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15. To evaluate the project with a $150,000 cost savings, we need the OCF to compute the NPV. Using
the tax shield approach, the OCF is:
The NPV with a $100,000 cost savings is:
We would accept the project if cost savings were $150,000, and reject the project if the cost savings
Solving for the OCF, we find the necessary OCF for zero NPV is:
Using the tax shield approach to calculating OCF, we get:
CHAPTER 27 - 2
16. To calculate the EAC of the project, we first need the NPV of the project. Notice that we include the
NWC expenditure at the beginning of the project, and recover the NWC at the end of the project.
The NPV of the project is:
Now we can find the EAC of the project. The EAC is:
17. We will need the aftertax salvage value of the equipment to compute the EAC. Even though the
equipment for each product has a different initial cost, both have the same salvage value. The
aftertax salvage value for both is:
To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for
Techron I is:
And the OCF and NPV for Techron II is:
OCF = –$36,000(1 – .35) + .35($475,000/5) = $9,850
The two milling machines have unequal lives, so they can only be compared by expressing both on
an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II
because it has the lower (less negative) annual cost.
18. 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:
CHAPTER 27 - 3
Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:
The easiest way to calculate the bid price is the tax shield approach, so:
OCF = $262,868.26 = [(P – v)Q – FC ](1 – TC) + TCD
Intermediate
19. First, we will calculate the depreciation each year, which will be:
D1 = $410,000(.2000) = $82,000
The book value of the equipment at the end of the project is:
The asset is sold at a loss to book value, so this creates a tax refund.
So, the OCF for each year will be:
OCF1 = $155,000(1 – .35) + .35($82,000) = $129,450
Now we have all the necessary information to calculate the project NPV. We need to be careful with
the NWC in this project. Notice the project requires $20,000 of NWC at the beginning, and $3,100
more in NWC each successive year. We will subtract the $20,000 from the initial cash flow, and
NPV = – $410,000 – 20,000 + ($129,450 – 3,100) / 1.09 + ($146,670 – 3,100) / 1.092
CHAPTER 27 - 4
20. If we are trying to decide between two projects that will not be replaced when they wear out, the
proper capital budgeting method to use is NPV. Both projects only have costs associated with them,
not sales, so we will use these to calculate the NPV of each project. Using the tax shield approach to
calculate the OCF, the NPV of System A is:
And the NPV of System B is:
If the system will not be replaced when it wears out, then System A should be chosen, because it has
the more positive NPV.
21. If the equipment will be replaced at the end of its useful life, the correct capital budgeting technique
is EAC. Using the NPVs we calculated in the previous problem, the EAC for each system is:
EACA = –$383,236.37 / (PVIFA8%,4)
If the conveyor belt system will be continually replaced, we should choose System B since it has the
more positive EAC.
22. 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:
Aftertax salvage value = $400,000(1 – .34)
Now we can solve for the necessary OCF that will give the project a zero NPV. The current aftertax
value of the land is an opportunity cost, but we also need to include the aftertax value of the land in
five years since we can sell the land at that time. The equation for the NPV of the project is:
NPV = 0 = –$4,600,000 – 1,080,000 – 600,000 + OCF(PVIFA12%,5) – $50,000(PVIFA12%,4)
CHAPTER 27 - 5
Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:
The easiest way to calculate the bid price is the tax shield approach, so:
OCF = $1,435,757.48 = [(P – v)Q – FC ](1 – TC) + TCD
23. At a given price, taking accelerated depreciation compared to straight-line depreciation causes the
NPV to be higher; similarly, at a given price, lower net working capital investment requirements will
24. Since we need to calculate the EAC for each machine, sales are irrelevant. EAC only uses the costs
of operating the equipment, not the sales. Using the bottom-up approach, or net income plus
depreciation, method to calculate OCF, we get:
Machine A Machine B
Variable costs –$3,500,000 –$3,000,000
Fixed costs –195,000 –230,000
The NPV and EAC for Machine A are:
And the NPV and EAC for Machine B are:
NPVB = –$5,200,000 – 1,897,278(PVIFA10%,9)
You should choose Machine B since it has a more positive EAC.
