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Chapter 06 - Making Capital Investment Decisions
28.
Now, we can use the depreciation tax shield approach to find the NPV of the project, which is: NPV = –$1,000,000 + ($3,234,520.16 – 1,234,696.52 – 720,699.92)(1 – .34) + ($720,699.92)(.34) + $25,000 / 1.115 NPV = $103,915.73 Challenge 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
–$23,000,000 –1,500,000 –$24,500,000
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 $2,400,000 per year. To calculate depreciation each year, we use the initial equipment cost of $23 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:
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 $19,713,300
$28,635,000 15,770,000 2,400,000 3,286,700 7,178,300 2,512,405 4,665,895 3,286,700 $7,952,595
$7,952,595 –465,750
$7,486,845 2 $14,080,600
$31,740,000 17,480,000 2,400,000 5,632,700 6,227,300 2,179,555 4,047,745 5,632,700 $9,680,445
$9,680,445 –621,000
$9,059,445 3 $10,057,900
$35,880,000 19,760,000 2,400,000 4,022,700 9,697,300 3,394,055 6,303,245 4,022,700 $10,325,945
$10,325,945
310,500
$10,636,445 4 $7,185,200
$33,810,000 18,620,000 2,400,000 2,872,700 9,917,300 3,471,055 6,446,245 2,872,700 $9,318,945
$9,318,945 724,500
$10,043,445 5 $5,131,300
$28,980,000 15,960,000 2,400,000 2,053,900 8,566,100 2,998,135 5,567,965 2,053,900 $7,621,865
$7,621,865 1,551,750 4,785,955 $13,959,570
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? 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
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Chapter 06 - Making Capital Investment Decisions
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($31,740,000 – 28,635,000) Increase in NWC for Year 1 = $465,750
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 company still has in the project. To calculate the aftertax salvage value, we first need the book value of the equipment. The book value at the end of the five years will be the purchase price, minus the total depreciation. So, the ending book value is:
Ending book value = $23,000,000 – ($3,286,700 + 5,632,700 + 4,022,700 + 2,872,700 + 2,053,900) Ending book value = $5,131,300
The market value of the used equipment is 20 percent of the purchase price, or $4.6 million, so the aftertax salvage value will be:
Aftertax salvage value = $4,600,000 + ($5,131,300 – 4,600,000)(.35) Aftertax salvage value = $4,785,955
The aftertax salvage value is included in the total cash flows as capital spending. Now we have all of the cash flows for the project. The NPV of the project is:
NPV = –$24,500,000 + $7,486,845/1.18 + $9,059,445/1.182 + $10,636,445/1.183 + $10,043,445/1.184 + $13,959,570/1.185 NPV = $6,106,958.94 And the IRR is: IRR = 0 = –$24,500,000 + $7,486,845/(1 + IRR) + $9,059,445/(1 + IRR)2 + $10,636,445/(1 + IRR)3 + $10,043,445/(1 + IRR)4 + $13,959,570/(1 + IRR)5 IRR = 27.54% We should accept the project.
29. To find the initial pretax cost savings necessary to buy the new machine, we should use the tax
shield approach to find the OCF. We begin by calculating the depreciation each year using the MACRS depreciation schedule. The depreciation each year is: D1 = $640,000(0.3333) = $213,312 D2 = $640,000(0.4445) = $284,480 D3 = $640,000(0.1481) = $94,784 D4 = $640,000(0.0741) = $47,424
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? 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 06 - Making Capital Investment Decisions
Using the tax shield approach, the OCF each year is: OCF1 = (S – C)(1 – 0.35) + 0.35($213,312) OCF2 = (S – C)(1 – 0.35) + 0.35($284,480) OCF3 = (S – C)(1 – 0.35) + 0.35($94,784) OCF4 = (S – C)(1 – 0.35) + 0.35($47,424) OCF5 = (S – C)(1 – 0.35)
Now we need the aftertax salvage value of the equipment. The aftertax salvage value is: After-tax salvage value = $60,000(1 – 0.35) = $39,000
To find the necessary cost reduction, we must realize that we can split the cash flows each year. The OCF in any given year is the cost reduction (S – C) times one minus the tax rate, which is an annuity for the project life, and the depreciation tax shield. To calculate the necessary cost reduction, we would require a zero NPV. The equation for the NPV of the project is:
NPV = 0 = – $640,000 – 55,000 + (S – C)(0.65)(PVIFA12%,5) + 0.35($213,312/1.12
+ $284,480/1.122 + $94,784/1.123 + $47,424/1.124) + ($55,000 + 39,000)/1.125 Solving this equation for the sales minus costs, we get: (S – C)(0.65)(PVIFA12%,5) = $461,465.41 (S – C) = $196,946.15
30. To find the bid price, we need to calculate all other cash flows for the project, and then solve for the
bid price. The aftertax salvage value of the equipment is: Aftertax salvage value = $150,000(1 – 0.35) = $97,500 Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for the
