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25. 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:
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:
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
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:
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:
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:
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:
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
$320,000 per year, and the new machine has a depreciation of $900,000 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:
Net income –$45,000
Taxes –360,000
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:
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:
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:
And the EAC for the RH45 is:
27. The project has a sales price that increases at 3 percent per year, and a variable cost per unit that
increases at 4 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
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:
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Revenues $860,000.00 $885,800.00 $912,374.00 $939,745.22 $967,937.58
Fixed costs 195,000.00 195,000.00 195,000.00 195,000.00 195,000.00
Variable costs 300,000.00 312,000.00 324,480.00 337,459.20 350,957.57
Capital
spending –$975,000
NWC –25,000 25,000
Total cash
flow –$1,000,000 $307,200.00 $316,308.00 $325,610.04 $335,108.77 $369,806.81
With these cash flows, the NPV of the project is:
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:
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 fixed costs = C({1 – [1 / (1 + r)]t } / r )
PV of depreciation = C({1 – [1 / (1 + r)]t } / r )
Now, we can use the depreciation tax shield approach to find the NPV of the project, which is:
Challenge
28. 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:
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 $1,850,000 per year. To calculate depreciation each year, we use the initial equipment
Year 1 2 3 4 5
Ending book value $16,713,450 $11,937,900 $8,527,350 $6,091,800 $4,350,450
Sales $27,945,000 $30,705,000 $33,465,000 $31,740,000 $26,565,000
Variable costs 15,390,000 16,910,000 18,430,000 17,480,000 14,630,000
Net cash flows
Operating cash flow $7,933,543 $9,435,693 $9,763,943 $8,918,943 $7,164,723
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
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, the NWC cash flow becomes positive when 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
The market value of the used equipment is 20 percent of the purchase price, or $3.9 million, so the
aftertax salvage value will be:
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:
IRR = 33.29%
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 = $710,000(.3333) = $236,643
Using the tax shield approach, the OCF each year is:
OCF1 = (S – C)(1 – .35) + .35($236,643)
OCF2 = (S – C)(1 – .35) + .35($315,595)
Now we need the aftertax salvage value of the equipment. The aftertax salvage value is:
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:
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:
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:
The easiest way to calculate the bid price is the tax shield approach, so:
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:
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 = $18 and units/year = 165,000
Year 1 2 3 4 5
Sales $2,970,000 $2,970,000 $2,970,000 $2,970,000 $2,970,000
Variable costs 1,526,250 1,526,250 1,526,250 1,526,250 1,526,250
Fixed costs 450,000 450,000 450,000 450,000 450,000
Change in NWC 130,000
Capital spending 97,500
Total CF $806,938 $806,938 $806,938 $806,938 $1,034,438
With these cash flows, the NPV of the project is:
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:
Now we can use the tax shield approach to solve for the minimum quantity as follows:
As a check, we can calculate the NPV of the project with this quantity. The calculations are:
Year 1 2 3 4 5
Sales $2,547,382 $2,547,382 $2,547,382 $2,547,382 $2,547,382
Variable costs 1,309,071 1,309,071 1,309,071 1,309,071 1,309,071
Fixed costs 450,000 450,000 450,000 450,000 450,000
Depreciation 460,000 460,000 460,000 460,000 460,000
EBIT $328,311 $328,311 $328,311 $328,311 $328,311
Taxes (35%) 114,909 114,909 114,909 114,909 114,909
NPV = –$2,300,000 – 130,000 + $673,402 (PVIFA14%,5) + [($130,000 + 97,500) / 1.145] $0
c. 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:
As a check, we can calculate the NPV of the project with this quantity. The calculations are:
Year 1 2 3 4 5
Sales $2,970,000 $2,970,000 $2,970,000 $2,970,000 $2,970,000
Variable costs 1,526,250 1,526,250 1,526,250 1,526,250 1,526,250
Fixed costs 655,439 655,439 655,439 655,439 655,439
Year 1 2 3 4 5
Operating CF $673,402 $673,402 $673,402 $673,402 $673,402
Change in NWC 0 0 0 0 130,000
Capital spending 0 0 0 0 97,500
32. We need to find the bid price for a project, but the project has extra cash flows. Since we don’t
already produce the keyboard, the sales of the keyboard outside the contract are relevant cash flows.
Since we know the extra sales number and price, we can calculate the cash flows generated by these
sales. The cash flow generated from the sale of the keyboard outside the contract is:
Year 1 Year 2 Year 3 Year 4
$1,740,00
So, the addition to NPV of these market sales is:
You may have noticed that we did not include the initial cash outlay, depreciation, or fixed costs in
the calculation of cash flows from the market sales. The reason is that it is irrelevant whether or not
we include these here. Remember that we are not only trying to determine the bid price, but we are
also determining whether or not the project is feasible. In other words, we are trying to calculate the
NPV of the project, not just the NPV of the bid price. We will include these cash flows in the bid
price calculation. Whether we include these costs in this initial calculation is irrelevant since you will
come up with the same bid price if you include these costs in this calculation, or if you include them
in the bid price calculation.
Next, we need to calculate the aftertax salvage value, which is:
Instead of solving for a zero NPV as is usual in setting a bid price, the company president requires an
NPV of $100,000, so we will solve for an NPV of that amount. The NPV equation for this project is
(remember to include the NWC cash flow at the beginning of the project, and the NWC recovery at
the end):
Now we can solve for the bid price as follows:
