You are considering adding a new software title to those published by your highl

Question

You are considering adding a new software title to those published by your highly successful software company. If you add the new product, it will use capacity on your disk duplicating machines that you had planned on using for your flagship product, “Battlin’ Bobby.” You had planned on using the unused capacity to start selling “BB” on the west coast in two years. You would eventually have had to purchase additional duplicating machines 10 years from today, but using the capacity for your new product will require moving this purchase up to 2 years from today. If the new machines will cost $112,000 and will be depreciated straight-line over a 5-year period to a zero salvage value, your marginal tax rate is 30 percent, and your cost of capital is 12 percent, what is the opportunity cost associated with using the unused capacity for the new product? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

As the use of the unused capacity for the new product will compel the company to purchase the additional duplicating machines in 2 years instead of 10 years, thus opportunity cost associated with using the unused capacity for the new product will be computed as follows:-

Associated Opportunity Cost = Present value of net cash flow related to the machinery in year 2 - Present value of net cash flow related to the machinery in year 10

= $87775.90 x 1/(1.12)2 - $87775.90 x 1/(1.12)10 (For $87775.90, See Working Note-1)

= $69974.41 - $28261.49

= $41712.92 (Answer)

Working Note 1

Present value of net cash flow related to the machinery = Cost of Machine - Present value of Annual tax saving on machinery depreciation

= $112000 - Annual Depreciation x Tax rate x PVIFA @ 12% for 5 years

= $112000 - ($112000/5) x 30% x 3.604776*

= $112000 - $24224.10

= $87775.90

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