3. The company is choosing between machine A and B (they are mutually exclusive

Question

3. 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

a)

PV Annuity factor = ( 1 - (1+r)-n ) / r

FV Annuity factor = ( (1+r)n -1 ) / r

PV(@ 7%) for 7 years = ( 1 - (1+7%)-7 ) / 7% = 5.39

PV(@ 7%) for 5 years = ( 1 - (1+7%)-5 ) / 7% = 4.10

b)

PV of A = -200000 - 30000*5.39 = -361678.68

PV of B = -120000 - 40000*4.10 = -284007.90

c)

PMT (@ 7%) for 7 years = 7% / ( 1 - (1+7%)-7 ) = 0.19

PMT (@ 7%) for 5 years = 7% / ( 1 - (1+7%)-5 ) = 0.24

equivalent annual annuity method of A = -200000*0.19 - 30000 = -67110.64

equivalent annual annuity method of B = -120000*0.19 - 40000 = -69266.88

Choose A

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