43,750,000 / 1.054 = $35,993,233.27 Now we can calculate the pro forma income statement each year in real terms. We can then add back depreciation to net income to find the operating cash flow each year. Doing so, we find the cash flow of the project each year is: Year 0 Revenues Labor cost Energy cost Depreciation EBT Taxes Net income OCF Capital spending Year 1 $82,500,000.0 0 30,150,000.00 761,250.00 41,666,666.67 $9,922,083.33 3,373,508.33 $6,458,575.00 $48,215,241.6 7 Year 2 $88,000,000.0 0 34,170,000.00 873,697.50 39,682,539.68 $13,273,762.8 2 4,513,079.36 $8,760,683.46 $48,443,223.1 4 Year 3 $99,000,000.0 0 36,596,070.00 946,057.58 37,792,894.94 $23,664,977.4 9 8,046,092.35 $15,618,885.1 4 $53,411,780.0 8 Year 4 $93,500,000.0 0 31,995,421.20 950,672.49 35,993,233.27 $24,560,673.0 4 8,350,628.83 $16,210,044.2 0 $52,203,277.4 8 –$175,000,000 182 Total CF –$175,000,000 $48,215,241.6 7 $48,443,223.1 4 $53,411,780.0 8 $52,203,277.4 8 183 We can use the total cash flows each year to calculate the NPV, which is: NPV = –$175,000,000 + $48,215,241.67 / 1.08 + $48,443,223.14 / 1.082 + $53,411,780.08 / 1.083 + $52,203,277.48 / 1.084 NPV = –$8,053,041.50 37. Here we have the sales price and production costs in real terms. The simplest method to calculate the project cash flows is to use the real cash flows. In doing so, we must be sure to adjust the depreciation, which is in nominal terms. We could analyze the cash flows using nominal values, which would require calculating the nominal discount rate, nominal price, and nominal production costs. This method would be more complicated, so we will use the real numbers. We will first calculate the NPV of the headache only pill. Headache only: We can find the real revenue and production costs by multiplying each by the units sold. We must be sure to discount the depreciation, which is in nominal terms. We can then find the pro forma net income, and add back depreciation to find the operating cash flow. Discounting the depreciation each year by the inflation rate, we find the following cash flows each year: Year 1 $21,000,000 9,800,000 4,761,905 $6,438,095 2,188,952 $4,249,143 $9,011,048 Year 2 $21,000,000 9,800,000 4,535,147 $6,664,853 2,266,050 $4,398,803 $8,933,950 Year 3 $21,000,000 9,800,000 4,319,188 $6,880,812 2,339,476 $4,541,336 $8,860,524 Sales Production costs Depreciation EBT Tax Net income OCF And the NPV of the headache only pill is: NPV = –$15,000,000 + $9,011,048 / 1.13 + $8,993,950 / 1.132 + $8,860,524 / 1.133 NPV = $6,111,759.36 Headache and arthritis: For the headache and arthritis pill project, the equipment has a salvage value....
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 Spring '10
 eshmalwi
 Finance, Corporate Finance

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