Question

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%).

Answer 1

PV of cash flows = CFt/ (1+k)^t

where CFt is cash flow in year t, k = Cost of capital (WACC) & t is the year of Cash flow

NPV = Sum of PV of all future cash flows - Investment

Expected Price = Sum of Probability X Estimated Price for each year

For Year 1 = 0.1 x 0.83 + 0.2 X 1.01 + 0.3 X 1.12 + 0.2 X 1.31 + 0.2 X 1.40 = 1.163

For Year 2 = 0.1 x 0.93 + 0.2 X 1.11 + 0.3 X 1.21 + 0.2 X 1.45 + 0.2 X 1.57 = 1.282

For Year 3 = 0.1 x 1.02 + 0.2 X 1.13 + 0.3 X 1.30 + 0.2 X 1.47 + 0.2 X 1.62 = 1.336

Forecast based on Assumption 1

	Year 0	Year 1	Year 2	Year 3
Expected Price (A)		$1.163	$1.282	$1.336
Fuel Used (B) in Gallons		10,000,000	10,000,000	10,000,000
Fuel cost(C = A x B)		11,630,000	12,820,000	13,360,000
Savings in Fuel cost (15.23%) (D = C x 15.23%)		1,771,249	1,952,486	2,034,728
Depreciation (E = H XL)		1,267,500	1,940,500	1,827,500
EBIT (F = D - E)		503,749	11,986	207,228
Taxes @39% (G = F x 39%)		196,462	4,675	80,819
Net Income (H = F - G)		307,287	7,311	126,409
Add : Depreciation (E )		1,267,500	1,940,500	1,827,500
CFAT (I = H+ E)		1,574,787	1,947,811	1,953,909
Investments	(5,000,000)
Discount Factor @10% J = 1/(1+10%)^t	1	0.9091	0.8264	0.7513
Discounted CF K = I x J	(5,000,000)	1,431,624	1,609,762	1,468,001
NPV	(490,613)
Depreciation Rate L		25.35%	38.81%	36.55%

NPV for Assumption 1

= (1574787 / (1+10%)^1 + 1947811/ (1+10%)^2 + 1953909 / / (1+10%)^3) - 5,000,000

= 1431624 + 1609762 + 1468001 - 5,000,000

= -490613

Fuel cost = Fuel used X Price of fuel

Savings = 15.23% x Fuel cost

Depreciation = Investment value X Depreciation rate for the year

Tax Rate = 39%

Cost of Capital = 10%

Assumption 2 Price

Expected Price = Sum of Probability X Estimated Price for each year

For Year 1 = 0.1 x 1.21+ 0.3 X 1.31 + 0.4 X 1.82 + 0.2 X 2.19 = 1.68

For Year 2 = 0.1 x 1.49+ 0.3 X 1.70 + 0.4 X 2.32 + 0.2 X 2.49 = 2.09

For Year 3 = = 0.1 x 1.72 + 0.3 X 2.01 + 0.4 X 2.53 + 0.2 X 2.79 = 2.35

Forecast based on Assumption 2

	Year0	Year1	Year2	Year3
Expected Price (A)		$1.68	$2.09	$2.35
Fuel Used (B) in Gallons		10,000,000	10,000,000	10,000,000
Fuel cost(C = A x B)		16,800,000	20,850,000	23,450,000
Savings in Fuel cost (15.23%) (D = C x 15.23%)		2,558,640	3,175,455	3,571,435
Depreciation (E = H XL)		1,267,500	1,940,500	1,827,500
EBIT (F = D - E)		1,291,140	1,234,955	1,743,935
Taxes @39% (G = F x 39%)		503,545	481,632	680,135
Net Income (H = F - G)		787,595	753,323	1,063,800
Add : Depreciation (E )		1,267,500	1,940,500	1,827,500
CFAT (I = H+ E)		2,055,095	2,693,823	2,891,300
Investments	(5,000,000)
Discount Factor @10% J = 1/(1+10%)^t	1	0.9091	0.8264	0.7513
Discounted CF K = I x J	(5,000,000)	1,868,269	2,226,300	2,172,277
NPV	1,266,845
Depreciation Rate L		25.35%	38.81%	36.55%

NPV for Assumption 2

= (2055095 / (1+10%)^1 + 2693823/ (1+10%)^2 + 2891300 / / (1+10%)^3) - 5,000,000

= 1,868,269 + 2226300 + 2,172,277 - 5,000,000

= 1266845

NPV for Assumption 2 = 1,266,845

Weighted Average NPV = 50% X -490613 + 50% x 1266845

= 388116

% Change from assumption 1 & Weighted Average NPV = (388116 - (-490613)) / -490613

= - 79.10% (Negative would appear because base value being negative)