Question

Firm BCD has the opportunity to invest in one of two mutually exclusive machines, which can both produce the same product. Machine A has a life of 9 years, costs $12 million and will produce after-tax inflows of $2.5 million per year at the end of each year. Machine B has a life of 7 years, costs $15 million and will produce after-tax inflows of $3.5 million per year at the end of each year. Assuming that the machines can be replaced indefinitely at constant prices, which machine should BCD choose? Assume a cost of capital of 12%.

plz give steps in detail, do not use excel

Answer 1

Since the machines have unequal lives, equivalent annual annuity will be used to compare these.

Machine A

NPV = Present value of cash inflows – Present value of cash outflows

= -12,000,000 + 2,500,000*PVAF(12%, 9 years)

= -12,000,000 + 2,500,000*5.3283

= $1,320,750

EAA = NPV/PVAF

= 1,320,750/5.3283

= $247,874.56

Machine B

NPV = --15,000,000 + 3,500,000*PVAF(!2%, 7 years)

= -15,000,000 + 3,500,000*4.5638

= $973,300

EAA = 973300/4.5638

= $213,265.26

Hence, Machine A must be chosen as it has higher EAA.