The company is choosing between machine A and B (they are mutually exclusive and
ID: 2791694 • 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 $200,000 and it will last for 7 years before it needs to be replaced. The cost of operating machine A each year is $30,000. The initial cost of Machine B is $120,000 and it will last for 5 years before it needs to be replaced. The cost of operating machine B is $40,000 in cash flow per year. If the required rate of return is 7%, (a) Calculate the 7 year and 5 year annuity factors at 7% 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 factor for 7 year at 7% annual interest=5.389
Annuity factor for 5 year at 7% annual interest=4.100
PV of cost of machine A=Initial cost +PV of operating cost
=200000+30000*5.389=361670
PV of cost of machine B=Initial cost+ PV of operating cost
=120000+40000*4.100=284000
To choose machine with different year we have to select machine whose annual cost charge is least
Annual cost charge of machine A=PV of total cost/Annuity factor=361670/5.389=67112.64
Annual cost charge of machine B=PV of total cost/Annuity factor=284000/4.100=69268.29
Hence Machine A is selected