The company is choosing between machine A and B (they are mutually exclusive and
ID: 2765558 • 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
(a) (b) and (c)
Machine A:
Year
Cash flows
Discounting
factor @10%
Discounted
Cash flows
0
$ 1,400,000
1
$ 1,400,000.00
1
$ 150,000
0.90909
$ 136,363.50
2
$ 150,000
0.82645
$ 123,967.50
3
$ 150,000
0.75131
$ 112,696.50
4
$ 150,000
0.68301
$ 102,451.50
5
$ 150,000
0.62092
$ 93,138.00
6
$ 150,000
0.56447
$ 84,670.50
7
$ 150,000
0.51316
$ 76,974.00
Total cash flows
$ 2,130,262
Yearly expenses = $2,130,262 / 5.86841
= $363,005
Machine B:
Year
Cash flows
Discounting
factor @10%
Discounted
Cash flows
0
$ 800,000
1
$ 800,000.00
1
$ 230,000
0.90909
$ 209,090.70
2
$ 230,000
0.82645
$ 190,083.50
3
$ 230,000
0.75131
$ 172,801.30
4
$ 230,000
0.68301
$ 157,092.30
5
$ 230,000
0.62092
$ 142,811.60
Total cash flows
$ 1,671,879
Yearly expenses = $ 1,671,879 / 4.79078
= $348,978
Machine B is better than machine A due to it has low maintenance charges compared to machine A.
Machine A:
Year
Cash flows
Discounting
factor @10%
Discounted
Cash flows
0
$ 1,400,000
1
$ 1,400,000.00
1
$ 150,000
0.90909
$ 136,363.50
2
$ 150,000
0.82645
$ 123,967.50
3
$ 150,000
0.75131
$ 112,696.50
4
$ 150,000
0.68301
$ 102,451.50
5
$ 150,000
0.62092
$ 93,138.00
6
$ 150,000
0.56447
$ 84,670.50
7
$ 150,000
0.51316
$ 76,974.00
Total cash flows
$ 2,130,262