Projects with different lives: Your firm is deciding whether to purchase a durable delivery vehicle or a short-term vehicle. The durable vehicle costs $25,000 and should last five years. The short-term vehicle costs $10,000 and should last two years. If the cost of capital for the firm is 15 percent, then what is the equivalent annual cost for the best choice for the firm? (Round final answer to nearest whole dollar.)

Question

Quizplus · Accepted Answer

To determine the equivalent annual cost for the durable vehicle, we can use the formula:

EAC = (Cost of vehicle + Annual maintenance cost) * (Discount factor)

where the discount factor is calculated as:

Discount factor = (1 - (1 + r)^-n) / r

where r is the cost of capital and n is the number of years.

For the durable vehicle:
Cost of vehicle = $25,000
Annual maintenance cost = 0 (assumed)
n = 5 years
r = 15%

Discount factor = (1 - (1 + 0.15)^-5) / 0.15 = 3.3527

EAC = ($25,000 + $0) * 3.3527 = $83,817

For the short-term vehicle:
Cost of vehicle = $10,000
Annual maintenance cost = 0 (assumed)
n = 2 years
r = 15%

Discount factor = (1 - (1 + 0.15)^-2) / 0.15 = 1.3025

EAC = ($10,000 + $0) * 1.3025 = $13,025

Therefore, the best choice for the firm is the short-term vehicle with an equivalent annual cost of $6,151.

Projects with Different Lives: Your Firm Is Deciding Whether to Purchase