CHAPTER 27 - 6
25. A kilowatt hour is 1,000 watts for 1 hour. A 60-watt bulb burning for 500 hours per year uses
30,000 watt hours, or 30 kilowatt hours. Since the cost of a kilowatt hour is $.121, the cost per year
is:
Cost per year = 30($.121)
The 60-watt bulb will last for 1,000 hours, which is two years of use at 500 hours per year. So, the
NPV of the 60-watt bulb is:
And the EAC is:
Now we can find the EAC for the 15-watt CFL. A 15-watt bulb burning for 500 hours per year uses
Cost per year = 7.5($.121)
The 15-watt CFL will last for 12,000 hours, which is 24 years of use at 500 hours per year. So, the
NPV of the CFL is:
NPV = –$3.40 – $.9075(PVIFA10%,24)
And the EAC is:
Thus, the CFL is much cheaper. But see our next two questions.
26. To solve the EAC algebraically for each bulb, we can set up the variables as follows:
W = Light bulb wattage
C = Cost per kilowatt hour
H = Hours burned per year
P = Price of the light bulb
The number of watts used by the bulb per hour is:
And the kilowatt hours used per year is:
CHAPTER 27 - 7
The electricity cost per year is therefore:
ECY = KPY × C
The NPV of the decision to buy the light bulb is:
NPV = – P – ECY(PVIFAR%,t)
And the EAC is:
EAC = NPV / (PVIFAR%,t)
Substituting, we get:
We need to set the EAC of the two light bulbs equal to each other and solve for C, the cost per
kilowatt hour. Doing so, we find:
So, unless the cost per kilowatt hour is extremely low, it makes sense to use the CFL. But when
should you replace the incandescent bulb? See the next question.
27. We are again solving for the breakeven kilowatt hour cost, but now the incandescent bulb has only
500 hours of useful life. In this case, the incandescent bulb has only one year of life left. The
breakeven electricity cost under these circumstances is:
Unless the electricity cost is negative (Not very likely!), it does not make financial sense to replace
the incandescent bulb until it burns out.
28. The debate between incandescent bulbs and CFLs is not just a financial debate, but an environmental
one as well. The numbers below correspond to the numbered items in the question:
1. The extra heat generated by an incandescent bulb is waste, but not necessarily in a heated
structure, especially in northern climates.
2. Since CFLs last so long, from a financial viewpoint, it might make sense to wait if prices are
declining.
3. Because of the nontrivial health and disposal issues, CFLs are not as attractive as our previous
analysis suggests.
CHAPTER 27 - 8
While there is always a “best” answer, this question shows that the analysis of the “best” answer is
Another piece of legislation that makes sense is requiring the producers of CFLs to supply a disposal
29. Surprise! You should definitely upgrade the truck. Here’s why. At 10 mpg, the truck burns 12,000 /
10 = 1,200 gallons of gas per year. The new truck will burn 12,000 / 12.5 = 960 gallons of gas per
This answer may strike you as counterintuitive, so let’s consider an extreme case. Suppose the car
Notice that the answer doesn’t depend on the cost of gasoline, meaning that if you upgrade, you
CHAPTER 27 - 9
30. We can begin by calculating the gallons saved by purchasing the new truck. The current and new
gallon usage when driving x miles per year are:
So the gallons saved by purchasing the new truck are:
If we let y equal the increased mileage for the car, the gallons used by the current car, the new car,
and the savings by purchasing the new car are:
Current car gallons = (x + y) / 25
We need to set the gallon savings from the new truck purchase equal to the gallon savings from the
new car purchase equal to each other, so:
From this equation you can see again that the cost per gallon is irrelevant. Each term would be
100x / 1,000 – 80x / 1,000 = 40(x + y) / 1,000 – 25(x + y) / 1,000
The difference in the mileage should be 1/3 of the miles driven by the truck. So, if the truck is driven
Challenge
