Chapter 06 - Making Capital Investment Decisions

Notice the calculation of the cash flow at time 0. The capital spending on equipment and investment in net working capital are cash outflows. The aftertax selling price of the land is also a cash outflow. Even though no cash is actually spent on the land because the company already owns it, the aftertax cash flow from selling the land is an opportunity cost, so we need to include it in the analysis. With all the project cash flows, we can calculate the NPV, which is:

NPV = –$4,120,000 + $1,146,625 / 1.13 + $1,393,559 / 1.132 + $1,246,279 / 1.133 + $2,274,825 / 1.134 NPV = $265,791.25

The company should accept the new product line.

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. We can calculate the operating cash flow created if the company purchases the new machine. The maintenance cost is an incremental cash flow, so using the pro forma income statement, and adding depreciation to net income, the operating cash flow created each year by purchasing the new machine will be:

Maintenance cost Depreciation EBT Taxes

Net income OCF

$330,000 860,000 –$1,190,000 –476,000 –$714,000 $146,000

25.

Notice the taxes are negative, implying a tax credit. The new machine also has a salvage value at the end of five years, so we need to include this in the cash flows analysis. The aftertax salvage value will be: Sell machine Taxes Total

$800,000 –320,000 $480,000

The NPV of purchasing the new machine is:

NPV = –$4,300,000 + $146,000(PVIFA8%,5) + $480,000 / 1.085 NPV = –$3,390,384.40

Notice the NPV is negative. This does not necessarily mean we should not purchase the new machine. In this analysis, we are only dealing with costs, so we would expect a negative NPV. The revenue is not included in the analysis since it is not incremental to the machine. Similar to an EAC analysis, we will use the machine with the least negative NPV. Now we can calculate the decision to keep the old machine:

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Chapter 06 - Making Capital Investment Decisions

Keep old machine:

The initial cash outlay for the keeping the old machine is the market value of the old machine, including any potential tax. 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 incur taxes. 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

–$2,200,000 320,000 –$1,880,000

Next, we can calculate the operating cash flow created if the company keeps the old machine. We need to account for the cost of maintenance, as well as the cash flow effects of depreciation. The pro forma income statement, adding depreciation to net income to calculate the operating cash flow will be:

Maintenance cost Depreciation EBT Taxes

Net income OCF

$845,000 280,000 –$1,125,000 –450,000 –$675,000 –$395,000

The old machine also has a salvage value at the end of five years, so we need to include this in the cash flows analysis. The aftertax salvage value will be: Sell machine Taxes Total

$120,000 –48,000 $72,000

So, the NPV of the decision to keep the old machine will be: NPV = –$1,880,000 – $395,000(PVIFA8%,5) + $72,000 / 1.085 NPV = –$3,408,118.47

The company should buy the new machine since it has a greater NPV.

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, 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:

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Chapter 06 - Making Capital Investment Decisions

Purchase new machine –$4,300,000 Sell old machine 2,200,000 Taxes on old machine –320,000 Total –$2,420,000

The cash flows from purchasing the new machine would be the difference in the operating expenses. We would also need to include the change in depreciation. The old machine has a depreciation of $280,000 per year, and the new machine has a depreciation of $860,000 per year, so the increased depreciation will be $580,000 per year. The pro forma income statement and operating cash flow under this approach will be: Maintenance cost Depreciation EBT Taxes

Net income OCF

–$515,000 580,000 –$65,000 –26,000 –$39,000 $541,000

The salvage value of the differential cash flow approach is more complicated. The company will sell the new machine, and incur taxes on the sale in five years. However, we must also include the lost sale of the old machine. Since we assumed we sold the old machine in the initial cash outlay, we lose the ability to sell the machine in five years. This is an opportunity loss that must be accounted for. So, the salvage value is:

Sell machine Taxes

Lost sale of old

Taxes on lost sale of old Total

The NPV under this method is:

NPV = –$2,420,000 + $541,000(PVIFA8%,5) + $408,000 / 1.08 NPV = $17,734.07

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 = –$3,390,384.40 – (–3,408,118.47) = $17,734.07

This is the exact same NPV we calculated when using the second analysis method.

