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Chapter 06 - Making Capital Investment Decisions
There is another way to analyze a replacement decision that is often used. It is an incremental cash flow analysis of the change in cash flows from the existing machine to the new machine, assuming the new machine is purchased. In this type of analysis, the initial cash outlay would be the cost of the new machine, the increased NWC, and the cash inflow (including any applicable taxes) of selling the old machine. In this case, the initial cash flow under this method would be:
Purchase new machine Net working capital Sell old machine
Taxes on old machine Total
–$18,000,000
–250,000 4,500,000 585,000 –$13,165,000
The cash flows from purchasing the new machine would be the saved operating expenses. We would also need to include the change in depreciation. The old machine has a depreciation of $1.5 million per year, and the new machine has a depreciation of $4.5 million per year, so the increased depreciation will be $3 million per year. The pro forma income statement and operating cash flow under this approach will be:
Operating expense savings Depreciation EBT Taxes
Net income OCF
The NPV under this method is:
NPV = –$13,165,000 + $5,257,000(PVIFA10%,4) + $250,000 / 1.104 NPV = $3,669,736.02 And the IRR is:
0 = –$13,165,000 + $5,257,000(PVIFAIRR,4) + $250,000 / (1 + IRR)4 Using a spreadsheet or financial calculator, we find the IRR is: IRR = 22.23%
So, this analysis still tells us the company should purchase the new machine. This is really the same type of analysis we originally did. Consider this: Subtract the NPV of the decision to keep the old machine from the NPV of the decision to purchase the new machine. You will get: Differential NPV = $439,107.30 – (–$3,230,628.71) = $3,669,736.02
This is the exact same NPV we calculated when using the second analysis method.
$6,700,000 3,000,000 $3,700,000 1,443,000 $2,257,000 $5,257,000
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Chapter 06 - Making Capital Investment Decisions
22. We can find the NPV of a project 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 $270,000 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 Year 1 Year 2 Year 3 $105,000.00 $110,250.00 $115,762.50 Revenues $30,000.00 Costs 31,800.00 33,708.00 Depreciation 38,571.43 38,571.43 38,571.43 EBT $36,428.57 $39,878.57 $43,483.07 Taxes 12,385.71 13,558.71 14,784.24 $24,042.86 $26,319.86 $28,698.83 Net income $62,614.29 $64,891.29 $67,270.26 OCF Capital spending –$270,000 Total cash flow –$270,000 $62,614.29 $64,891.29 $67,270.26 Year 4 Year 5 Year 6 Year 7 Revenues $121,550.63 $127,628.16 $134,009.56 $140,710.04 Costs 35,730.48 37,874.31 40,146.77 42,555.57 Depreciation 38,571.43 38,571.43 38,571.43 38,571.43 EBT $47,248.72 $51,182.42 $55,291.37 $59,583.04 Taxes 16,064.56 17,402.02 18,799.07 20,258.23 Net income $31,184.15 $33,780.40 $36,492.30 $39,324.81 OCF $69,755.58 $72,351.83 $75,063.73 $77,896.24 Capital spending Total cash flow $69,755.58 $72,351.83 $75,063.73 $77,896.24 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%
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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
So, the NPV of the project using nominal cash flows is:
NPV = –$270,000 + $62,614.29 / 1.1340 + $64,891.29 / 1.13402 + $67,270.26 / 1.13403
+ $69,755.58 / 1.13404 + $72,351.83 / 1.13405 + $75,063.73 / 1.13406 + $77,896.24 / 1.13407 NPV = $30,170.71
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 = $105,000{[1/(.134 – .05)] – [1/(.134 –.05)] × [(1 + .05)/(1+.134)]7}(1–.34) PV of aftertax revenues = $343,620.42
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 = $30,000{[1/(.134 – .06)] – [1/(.134 – .06)] × [(1 + .06)/(1 + .134)]7}(1 – .34) PV of aftertax costs = $100,734.11
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 = ($270,000/7)(.34)(PVIFA13.40%,7) PV of depreciation tax shield = $57,284.40
