Chapter 06 - Making Capital Investment Decisions

The real aftertax costs in year 1 will be:

Aftertax costs in year 1 in real terms = (2,800,000 × $0.90)(1 – 0.34) Aftertax costs in year 1 in real terms = $1,663,200

Costs will grow at five percent per year in real terms forever. Applying the growing perpetuity formula, we find the present value of the costs is:

PV of costs = C1 / (R – g) PV of costs = $1,663,200 / (0.10 – 0.05) PV of costs = $33,264,000 Now we can find the value of the firm, which is: Value of the firm = PV of revenues – PV of costs Value of the firm = $57,750,000 – 33,264,000 Value of the firm = $24,486,000

17. To calculate the nominal cash flows, we increase each item in the income statement by the inflation

rate, except for depreciation. Depreciation is a nominal cash flow, so it does not need to be adjusted for inflation in nominal cash flow analysis. Since the resale value is given in nominal terms as of the end of year 5, it does not need to be adjusted for inflation. Also, no inflation adjustment is needed for net working capital since it already expressed in nominal terms. Note that an increase in required net working capital is a negative cash flow whereas a decrease in required net working capital is a positive cash flow. We first need to calculate the taxes on the salvage value. Remember, to calculate the taxes paid (or tax credit) on the salvage value, we take the book value minus the market value, times the tax rate, which, in this case, would be: Taxes on salvage value = (BV – MV)tC Taxes on salvage value = ($0 – 45,000)(.34) Taxes on salvage value = –$15,300 So, the nominal aftertax salvage value is: Market price $45,000 Tax on sale –15,300 Aftertax salvage value $29,700

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Chapter 06 - Making Capital Investment Decisions

Now we can find the nominal cash flows each year using the income statement. Doing so, we find: Sales Expenses Depreciation EBT Tax

Net income

Year 0

Year 1 $245,000 70,000 73,000 $102,000 34,680 $67,320 $140,320

$140,320

Year 2 $252,350 72,100 73,000 $107,250 36,465 $70,785 $143,785

$143,785

Year 3 $259,921 74,263 73,000 $112,658 38,304 $74,354 $147,354

$147,354

Year 4 $267,718 76,491 73,000 $118,227 40,197 $78,030 $151,030

$151,030

Year 5 $275,750 78,786 73,000 $123,964 42,148 $81,816 $154,816

29,700 10,000 $194,516

OCF Capital spending –$365,000 NWC –10,000 Total cash flow –$375,000

18. The present value of the company is the present value of the future cash flows generated by the

company. Here we have real cash flows, a real interest rate, and a real growth rate. The cash flows are a growing perpetuity, with a negative growth rate. Using the growing perpetuity equation, the present value of the cash flows is: PV = C1 / (R – g) PV = $190,000 / [.11 – (–.04)] PV = $1,266,666.67

19. To find the EAC, we first need to calculate the NPV of the incremental cash flows. We will begin

with the aftertax salvage value, which is: Taxes on salvage value = (BV – MV)tC Taxes on salvage value = ($0 – 18,000)(.34) Taxes on salvage value = –$6,120 Market price $18,000 Tax on sale –6,120 Aftertax salvage value $11,880 Now we can find the operating cash flows. Using the tax shield approach, the operating cash flow

each year will be: OCF = –$8,600(1 – 0.34) + 0.34($94,000/3) OCF = $4,977.33 So, the NPV of the cost of the decision to buy is: NPV = –$94,000 + $4,977.33(PVIFA12%,3) + ($11,880/1.123) NPV = –$73,589.34

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Chapter 06 - Making Capital Investment Decisions

In order to calculate the equivalent annual cost, set the NPV of the equipment equal to an annuity with the same economic life. Since the project has an economic life of three years and is discounted at 12 percent, set the NPV equal to a three-year annuity, discounted at 12 percent.

EAC = –$73,589.34 / (PVIFA12%,3) EAC = –$30,638.84

20. We will calculate the aftertax salvage value first. The aftertax salvage value of the equipment will be: Taxes on salvage value = (BV – MV)tC Taxes on salvage value = ($0 – 60,000)(.34) Taxes on salvage value = –$20,400 Market price $60,000 Tax on sale –20,400 Aftertax salvage value $39,600 Next, we will calculate the initial cash outlay, that is, the cash flow at Time 0. To undertake the

project, we will have to purchase the equipment. The new project will decrease the net working capital, so this is a cash inflow at the beginning of the project. So, the cash outlay today for the project will be: Equipment –$360,000 NWC 80,000 Total –$280,000 Now we can calculate the operating cash flow each year for the project. Using the bottom up

approach, the operating cash flow will be:

Saved salaries $105,000 Depreciation 72,000 EBT $33,000 Taxes 11,220 Net income $21,780 And the OCF will be: OCF = $21,780 + 72,000 OCF = $93,780 Now we can find the NPV of the project. In Year 5, we must replace the saved NWC, so: NPV = –$280,000 + $93,780(PVIFA12%,5) + ($39,600 – 80,000) / 1.125 NPV = $35,131.87

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Chapter 06 - Making Capital Investment Decisions

21. Replacement decision analysis is the same as the analysis of two competing projects, in this case,

keep the current equipment, or purchase the new equipment. We will consider the purchase of the new machine first. Purchase new machine: The initial cash outlay for the new machine is the cost of the new machine, plus the increased net

working capital. So, the initial cash outlay will be: Purchase new machine –$18,000,000 Net working capital –250,000 Total –$18,250,000 Next, we can calculate the operating cash flow created if the company purchases the new machine.

The saved operating expense is an incremental cash flow. Additionally, the reduced operating expense is a cash inflow, so it should be treated as such in the income statement. The pro forma income statement, and adding depreciation to net income, the annual operating cash flow created by purchasing the new machine will be: Operating expense $6,700,000 Depreciation 4,500,000 EBT $2,200,000 Taxes 858,000 Net income $1,342,000 OCF $5,842,000 So, the NPV of purchasing the new machine, including the recovery of the net working capital, is: NPV = –$18,250,000 + $5,842,000(PVIFA10%,4) + $250,000 / 1.104 NPV = $439,107.30 And the IRR is: 0 = –$18,250,000 + $5,842,000(PVIFAIRR,4) + $250,000 / (1 + IRR)4 Using a spreadsheet or financial calculator, we find the IRR is: IRR = 11.10%

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Chapter 06 - Making Capital Investment Decisions

Now we can calculate the decision to keep the old machine: Keep old machine:

The initial cash outlay for the old machine is the market value of the old machine, including any potential tax consequence. The decision to keep the old machine has an opportunity cost, namely, the company could sell the old machine. Also, if the company sells the old machine at its current value, it will receive a tax benefit. Both of these cash flows need to be included in the analysis. So, the initial cash flow of keeping the old machine will be:

Keep machine Taxes Total

–$4,500,000 –585,000 –$5,085,000

Next, we can calculate the operating cash flow created if the company keeps the old machine. There are no incremental cash flows from keeping the old machine, but we need to account for the cash flow effects of depreciation. The income statement, adding depreciation to net income to calculate the operating cash flow will be:

Depreciation EBT Taxes

Net income OCF

$1,500,000 –$1,500,000 –585,000 –$915,000 $585,000

So, the NPV of the decision to keep the old machine will be: NPV = –$5,085,000 + $585,000(PVIFA10%,4) NPV = –$3,230,628.71 And the IRR is:

0 = –$5,085,000 + $585,000(PVIFAIRR,4)

Using a spreadsheet or financial calculator, we find the IRR is: IRR = –25.15%

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