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18. To calculate the EAC of the project, we first need the PV of the costs 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 PV of the costs of the project is:
Now we can find the EAC of the project. The EAC is:
19. 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 PV of costs of each option. The OCF and PV of
costs for Techron I is:
And the OCF and PV of costs for Techron II is:
The two milling machines have unequal lives, so they can only be compared by expressing both on
20. 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:
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:
Intermediate
21. First, we will calculate the depreciation each year, which will be:
D1 = $385,000(.2000) = $77,000
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 = $145,000(1 – .22) + .22($77,000) = $130,040
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
22. The aftertax salvage value is:
And the OCF each year will be:
Year 1 Years 2-5
Sales $275,000 $275,000
Variable costs 96,250 96,250
Now we have all the necessary information to calculate the project NPV. The project NPV is:
23. If we are trying to decide between two projects that will not be replaced when they wear out, the
And the NPV of System B is:
24. If the equipment will be replaced at the end of its useful life, the correct capital budgeting technique
is EAC. Using the PV of costs (NPVs) we calculated in the previous problem, the EAC for each
system is:
If the conveyor belt system will be continually replaced, we should choose System B since it has the
more positive EAC.
25. 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 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:
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:
27. 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 method, or net income plus
depreciation, to calculate OCF, we get:
Machine A Machine B
Variable costs –$4,550,000 –$3,900,000
Fixed costs –210,000 –245,000
The PV of costs and EAC for Machine A are:
And the PV of costs and EAC for Machine B are:
You should choose Machine B since it has a less negative EAC.
28. A kilowatt hour is 1,000 watts for 1 hour. A 60-watt bulb burning for 500 hours per year uses
The 60-watt bulb will last for 1,000 hours, which is two years of use at 500 hours per year. So, the
PV of costs of the 60-watt bulb is:
And the EAC is:
Now we can find the EAC for the 7-watt LED. A 7-watt bulb burning for 500 hours per year uses
The 7-watt LED will last for 40,000 hours, which is 80 years of use at 500 hours per year. So, the PV
of costs of the LED is:
And the EAC is:
Thus, the LED is much cheaper. But see our next two questions.
29. 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:
The electricity cost per year is therefore:
The PV of costs of the decision to buy the light bulb is:
And the EAC is:
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 negative (Not very likely!), it makes sense to use the LED.
But when should you replace the incandescent bulb? See the next question.
30. We are again solving for the break-even 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 break-
even electricity cost under these circumstances is:
Again, unless the electricity cost is negative, it does not make financial sense to replace the
incandescent bulb until it burns out.
31. 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.
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
32. Surprise! You should definitely upgrade the truck. Here’s why. At 10 mpg, the truck burns 12,000/10
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
should always upgrade the truck. In fact, it doesn’t depend on the miles driven, as long as the miles
driven are the same.
33. 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:
We need to set the gallon savings from the new truck purchase equal to the gallon savings from the
new car purchase, 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
34. We will begin by calculating the aftertax salvage value of the equipment at the end of the project’s
life. The aftertax salvage value is the market value of the equipment minus any taxes paid (or
refunded), so the aftertax salvage value in four years will be:
Taxes on salvage value = (BV – MV)TC
Market price $395,000
Now we need to calculate the operating cash flow each year. Using the bottom up approach to
calculating operating cash flow, we find:
Year 0 Year 1 Year 2 Year 3 Year 4
Revenues $2,167,500 $2,465,000 $2,720,000 $1,997,500
Fixed costs 345,000 345,000 345,000 345,000
Notice the calculation of the cash flow at Time 0. The capital spending on equipment and investment
in net working capital are both 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. The company can sell the land at the end of the project, so we need to include that value as
well. With all the project cash flows, we can calculate the NPV, which is:
The company should accept the new product line.
