Unformatted text preview: Depreciation EBT Taxes Net income OCF Capital spending NWC –$530,000 25,000 Year 1 $600,000.0 0 75,000.00 300,000.00 106,000.00 $119,000.0 0 40,460.00 $78,540.00 $184,540.0 0 Year 2 $630,000.0 0 75,000.00 318,000.00 106,000.00 $131,000.0 0 44,540.00 $86,460.00 $192,460.0 0 Year 3 $661,500.0 0 75,000.00 337,080.00 106,000.00 $143,420.0 0 48,762.80 $94,657.20 $200,657.2 0 Year 4 $694,575.0 0 75,000.00 357,304.80 106,000.00 $156,270.2 0 53,131.87 $103,138.3 3 $209,138.3 3 Year 5 $729,303.7 5 75,000.00 378,743.09 106,000.00 $169,560.6 6 57,650.63 $111,910.0 4 $217,910.0 4 25,000 $184,540.0 0 $192,460.0 0 $200,657.2 0 $209,138.3 3 $242,910.0 4 Total cash flow –$555,000 With these cash flows, the NPV of the project is: NPV = –$555,000 + $184,540 / 1.15 + $192,460 / 1.152 + $200,657.20 / 1.153 + $209,138.33 / 1.154 +$242,910.04 / 1.155 NPV = $123,277.08 We could also answer this problem using the depreciation tax shield approach. The revenues and variable costs are growing annuities, growing at different rates. The fixed costs and depreciation are ordinary annuities. Using the growing annuity equation, the present value of the revenues is: PV of revenues = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}(1 – tC) PV of revenues = $600,000{[1/(.15 – .05)] – [1/(.15 – .05)] × [(1 + .05)/(1 + .15)]5} PV of revenues = $2,192,775.00 And the present value of the variable costs will be: PV of variable costs = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}(1 – tC) PV of variable costs = $300,000{[1/(.15 – .06)] – [1/(.15 – .06)] × [(1 + .06)/(1 + .15)]5} PV of variable costs = $1,115,551.25 The fixed costs and depreciation are both ordinary annuities. The present value of each is: PV of fixed costs = C({1 – [1/(1 + r)]t } / r ) PV of fixed costs = $75,000({1 – [1/(1 + .15)]5 } / .15) PV of fixed costs = $251,411.63 168 PV of depreciation = C({1 – [1/(1 + r)]t } / r ) PV of depreciation = $106,000({1 – [1/(1 + .15)]5 } / .15) PV of depreciation = $355,328.44 169 Now, we can use the depreciation tax shield approach to find the NPV of the project, which is: NPV = –$555,000 + ($2,192,775 – 1,115,551.25 – 251,411.63)(1 – .34) + ($355,328.44)(.34) + $25,000 / 1.155 NPV = $123,277.08 Challenge 28. This is an indepth capital budgeting problem. Probably the easiest OCF calculation for this problem is the bottom up approach, so we will construct an income statement for each year. Beginning with the initial cash flow at time zero, the project will require an investment in equipment. The project will also require an investment in NWC of $1,500,000. So, the cash flow required for the project today will be: Capital spending Change in NWC Total cash flow –$18,000,000 –1,500,000 –$19,500,000 Now we can begin the remaining calculations. Sales figures are given for each year, along with the price per unit. The variable costs per unit are used to calculate total variable costs, and fixed costs are given at $700,000 per year. To calculate depreciation each year, we use the initial equipment cost of $18 million, times the appropriate MACRS depreciation each year. The remainder of each income statement is calculated below. Notice at the bottom of the income statement we added back depreciation to get the OCF for each year. The section labeled “Net cash flows” will be discussed below: 170 Year Ending book value Sales Variable costs Fixed costs Depreciation EBIT Taxes Net income Depreciation Operating cash flow Net cash flows Operating cash flow Change in NWC Capital spending Total cash flow 1 $15,426,000 $28,275,000 20,880,000 700,000 2,574,000 4,121,000 1,442,350 2,678,650 2,574,000 $5,252,650 2 $11,016,000 $30,550,000 22,560,000 700,000 4,410,000 2,880,000 1,008,000 1,872,000 4,410,000 $6,282,000 3 $7,866,000 $38,350,000 28,320,000 700,000 3,150,000 6,180,000 2,163,000 4,017,000 3,150,000 $7,167,000 4 $5,616,000 $35,425,000 26,160,000 700,000 2,250,000 6,315,000 2,210,250 4,104,750 2,250,000 $6,354,750 5 $4,014,000 $30,875,000 22,800,000 700,000 1,602,000 5,773,000 2,020,550 3,752,450 1,602,000 $5,354,450 $5,252,650 –341,250 $4,911,400 $6,282,000 –1,170,000 $5,112,000 $7,167,000 438,750 $7,605,750 $6,354,750 682,500 $7,037,250 $5,354,450 1,890,000 3,744,900 $10,989,350 After we calculate the OCF for each year, we need to account for any other cash flows. The other cash flows in this case are NWC cash flows and capital spending, which is the aftertax salvage of the equipment. The required NWC is 15 percent of the sales increase in the next year. We will work through the NWC cash flow for Year 1. The total NWC in Year 1 will be 15 percent of sales increase from Year 1 to Year 2, or: Increase in NWC for Year 1 = .15($30,550,000 – 28,275,000) Increase in NWC for Year 1 = $341,250 Notice that the NWC cash flow is negative. Since the sales are increasing, we will have to spend more money to increase NWC. In Year 4, the NWC cash flow is positive since sales are declining. And, in Year 5, the NWC cash flow is the recovery of all NWC the c...
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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 TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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