The company is choosing between machine A and B (they are mutually exclusive and
ID: 2713840 • Letter: T
Question
The company is choosing between machine A and B (they are mutually exclusive and the company can only pick one). The initial cost of machine A is $400,000 and it will last for 7 years before it needs to be replaced. The cost of operating machine A each year is $50,000. The initial cost of Machine B is $280,000 and it will last for 5 years before it needs to be replaced. The cost of operating machine B is $70,000 in cash flow per year. If the required rate of return is 9%,
(a) Calculate the 7 year and 5 year annuity factors at 9% annual interest.
(b) Using the annuity factors, find the PV of Machine A and Machine B including all costs (initial + operating).
(c) Which machine is a better choice for the company after considering the different lives of the projects? (Note: be sure to use the equivalent annual annuity method)
Explanation / Answer
(a) PVIFA (r%, n) = [1 - (1 + r)-n] / r
PVIFA (9%, 7 years) = [1 - (1.09)-7] / 0.09 = 5.033
PVIFA (9%, 5 years) = [1 - (1.09)-5] / 0.09 = 3.8897
(b)
PV, machine A ($) = 400,000 + 50,000 x 5.033 = 400,000 + 251,650 = 651,650
PV, machine B ($) = 280,000 + 70,000 x 3.8897 = 280,000 + 272,279 = 552,279
(c) We need to find out Equivalent Annual Worth (EAW) for each machine.
Machine A = 400,000 x A/P(9%, 7 years) + 50,000 = 400,000 x 0.2 + 50,000 = 80,000 + 50,000 = 130,000
Machine B = 2800,000 x A/P(9%, 5 years) + 70,000 = 280,000 x 0.26 + 70,000 = 72,800 + 70,000 = 142,800
Since machine A has a lower EAW, it is a better choice.