Question 17.11: Your company needs to purchase a dump truck and has narrowed...
Your company needs to purchase a dump truck and has narrowed the selection down to two alternatives. The first alternative is to purchase a new dump truck for $65,000. At the end of the seventh year the salvage value of the new dump truck is estimated to be $15,000.
The second alternative is to purchase a used dump truck for $50,000. At the end of the fourth year, the salvage value of the used dump truck is estimated to be $5,000. The annual profits, revenues less operation costs, are $17,000 per year for either truck. Using a MARR of 18%, calculate the annual worth for each of the dump trucks. Which truck should your company purchase?
The useful life of the new truck is seven years, which is used as the study period for the new truck. The purchase price for the new truck is converted to a uniform series of annual cash flows by Eq. (15-11) as follows:
A=P\left[\frac{i(1+i)^{n}}{(1+i)^{n}-1}\right] (15-11)
A_{ PP }=-\$ 65,000\left[\frac{0.18(1+0.18)^{7}}{(1+0.18)^{7}-1}\right]=-\$ 17,054
The salvage value for the new truck is converted to a uniform series of annual cash flows by Eq. (15-7) as follows:
A=F\left[\frac{i}{(1+i)^{n}-1}\right] (15-7)
A_{ SV }=\$ 15,000\left[\frac{0.18}{(1+0.18)^{7}-1}\right]=\$ 1,235
The annual profits for the new truck are already a uniform series. The annual equivalent for purchasing the truck equals the sum of the uniform series representing each of the individual cash flows and is calculated as follows:
A E=-\$ 17,054+\$ 1,235+\$ 17,000=\$ 1,181
The useful life of the used truck is four years, which is used as the study period for the used truck. The purchase price for the used truck is converted to a uniform series of annual cash flows by Eq. (15-11) as follows:
A_{ PP }=-\$ 50,000\left[\frac{0.18(1+0.18)^{4}}{(1+0.18)^{4}-1}\right]=-\$ 18,587
The salvage value for the used truck is converted to a uniform series of annual cash flows by Eq. (15-7) as follows:
A_{ SV }=\$ 5,000\left[\frac{0.18}{(1+0.18)^{4}-1}\right]=\$ 959
The annual profits for the used truck are already a uniform series. The annual equivalent for purchasing the truck equals the sum of the uniform series representing each of the individual cash flows and is calculated as follows:
AE =-\$ 18,587+\$ 959+\$ 17,000=-\$ 628
The new truck has the highest annual equivalent; therefore, your company should purchase the new truck.