The company is choosing between machine A and B (they are mutually exclusive and
ID: 2633502 • 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 $40,000. The initial cost of Machine B is $200,000 and it will last for 5 years before it needs to be replaced. The cost of operating machine B is $75,000 in cash flow per year. If the required rate of return is 8%,
(a) Calculate the 7 year and 5 year annuity factors at 8% 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)
annuity factor(7,8%) = [1-(1+i)-n]/i = [1-(1+8%)-7]/8% = 5.2064
annuity factor(5,8%)? = [1-(1+i)-n]/i = [1-(1+8%)-5]/8% = 3.9927
(b)
PV of Machine A = -$400,000 - $40,000 * 5.2064 = -$608,256
PV of Machine B = -$200,000 - $75,000 * 3.9927 = -$499,452.5
(c)
Equivalent Annual Cost of Machine A = -$608,256/5.2064 = -$116,828.52
Equivalent Annual Cost of Machine B = -$499,452.5/3.9927 = -$125,091.42
Therefore,machine A is a better choice because it has the lower annual cost.