26. 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
income, the operating cash flow created by purchasing the new machine each year will be:
Maintenance cost
$275,200
Depreciation
874,000
EBT
–$1,149,200
Taxes
–390,728
Net income
–$758,472
OCF
$115,528
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
$624,000
Taxes
–212,160
Total
$411,840
The NPV of purchasing the new machine is:
NPV = –$4,370,000 + $115,528(PVIFA12%,5) + $411,840/1.125
NPV = –$3,719,858.34
Notice the NPV is negative. This does not necessarily mean we should not purchase the new machine.
will use the machine with the least negative NPV. Now we can calculate the decision to keep the old
machine:
Keep old machine:
The initial cash outlay for keeping the old machine is the market value of the old machine, including
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
–$1,870,000
Taxes
248,200
Total
–$1,621,800
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 income
statement, adding depreciation to net income to calculate the operating cash flow will be:
Maintenance cost
$780,000
Depreciation
228,000
EBT
–$1,008,000
Taxes
–342,720
Net income
–$665,280
OCF
–$437,280
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
$182,000
Taxes
–61,880
Total
$120,120
So, the NPV of the decision to keep the old machine will be:
The company should keep the old machine since it has a greater (less negative) NPV.
There is another way to analyze a replacement decision that is often used. It is an incremental cash
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:
Purchase new machine
–$4,370,000
Sell old machine
1,870,000
Taxes on old machine
– 248,200
Total
–$2,748,200
The cash flows from purchasing the new machine would be the difference in the operating expenses.
of $228,000 per year, and the new machine has a depreciation of $874,000 per year, so the increased
depreciation will be $646,000 per year. The pro forma income statement and operating cash flow under
this approach will be:
Maintenance cost
–$504,800
Depreciation
646,000
EBT
–$141,200
Taxes
–48,008
Net income
–$93,192
OCF
$552,808
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 = –$589,921.11
So, this analysis still tells us the company should not purchase the new machine. This is really the
same type of analysis as we did considering the replacement decision as mutually exclusive projects.
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:
27. Here we have a situation where a company is going to buy one of two assets, so we need to calculate
the EAC of each asset. To calculate the EAC, we can calculate the EAC of the combined costs of each
SAL 5000:
Taxes on salvage value = –$68
Market price
$200
Tax on sale
– 68
Aftertax salvage value
$132
The incremental costs will include the maintenance costs, depreciation, and taxes. Notice the taxes are
negative, signifying a lower tax bill. So, the incremental cash flows will be:
Maintenance cost
$370.00
Depreciation
425.00
EBT
–$795.00
Tax
– 270.30
Net income
–$524.70
OCF
–$99.70
So, the NPV of the decision to buy one unit is:
NPV = –$3,855.79
And the EAC on a per unit basis is:
Since the company must buy 9 units, the total EAC of the decision is:
Total EAC = –$6,743.35
And the EAC for the HAL 1000:
Taxes on salvage value = –$74.80
Market price
$220.00
Tax on sale
–74.80
Aftertax salvage value
$145.20
The incremental costs will include the maintenance costs, depreciation, and taxes. Notice the taxes are
negative, signifying a lower tax bill. So, the incremental cash flows will be:
Maintenance cost
$345.00
Depreciation
683.33
EBT
–$1,028.33
Tax
–349.63
Net income
–$678.70
OCF
$4.63
So, the NPV of the decision to buy one unit is:
NPV = –$4,002.77
And the EAC on a per unit basis is:
EAC = –$946.16
Since the company must buy 7 units, the total EAC of the decision is:
Total EAC = –$6,623.12
28. Here we are comparing two mutually exclusive projects 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:
r = .0667, or 6.67%
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:
So, the EAC for the XX40 is:
EAC = –$978.21
And the EAC for the RH45 is:
The company should choose the RH45 because it has the lower (less negative) EAC.
29. The project has a sales price that increases at 5 percent per year, and a variable cost per unit that
increases at 7 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
$87.00
$91.35
$95.92
$100.71
$105.75
Cost per unit
$29.00
$31.03
$33.20
$35.53
$38.01
Using the sales price and variable cost, we can now construct the pro forma income statement for each
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:
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Revenues
$1,131,000.00
$1,187,550.00
$1,246,927.50
$1,309,273.88
$1,374,737.57
Fixed costs
315,000.00
315,000.00
315,000.00
315,000.00
315,000.00
VC
377,000.00
403,390.00
431,627.30
461,841.21
494,170.10
Dep.
198,000.00
198,000.00
198,000.00
198,000.00
198,000.00
EBT
$241,000.00
$271,160.00
$302,300.20
$334,432.66
$367,567.47
Taxes
81,940.00
92,194.40
102,782.07
113,707.11
124,972.94
Net income
$159,060.00
$178,965.60
$199,518.13
$220,725.56
$242,594.53
OCF
$357,060.00
$376,965.60
$397,518.13
$418,725.56
$440,594.53
Equipment
–$990,000
NWC
–145,000
145,000
Total CF
–$1,135,000
$357,060.00
$376,965.60
$397,518.13
$418,725.56
$585,594.53
With these cash flows, the NPV of the project is:
NPV = $406,640.59
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:
And the present value of the variable costs will be:
The fixed costs and depreciation are both ordinary annuities. The present value of each is:
PV of depreciation = $731,787.61
Now, we can use the depreciation tax shield approach to find the NPV of the project, which is:
Challenge
30. 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 Year 0, the project will
require an investment in equipment. The project will also require an investment in NWC. So, the cash
flow required for the project today will be:
Capital spending
–$19,500,000
Change in NWC
–1,600,000
Total cash flow
–$21,100,000
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
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
0
Year 1
Year 2
Year 3
Year 4
Year 5
Ending book value
$16,713,450
$11,937,900
$8,527,350
$6,091,800
$4,350,450
Sales
$27,600,000
$33,465,000
$37,605,000
$35,535,000
$26,910,000
Variable costs
15,600,000
18,915,000
21,255,000
20,085,000
15,210,000
Fixed costs
1,900,000
1,900,000
1,900,000
1,900,000
1,900,000
Depreciation
2,786,550
4,775,550
3,410,550
2,435,550
1,741,350
EBIT
$7,313,450
$7,874,450
$11,039,450
$11,114,450
$8,058,650
Taxes
2,559,708
2,756,058
3,863,808
3,890,058
2,820,528
Net income
$4,753,743
$5,118,393
$7,175,643
$7,224,393
$5,238,123
Depreciation
2,786,550
4,775,550
3,410,550
2,435,550
1,741,350
OCF
$7,540,293
$9,893,943
$10,586,193
$9,659,943
$6,979,473
Net cash flows
OCF
$7,540,293
$9,893,943
$10,586,193
$9,659,943
$6,979,473
Change in NWC
–$1,600,000
–879,750
–621,000
310,500
1,293,750
1,496,500
Capital spending
–19,500,000
4,057,658
Total cash flow
–$21,100,000
$6,660,543
$9,272,943
$10,896,693
$10,953,693
$12,533,630
After we calculate the OCF for each year, we need to account for any other cash flows. The other cash
equipment. The required NWC capital is 15 percent of the sales change. 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:
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 3 and 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: