The company is choosing between machine A and B (they are mutually exclusive and
ID: 2765705 • 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 $1,400,000 and it will last for 7 years before it needs to be replaced. The cost of operating machine A each year is $150,000. The initial cost of Machine B is $800,000 and it will last for 5 years before it needs to be replaced. The cost of operating machine B is $230,000 in cash flow per year. If the required rate of return is 10%,
(a) Calculate the 7 year and 5 year annuity factors at 10% 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
Annuity factors for 7 years = (1-1/{1+k]^n).k = 4.868419
Annuity factors for 10 years = (1-1/{1+k]^n).k = 6.144567
Using the annuity factors, find the PV of Machine A and Machine B including all costs
PV(MACHINE A) = 1,400,000+150,000 = 1,550,000*4868419 = $7,546,049.17
PV(MACHINE B) = $800,000+$230,000 = $1,030,000*6.144567 = $9,524,079.01
mACHINE b IS BETTER