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 = –$270,000 + $343,620.42 – 100,734.11 + 57,284.40 NPV = $30,170.71
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 = 7,000 Year 2 quantity = 7,000(1 + .08) = 7,560 Year 3 quantity = 7,560(1 + .08) = 8,165 Year 4 quantity = 8,165(1 + .08) = 8,818 Year 5 quantity = 8,818(1 + .08) = 9,523
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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
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:
Revenues Fixed costs Variable costs Depreciation EBT Taxes
Net income OCF
Capital spending NWC
Total cash flow
Year 0
Year 1 $336,000.00 95,000.00 140,000.00 35,000.00 $66,000.00 22,440.00 $43,560.00
Year 2 $362,880.00 95,000.00 151,200.00 35,000.00 $81,680.00 27,771.20 $53,908.80
Year 3 $391,910.40 95,000.00 163,296.00 35,000.00 $98,614.40 33,528.90 $65,085.50
Year 4 $423,263.23 95,000.00 176,359.68 35,000.00 $116,903.55 39,747.21 $77,156.34
Year 5 $457,124.29 95,000.00 190,468.45 35,000.00 $136,655.84 46,462.98 $90,192.85
$78,560.00 $88,908.80 $100,085.50 $112,156.34 $125,192.85
–$175,000 –35,000 35,000
–$210,000 $78,560.00 $88,908.80 $100,085.50 $112,156.34 $160,192.85
So, the NPV of the project is:
NPV = –$210,000 + 75,860 / 1.25 + $88,908.80 / 1.252 + $100,085.50 / 1.253 + $112,156.34 / 1.254 + $160,192.85 / 1.255 NPV = $59,424.64
We could also have calculated the cash flows using the tax shield approach, with growing annuities and ordinary annuities. The sales and variable costs increase at the same rate as sales, so both are growing annuities. The fixed costs and depreciation are both 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} PV of revenues = $336,000{[1/(.25 – .08)] – [1/(.25 – .08)] × [(1 + .08)/(1 + .25)]5} PV of revenues = $1,024,860.43
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} PV of variable costs = $140,000{[1/(.25 – .08)] – [1/(.25 – .08)] × [(1 + .08)/(1 + .25)]5} PV of variable costs = $427,025.18
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 = $95,000(PVIFA25%,5) PV of fixed costs = $255,481.60
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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
24.
PV of depreciation = C({1 – [1/(1 + r)]t } / r ) PV of depreciation = $35,000(PVIFA25%,5) PV of depreciation = $94,124.80
Now, we can use the depreciation tax shield approach to find the NPV of the project, which is: NPV = –$210,000 + ($1,024,860.43 – 427,025.18 – 255,481.60)(1 – .34) + ($94,124.80)(.34) + $35,000 / 1.255 NPV = $59,424.64
We will begin by calculating the aftertax salvage value of the equipment at the end of the project’s life. The aftertax salvage value is the market value of the equipment minus any taxes paid (or refunded), so the aftertax salvage value in four years will be: Taxes on salvage value = (BV – MV)tC
Taxes on salvage value = ($0 – 300,000)(.38) Taxes on salvage value = –$114,000 Market price Tax on sale
Aftertax salvage value
$300,000 –114,000 $186,000
Now we need to calculate the operating cash flow each year. Note, we assume that the net working capital cash flow occurs immediately. Using the bottom up approach to calculating operating cash flow, we find:
Revenues Fixed costs Variable costs Depreciation EBT Taxes
Net income OCF
Capital spending Land NWC
Total cash flow
Year 0
–$3,100,000 –900,000 –120,000
–$4,120,000
Year 1 $1,842,500 350,000 276,375 1,033,230 $182,895 69,500 $113,395 $1,146,625
$1,146,625
Year 2 $2,062,500 350,000 309,375 1,377,950 $25,175 9,567 $15,609 $1,393,559
$1,393,559
Year 3 $2,502,500 350,000 375,375 459,110 $1,318,015 500,846 $817,169 $1,276,279
$1,276,279
Year 4 $1,705,000 350,000 255,750 229,710 $869,540 330,425 $539,115 $768,825
186,000 1,200,000 120,000
$2,274,825
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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.