In: Accounting
Five years ago, a company was considering the purchase of 74 new diesel trucks that were 15.13% 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 74 new trucks will cost the firm $5 million. Depreciation will be 25.35% in year 1, 38.81% in year 2, and 36.55% in year 3. The firm is in a 39% income tax bracket and uses a 10% 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 |
$0.83 |
$0.93 |
$1.02 |
0.2 |
$1.01 |
$1.11 |
$1.13 |
0.3 |
$1.12 |
$1.21 |
$1.3 |
0.2 |
$1.31 |
$1.45 |
$1.47 |
0.2 |
$1.4 |
$1.57 |
$1.62 |
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 |
$1.21 |
$1.49 |
$1.72 |
0.3 |
$1.31 |
$1.7 |
$2.01 |
0.4 |
$1.82 |
$2.32 |
$2.53 |
0.2 |
$2.19 |
$2.49 |
$2.79 |
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.
Answer% Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places (for example: 28.31%).
Note: The educational purpose of this problem targets the students’ ability to read + follow instructions.
Further Information (solution steps):
Part (1) Calculations for Assumption #1
Step (1) | ||||||
Calculation of annual expected price of diesel per gallon under assumption #1 (low fuel prices) | ||||||
Probability (1) | Year 1 (2) | Expected price (3) = (1 x 2) | Year 2 (4) | Expected price (5) = (1 x 4) | Year 3 (6) | Expected price (7) = (1 x 6) |
0.1 | $0.83 | $0.083 | $0.93 | $0.09 | $1.02 | $0.10 |
0.2 | $1.01 | $0.202 | $1.11 | $0.22 | $1.13 | $0.23 |
0.3 | $1.12 | $0.336 | $1.21 | $0.36 | $1.30 | $0.39 |
0.2 | $1.31 | $0.262 | $1.45 | $0.29 | $1.47 | $0.29 |
0.2 | $1.4 | $0.280 | $1.57 | $0.31 | $1.62 | $0.32 |
Expected price | $1.16 | $1.28 | $1.34 |
Step (2) | ||
Calculation of increase in annual savings | ||
Year | Expected price of diesel | Annual savings(1.5 million) |
1 | $1.16 | 1.74 |
2 | $1.28 | 1.92 |
3 | $1.34 | 2.01 |
Note:Annual savings 1.5 million gallons,it is given in the question itself |
Step (3) | |||
Calculation of increase in cashflows | |||
Year | 1 | 2 | 3 |
Annual savings | 1.74 | 1.92 | 2.01 |
Depreciation % | 25.35% | 38.81% | 36.55% |
Less: deprecaition on (cost $5 million) | 1.2675 | 1.9405 | 1.8275 |
Saving after depreciation | 0.4725 | -0.0205 | 0.1825 |
Less:Tax @ 39% | 0.184275 | 0 | 0.071175 |
Savings after tax | 0.288225 | -0.0205 | 0.111325 |
Add:depreciation (non cash expense) | 1.2675 | 1.9405 | 1.8275 |
Cash flow after taxes (CAFT) | 1.555725 | 1.92 | 1.938825 |
Step (4) | |||
Calculation of NPV | |||
Year | 1 | 2 | 3 |
CAFT | 1.555725 | 1.92 | 1.938825 |
Discount rate @ 10% | 0.909 | 0.826 | 0.751 |
Discounted cashflow | 1.414295 | 1.58677686 | 1.4566679 |
Total of discounted cashflow | $4.46 | ||
Cost of investment | $ 5 | ||
Hence NPV is ($4.4577-$5) | -$0.54 |
Part (2) Calculation for Assumption #2
Step (1) | ||||||
Calculation of annual expected price of diesel per gallon under assumption #2 (high fuel prices) | ||||||
Probability (1) | Year 1 (2) | Expected price (3) = (1 x 2) | Year 2 (4) | Expected price (5) = (1 x 4) | Year 3 (6) | Expected price (7) = (1 x 6) |
0.1 | 1.21 | $0.121 | $1.49 | $0.15 | $1.72 | $0.17 |
0.3 | 1.31 | $0.393 | $1.70 | $0.51 | $2.01 | $0.60 |
0.4 | 1.82 | $0.728 | $2.32 | $0.93 | $2.53 | $1.01 |
0.2 | 2.19 | $0.438 | $2.49 | $0.50 | $2.79 | $0.56 |
Expected price | $1.68 | $2.09 | $2.35 |
Step (2) | ||
Calculation of increase in annual savings | ||
Year | Expected price of diesel | Annual savings(1.5 million) |
1 | $1.68 | $2.52 |
2 | $2.09 | $3.13 |
3 | $2.35 | $3.52 |
Note:Annual savings 1.5 million gallons,it is given in the question itself |
Step (3) | |||
Calculation of increase in cashflows | |||
Year | 1 | 2 | 3 |
Annual savings | $2.52 | $3.13 | $3.52 |
Depreciation % | 25.35% | 38.81% | 36.55% |
Less: deprecaition on (cost $5 million) | 1.2675 | 1.9405 | 1.8275 |
Saving after depreciation | $1.25 | $1.19 | $1.69 |
Less:Tax @ 39% | $0.49 | $0.46 | $0.66 |
Savings after tax | $0.76 | $0.72 | $1.03 |
Add:depreciation (non cash expense) | 1.2675 | 1.9405 | 1.8275 |
Cash flow after taxes (CAFT) | $2.03 | $2.66 | $2.86 |
Step (4) | |||
Calculation of NPV | |||
Year | 1 | 2 | 3 |
CAFT | $2.03 | $2.66 | $2.86 |
Discount rate @ 10% | 0.909 | 0.826 | 0.751 |
Discounted cashflow | 1.847 | 2.202 | 2.148 |
Total of discounted cashflow | $6.20 | ||
Cost of investment | $ 5 | ||
Hence NPV is ($6.20-$5) | $1.20 |
Part (3) Calculation of combined NPV
Step (5) | |||
Calculation of combined NPV weighed by the probablity of each assumption | |||
Assumption #1 | Assumption #2 | ||
NPV | -$0.54 | $1.20 | |
Probabity | 0.5 | 0.5 | |
Combined NPV | -$0.27 | $0.60 | |
Total of combined NPV | $0.33 | ||
Note:Both assumption have equal chance of being realized,hence probablity is 50% each assumption |
Part (4) Calculation of percentage of difference
Step (6) | |
Calculation of percentage of difference between combined NPV and NPV of Assumption #1 | |
NPV of assumption #1 | -0.54 |
Combined NPV | 0.33 |
Increase | 0.87 |
% of increase (0.87/.54) | -161 |
Or (ignore minus symbol) | 160% |
The percentafe of increase is 160%