NPV of the project is: NPV = 0 = – $1,800,000 – 130,000 + OCF(PVIFA14%,5) + [($130,000 + 97,500) / 1.145] Solving for the OCF, we find the OCF that makes the project NPV equal to zero is: OCF = $1,811,843.63 / PVIFA14%,5 = $527,760.24 The easiest way to calculate the bid price is the tax shield approach, so: OCF = $527,760.24 = [(P – v)Q – FC ](1 – tc) + tcD $527,760.24 = [(P – $8.50)(140,000) – $265,000 ](1 – 0.35) + 0.35($1,800,000/5) P = $14.81
31. a. This problem is basically the same as the previous problem, except that we are given a sales
price. The cash flow at Time 0 for all three parts of this question will be:
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? 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 06 - Making Capital Investment Decisions
Capital spending Change in NWC Total cash flow
–$1,800,000 –130,000 –$1,930,000
We will use the initial cash flow and the salvage value we already found in that problem. Using the bottom up approach to calculating the OCF, we get:
Assume price per unit = $16 and units/year = 140,000
Year 1 2 3 4 5 Sales $2,240,000 $2,240,000 $2,240,000 $2,240,000 $2,240,000 Variable costs 1,190,000 1,190,000 1,190,000 1,190,000 1,190,000 Fixed costs 265,000 265,000 265,000 265,000 265,000 Depreciation 360,000 360,000 360,000 360,000 360,000 EBIT $425,000 $425,000 $425,000 $425,000 $425,000 Taxes (35%) 148,750 148,750 148,750 148,750 148,750 Net Income $276,250 $276,250 $276,250 $276,250 $276,250 Depreciation 360,000 360,000 360,000 360,000 360,000 Operating CF $636,250 $636,250 $636,250 $636,250 $636,250
Year 1 2 3 4 5 Operating CF $636,250 $636,250 $636,250 $636,250 $636,250 Change in NWC 130,000 Capital spending 97,500 Total CF $636,250 $636,250 $636,250 $636,250 $863,750 With these cash flows, the NPV of the project is: NPV = – $1,800,000 – 130,000 + $636,250(PVIFA14%,5) + [($130,000 + 97,500) / 1.145] NPV = $372,454.14 If the actual price is above the bid price that results in a zero NPV, the project will have a
positive NPV. As for the cartons sold, if the number of cartons sold increases, the NPV will increase, and if the costs increase, the NPV will decrease.
b. To find the minimum number of cartons sold to still breakeven, we need to use the tax shield
approach to calculating OCF, and solve the problem similar to finding a bid price. Using the initial cash flow and salvage value we already calculated, the equation for a zero NPV of the project is:
NPV = 0 = – $1,800,000 – 130,000 + OCF(PVIFA14%,5) + [($130,000 + 97,500) / 1.145] So, the necessary OCF for a zero NPV is: OCF = $1,811,843.63 / PVIFA14%,5 = $527,760.24
Now we can use the tax shield approach to solve for the minimum quantity as follows:
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? 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 06 - Making Capital Investment Decisions
OCF = $527,760.24 = [(P – v)Q – FC ](1 – tc) + tcD
$527,760.24 = [($16.00 – 8.50)Q – 265,000 ](1 – 0.35) + 0.35($1,800,000/5) Q = 117,746
As a check, we can calculate the NPV of the project with this quantity. The calculations are:
1 $1,883,931 1,000,838 265,000 360,000 $258,093 90,332 $167,760 360,000 $527,760 1 $527,760
0 0 $527,760 2 $1,883,931 1,000,838 265,000 360,000 $258,093 90,332 $167,760 360,000 $527,760 2 $527,760
0 0 $527,760 3 $1,883,931 1,000,838 265,000 360,000 $258,093 90,332 $167,760 360,000 $527,760 3 $527,760
0 0 $527,760 4 $1,883,931 1,000,838 265,000 360,000 $258,093 90,332 $167,760 360,000 $527,760 4 $527,760
0 0 $527,760 5 $1,883,931 1,000,838 265,000 360,000 $258,093 90,332 $167,760 360,000 $527,760 5 $527,760 130,000 97,500 $755,260 Year Sales
Variable costs Fixed costs Depreciation EBIT
Taxes (35%) Net Income Depreciation Operating CF
Year Operating CF Change in NWC Capital spending Total CF
c.
NPV = – $1,800,000 – 130,000 + $527,760 (PVIFA14%,5) + [($130,000 + 97,500) / 1.145] ? $0 Note that the NPV is not exactly equal to zero because we had to round the number of cartons sold; you cannot sell one-half of a carton.
To find the highest level of fixed costs and still breakeven, we need to use the tax shield approach to calculating OCF, and solve the problem similar to finding a bid price. Using the initial cash flow and salvage value we already calculated, the equation for a zero NPV of the project is:
NPV = 0 = – $1,800,000 – 130,000 + OCF(PVIFA14%,5) + [($130,000 + 97,500) / 1.145] OCF = $1,811,843.63 / PVIFA14%,5 = $527,760.24
Notice this is the same OCF we calculated in part b. Now we can use the tax shield approach to solve for the maximum level of fixed costs as follows:
OCF = $527,760.24 = [(P–v)Q – FC ](1 – tC) + tCD
$527,760.24 = [($16.00 – $8.50)(140,000) – FC](1 – 0.35) + 0.35($1,800,000/5) FC = $431,907.33
As a check, we can calculate the NPV of the project with this quantity. The calculations are:
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? 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.