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# Capital Budgeting, NPV

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Ace Trucking Company is considering buying 50 new diesel trucks that are 15 percent more fuel-efficient than the ones the firm is now using. Mr. King, the president, has found that the company uses an average of 10 million gallons of diesel fuel per year at a price of \$1.20 per gallon. If he can cut fuel consumption by 15 percent, he will save \$1,800,000 per year (1,500,000 gallons times \$1.20).

Mr. King assumes the price of diesel fuel is an external market force he cannot control and any increased costs of fuel will be passed on to the shipper through higher rates endorsed by the Interstate Commerce Commission. If this is true, then fuel efficiency would save more money as the price of diesel fuel rises (at \$1.30 per gallon, he would save \$1,950,000 in total if he buys the new trucks).

Mr. King has come up with two possible forecasts as shown below-each of which he believes has about a 50 percent chance of coming true. Under assumption one, diesel prices will stay relatively low; under assumption two, diesel prices will rise considerably.

Fifty new trucks will cost AceTrucking \$5 million. Under a special provision from the Interstate Commerce Commission, the allowable deprecation will be 25 percent in year one, 38 percent in year two, and 37 percent in year three. The firm has a tax rate of 40 percent and a cost of capital of 11 percent.

a. First compute the yearly expected costs of diesel fuel for both assumption one (relatively low prices) and assumption two (high prices) from the following forecasts.

Forecast for assumption one:

Probability
(same for
each year) Price of Diesel Fuel per Gallon

Year 1
Year 2
Year 3
.1 \$ .70 \$ .90 \$1.00
.2 .90 1.10 1.20
.3 1.00 1.20 1.30
.2 1.20 1.45 1.50
.2 1.30 1.55 1.70

Forecast for assumption two:

Probability
(same for
each year) Price of Diesel Fuel per Gallon

Year 1
Year 2
Year 3
.1 \$1.30 \$1.50 \$1.90
.3 1.40 1.70 2.20
.4 1.90 2.30 2.70
.2 2.30 2.50 3.00

b. What will be the dollar savings in diesel expenses each year for assumption one and for assumption two?
c. Find the increased cash flow after taxes for both forecasts.
d. Compute the net present value of the truck purchases for each fuel forecast assumption and the combined net present value (that is, weigh the NPVs by .5).
e. If you were Mr. King, would you go ahead with this capital investment?
f. How sensitive to fuel prices is this capital investment?

#### Solution Preview

a. First compute the yearly expected costs of diesel fuel for both assumption one (relatively low prices) and assumption two (high prices) from the following forecasts.

The expected price for each year under the two assumptions :

Forecast for assumption one:

Probability Year 1 Year 2 Year 3
0.1 \$0.70 \$0.90 \$1.00
0.2 \$0.90 \$1.10 \$1.20
0.3 \$1.00 \$1.20 \$1.30
0.2 \$1.20 \$1.45 \$1.50
0.2 \$1.30 \$1.55 \$1.70

Year Fuel Cost
1 \$1.05 =0.1x0.7+0.2x0.9+0.3x1+0.2x1.2+0.2x1.3
2 \$1.27 =0.1x0.9+0.2x1.1+0.3x1.2+0.2x1.45+0.2x1.55
3 \$1.37 =0.1x1+0.2x1.2+0.3x1.3+0.2x1.5+0.2x1.7

Forecast for assumption two:

Probability Year 1 Year 2 Year 3
0.1 \$1.30 \$1.50 \$1.90
0.3 \$1.40 \$1.70 \$2.20
0.4 \$1.90 \$2.30 \$2.70
0.2 \$2.30 \$2.50 \$3.00

Year Fuel Cost
1 \$1.77 =0.1x1.3+0.3x1.4+0.4x1.9+0.2x2.3
2 \$2.08 =0.1x1.5+0.3x1.7+0.4x2.3+0.2x2.5
3 \$2.53 =0.1x1.9+0.3x2.2+0.4x2.7+0.2x3

b. What will be the dollar savings in diesel expenses each year for assumption one and for assumption two?

Diesel saved each ...

#### Solution Summary

Analyses a capital budgeting decision.

\$2.19