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

Question

2. 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 $50,000. The initial cost of Machine B is $280,000 and it will last for 5 years before it needs to be replaced. The cost of operating machine B is $70,000 in cash flow per year. If the required rate of return is 9%,

            (a) Calculate the 7 year and 5 year annuity factors at 9% 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) Calculate the 7 year and 5 year annuity factors at 9% annual interest.

7 Year PV Annuity Factor = (1-(1-r)^-n)/r

7 Year PV Annuity Factor = (1-(1+9%)^-7)/9%

7 Year PV Annuity Factor = 5.032953

5 Year PV Annuity Factor = (1-(1-r)^-n)/r

5 Year PV Annuity Factor = (1-(1+9%)^-5)/9%

5 Year PV Annuity Factor = 3.889651

(b) Using the annuity factors, find the PV of Machine A and Machine B including all costs (initial + operating).

PV of Machine A = (initial + Annual operating Cost*7 Year PV Annuity Factor )

PV of Machine A = (400000 + 50000*5.032953)

PV of Machine A = $ 651,647.65

PV of Machine B = (initial + Annual operating Cost*5 Year PV Annuity Factor )

PV of Machine B = (280000 + 70000*3.889651)

PV of Machine B = $ 552,275.57

(c) Which machine is a better choice for the company after considering the different lives of the projects?

Equivalent annual cost of Machine A = PV of Machine A / 7 Year PV Annuity Factor

Equivalent annual cost of Machine A = 651,647.65/5.032953

Equivalent annual cost of Machine A = 129,476.20

Equivalent annual cost of Machine B = PV of Machine 5 / 5 Year PV Annuity Factor

Equivalent annual cost of Machine B = 552,275.57/3.889651

Equivalent annual cost of Machine B = 141,985.89

Decison : Machine A is a better choice for the company after considering the different lives of the projects as its Equivalent annual cost is lower

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