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 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.

Answer 1

Low fuel prices

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
1.Expected price(sum of prob.*Price)	1.16	1.28	1.33
2.savings in Fuel usage(in gallons)	1500000	1500000	1500000
3.$ savings in fuel costs/yr.(1*2)	1743000	1921500	1996500
4. After-tax savings /yr.(3*(1-39%))	1063230	1172115	1217865

NPV under Assumption --1 --Low fuel prices
Year	0	1	2	3
1.Incremental cost of trucks	-5000000
2.Incl. after-tax fuel cost savings(as per Table-1)		1063230	1172115	1217865
3.Incl.depn. Tax shields(5 mln.*depn. %*39%)		497055	750750	708825
4.Incl. annual FCFs	-5000000	1560285	1922865	1926690
5.PV F at 9%(1/1.09^Yr.n)	1	0.91743	0.84168	0.77218
6.PV at 9% (4*5)	-5000000	1431454	1618437	1487758
7.Incl.NPV under Assumption --1 --Low fuel prices	-462351

High fuel prices

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
1.Expected price(sum of (prob.*Price))	1.69	2.10	2.33
2.savings in Fuel usage(in gallons)	1500000	1500000	1500000
3.$ savings in fuel costs/yr.(1*2)	2538000	3142500	3496500
4. After-tax savings /yr.(3*(1-39%))	1548180	1916925	2132865

NPV under Assumption --2 --high fuel prices
Year	0	1	2	3
1.Incremental cost of trucks	-5000000
2.Incl. after-tax fuel cost savings(as per Table-1)		1548180	1916925	2132865
3.Incl.depn. Tax shields(5 mln.*depn. %*39%)		497055	750750	708825
4.Incl. annual FCFs	-5000000	2045235	2667675	2841690
5.PV F at 9%(1/1.09^Yr.n)	1	0.91743	0.84168	0.77218
6.PV at 9%	-5000000	1876362	2245329	2194306
7.Incl.NPV under Assumption --1 --diesel prices stay relatively low	1315997
8. Incremental NPV(Assumption 2-1)	1778348
(1315997-(-462351))
9. % change in NPV
(1315997-(-462351))/462351=	384.63%