Five years ago, a company was considering the purchase of 72 new diesel trucks that were...

Five years ago, a company was considering the purchase of 72 new diesel trucks that were 14.56% 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 72 new trucks will cost the firm $5 million. Depreciation will be 24.84% in year 1, 38.39% in year 2, and 36.46% in year 3. The firm is in a 40% 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	$0.81	$0.89	$1.01
0.2	$1.02	$1.11	$1.11
0.3	$1.11	$1.23	$1.32
0.2	$1.3	$1.48	$1.46
0.2	$1.4	$1.58	$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	$1.22	$1.52	$1.69
0.3	$1.3	$1.7	$2.01
0.4	$1.81	$2.32	$2.52
0.2	$2.21	$2.53	$2.83

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%).

Further Information (solution steps):

Step (1): Calculate the annual expected price of diesel per gallon under each assumption, based on the probabilities outlined in the inputs section.

Step (2): Using the annual expected fuel prices calculated in step (1), determine the increase in annual savings created by the proposed efficiency for each assumption.

Step (3): Find the increased cash flow after taxes (CFAT) for both forecasts, based on the annual increase in fuel savings determined in step (2) as the increase in earnings before depreciation and taxes (EBDT), and the starting point from which profit is calculated for each assumption. As part of this step, you must establish annual depreciation (remember: depreciation is a noncash charge).

Step (4): Considering the increased annual CFAT produced in step (3), calculate the NPV of the truck purchases for each assumption, based on the discount rate (cost of capital) indicated in the inputs section

Step (5): In view of the outcomes produced in step (4), estimate the combined NPV weighed by the probability of each assumption.

Step (6): Finally, calculate the percentage difference hypothesizing that an increase took place starting from the NPV for assumption #1 to the combined NPV worked out in step (5).

Solutions

Expert Solution

Assumption1

Computation of Yearly rates

Year	Year 1	Year 2	Year 3
Probability	Rate	Probability weighted rate (Rate x Probability)	Rate	Probability weighted rate (Rate x Probability)	Rate	Probability weighted rate (Rate x Probability)
0.1	0.8100	0.0810	0.8900	0.0890	1.0100	0.1010
0.2	1.0200	0.2040	1.1100	0.2220	1.1100	0.2220
0.3	1.1100	0.3330	1.2300	0.3690	1.3200	0.3960
0.2	1.3000	0.2600	1.4800	0.2960	1.4600	0.2920
0.2	1.4000	0.2800	1.5800	0.3160	1.6100	0.3220
Yearly rate ( Aggregate of probability weighted rates)	1.1580	1.2920	1.3330

Annual savings on fuel efficiency from purchase of new trucks

Year	Year1	Year2	Year3
Yearly rates computed (refer computation of yearly rate table)	1.1580	1.2920	1.3330
Savings (Mn gallons)	1.5000	1.5000	1.5000
Savings (in Mn $) (Yearly rate x savings (Mn gallons)	1.7370	1.9380	1.9995

Depreciation computation

Purchase value of trucks ( 72 new trucks) in Mn $	5.0000
Year 1 depreciation @ 24.84% (Purchase value x depreciation rate)	1.2420
Year 2 depreciation @ 38.39% (Purchase value x depreciation rate)	1.9195
Year 2 depreciation @ 36.46% (Purchase value x depreciation rate)	1.8230

Cashflow table and NPV computation

Year	0	1	2	3
Initial cashflows (in Mn $)
Purchase value of 72 trucks	(5.0000)
Intermediate cashflows (in Mn $)
Annual savings		1.7370	1.9380	1.9995
Less : Depreciation on new trucks		1.2420	1.9195	1.8230
Profit before taxes		0.4950	0.0185	0.1765
Less : Taxes @ 40%		0.1980	0.0074	0.0706
Profit after taxes		0.2970	0.0111	0.1059
Add : Depreciation		1.2420	1.9195	1.8230
Cashflow after taxes (in Mn $)		1.5390	1.9306	1.9289
Net cashflows ( Initial + Intermediate) (in Mn $)	(5.0000)	1.5390	1.9306	1.9289
PV factor @ 10%	1.0000	0.9091	0.8264	0.7513
Present vale of cashflows	(5.0000)	1.3991	1.5955	1.4492
Net Present value of cashflows (in Mn $)	(0.5562)

Note 1: Depreciation has been added back to profit after tax to arrive at Cashflow after taxes as it is a non cash expense.

Note 2: PV factor is computed based on the formula ---> 1/ (1+discounting rate)^year; Year 1 --> 1/ (1+10%)^1; Year 2 ---> 1/ (1+10%)^2; Year 3--> 1/(1+10%)^3. Discounting rate is picked from cost of capital at 10% (mentioned in the question).

Assumption 2

Computation of Yearly rate

Year	Year 1	Year 2	Year 3
Probability	Rate	Probability weighted rate (Rate x Probability)	Rate	Probability weighted rate (Rate x Probability)	Rate	Probability weighted rate (Rate x Probability)
0.1	1.2200	0.1220	1.5200	0.1520	1.6900	0.1690
0.3	1.3000	0.3900	1.7000	0.5100	2.0100	0.6030
0.4	1.8100	0.7240	2.3200	0.9280	2.5200	1.0080
0.2	2.2100	0.4420	2.5300	0.5060	2.8300	0.5660
Yearly rate ( Aggregate of probability weighted rates)	1.6780	2.0960	2.3460