$800,000 –320,000 –120,000 48,000 $408,000

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Chapter 06 - Making Capital Investment Decisions

26. Here we are comparing two mutually exclusive assets, with inflation. Since each will be replaced

when it wears out, we need to calculate the EAC for each. We have real cash flows. Similar to other capital budgeting projects, when calculating the EAC, we can use real cash flows with the real interest rate, or nominal cash flows and the nominal interest rate. Using the Fisher equation to find the real required return, we get: (1 + R) = (1 + r)(1 + h) (1 + .14) = (1 + r)(1 + .05) r = .0857 or 8.57% This is the interest rate we need to use with real cash flows. We are given the real aftertax cash flows

for each asset, so the NPV for the XX40 is: NPV = –$900 – $120(PVIFA8.57%,3) NPV = –$1,206.09 So, the EAC for the XX40 is: –$1,206.09 = EAC(PVIFA8.57%,3) EAC = –$472.84 And the EAC for the RH45 is: NPV = –$1,400 – $95(PVIFA8.57%,5) NPV = –$1,773.66 –$1,773.66 = EAC(PVIFA8.57%,5) EAC = –$450.94 The company should choose the RH45 because it has the greater EAC.

27. The project has a sales price that increases at 5 percent per year, and a variable cost per unit that

increases at 6 percent per year. First, we need to find the sales price and variable cost for each year. The table below shows the price per unit and the variable cost per unit each year.

Year 1 Year 2 Year 3 Year 4 Year 5 Sales price $40.00 $42.00 $44.10 $46.31 $48.62 Cost per unit $15.00 $15.90 $16.85 $17.87 $18.94 Using the sales price and variable cost, we can now construct the pro forma income statement for

each year. We can use this income statement to calculate the cash flow each year. We must also make sure to include the net working capital outlay at the beginning of the project, and the recovery of the net working capital at the end of the project. The pro forma income statement and cash flows for each year will be:

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Chapter 06 - Making Capital Investment Decisions

Revenues Fixed costs Variable costs Depreciation EBT Taxes

Net income

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 $800,000.00 $840,000.00 $882,000.00 $926,100.00 $972,405.00 195,000.00 195,000.00 195,000.00 195,000.00 195,000.00 300,000.00 318,000.00 337,080.00 357,304.80 378,743.09 195,000.00 195,000.00 195,000.00 195,000.00 195,000.00 $110,000.00 $132,000.00 $154,920.00 $178,795.20 $203,661.91 37,400.00 44,880.00 52,672.80 60,790.37 69,245.05 $72,600.00 $87,120.00 $102,247.20 $118,004.83 $134,416.86 OCF $267,600.00 $282,120.00 $297,247.20 $313,004.83 $329,416.86 Capital spending –$975,000 NWC –25,000 25,000 Total cash flow –$1,000,000 $267,600.00 $282,120.00 $297,247.20 $313,004.83 $354,416.86 With these cash flows, the NPV of the project is:

NPV = –$1,000,000 + $267,600 / 1.11 + $282,120 / 1.112 + $297,247.20 / 1.113 + $313,004.83 / 1.114 +$354,416.86 / 1.115 NPV = $103,915.73

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} PV of revenues = $800,000{[1/(.11 – .05)] – [1/(.11 – .05)] × [(1 + .05)/(1 + .11)]5} PV of revenues = $3,234,520.16

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 = $300,000{[1/(.11 – .06)] – [1/(.11 – .06)] × [(1 + .06)/(1 + .11)]5} PV of variable costs = $1,234,969.52

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 = $195,000({1 – [1/(1 + .11)]5 } / .11) PV of fixed costs = $720,699.92

PV of depreciation = C({1 – [1/(1 + r)]t } / r )

PV of depreciation = $195,000({1 – [1/(1 + .11)]5 } / .11) PV of depreciation = $720,699.92

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