Question

You are asked by your boss to conduct a life cycle cost analysis and make a decision on a truck purchase. There are two alternatives:

(a) Diesel Truck: first cost - $22,000, service life - 4 years, annual operation costs - $5,000, maintenance/repair costs - $1,000 after 2 years and $1,000 after 4 years, salvage value - $12,000;

(b) (a) Gas Truck: first cost - $20,000, service life - 4 years, annual operation costs - $6,250, maintenance/repair costs - $1,000 after 2 years and $3,000 after 4 years, salvage value - $10,000. Assume a 10% discount rate. Draw the cash flow diagram and calculate the life cycle cost for each alternative using present value method. What is your recommendation to your boss?

Answer 1

(1) Cash flow diagram as follows (all values in $).

(2)

Present value of costs for both trucks is computed as follows. Note:

(i) For both trucks, cost in year 4 will be lower by the amount of salvage value (leading to a negative cost value)

(ii) PV Factor in year N = (1.1)^-N

DIESEL TRUCK
Year	Cost ($)	PV Factor @10%	Discounted Cost ($)
	(A)	(B)	(A) x (B)
0	22,000	1.0000	22,000
1	5,000	0.9091	4,545
2	6,000	0.8264	4,959
3	5,000	0.7513	3,757
4	-6,000	0.6830	-4,098
		PW of Costs ($) =	31,163
GAS TRUCK
Year	Cost ($)	PV Factor @10%	Discounted Cost ($)
	(A)	(B)	(A) x (B)
0	20,000	1.0000	20,000
1	6,250	0.9091	5,682
2	7,250	0.8264	5,992
3	6,250	0.7513	4,696
4	-750	0.6830	-512
		PW of Costs ($) =	35,857

Since Diesel truck has a lower PW of costs, this should be selected.