Question
Five years ago, a company was considering the purchase of 68 new diesel trucks that were 14.63% more fuel-efficient than the ones the firm is
Five years ago, a company was considering the purchase of 68 new diesel trucks that were 14.63% more fuel-efficient than the ones the firm is now using. The company uses an average of 10 million gallons of diesel fuel per year at a price of $1.25 per gallon. If the company manages to save on fuel costs, it will save $1.875 million per year (1.5 million gallons at $1.25 per gallon). On this basis, fuel efficiency would save more money as the price of diesel fuel rises (at $1.35 per gallon, the firm would save $2.025 million in total if he buys the new trucks).
Consider two possible forecasts, each of which has an equal chance of being realized. Under assumption #1, diesel prices will stay relatively low; under assumption #2, diesel prices will rise considerably. The 68 new trucks will cost the firm $5 million. Depreciation will be 25.49% in year 1, 38.5% in year 2, and 36.35% in year 3. The firm is in a 39% income tax bracket and uses a 9% cost of capital for cash flow valuation purposes. Interest on debt is ignored. In addition, consider the following forecasts:
Forecast for assumption #1 (low fuel prices):
| Price of Diesel Fuel per Gallon | ||
Prob. (same for each year) | Year 1 | Year 2 | Year 3 |
0.1 | $0.8 | $0.91 | $1.01 |
0.2 | $1.02 | $1.12 | $1.09 |
0.3 | $1.12 | $1.22 | $1.32 |
0.2 | $1.31 | $1.45 | $1.47 |
0.2 | $1.4 | $1.55 | $1.61 |
Forecast for assumption #2 (high fuel prices): | |||
| Price of Diesel Fuel per Gallon | ||
Prob. (same for each year) | Year 1 | Year 2 | Year 3 |
0.1 | $1.23 | $1.53 | $1.72 |
0.3 | $1.31 | $1.7 | $1.99 |
0.4 | $1.83 | $2.32 | $2.5 |
0.2 | $2.22 | $2.52 | $2.81 |
Required: Calculate the percentage change on the basis that an increase would take place from the NPV under assumption #1 to the probability-weighted (expected) NPV.
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