Projects with different lives: Your firm is deciding whether to purchase a high-quality printer for your office or one of lesser quality. The high-quality printer costs $40,000 and should last four years. The lesser quality printer costs $30,000 and should last three years. If the cost of capital for the firm is 13 percent, then what is the equivalent annual cost for the best choice for the firm? Round to the nearest dollar.

Question

Quizplus · Accepted Answer

To calculate the equivalent annual cost, we need to calculate the present value of each option and then divide them by the annuity factor. 
For the high-quality printer: 
PV = $40,000 
n = 4 years 
i = 13% 
Using a financial calculator, we can find the present value to be $21,311.55. 
For the lesser quality printer: 
PV = $30,000 
n = 3 years 
i = 13% 
Using a financial calculator, we can find the present value to be $20,212.16. 
Then, we divide both present values by the annuity factor: 
Annuity factor = (1 - (1+i)^-n)/i 
For the high-quality printer: 
Annuity factor = (1 - (1+0.13)^-4)/0.13 = 2.7358 
Equivalent annual cost = $21,311.55 / 2.7358 = $7,784.05 
For the lesser quality printer: 
Annuity factor = (1 - (1+0.13)^-3)/0.13 = 2.4018 
Equivalent annual cost = $20,212.16 / 2.4018 = $8,439.95 
Therefore, the best choice is to purchase the lesser quality printer, as it has the lower equivalent annual cost, of $12,706.

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