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 $115,000 and will be depreciated straight-line over a 5-year period to a zero salvage value, your marginal tax rate is 32 percent, and your cost of capital is 16 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.)

Opportunity cost

$

Answer 1

Depreciation for year 1 = Cost / Life of the asset

                                             = 115000/10

                                             = $11,500

Depreciation in the subsequent years = 115,000 /5

                                                                      = $23,000

Depreciation tax shield is Depreciation x tax rate.

Year	1	2	3	4	5	6
Depreciation	11500	23000	23000	23000	23000	23000
Tax rate	30%	30%	30%	30%	30%	30%
Depreciation Tax shield	3450	6900	6900	6900	6900	6900

Now the Present value of Depreciation tax shield would be Depreciation tax shield times PV factor.

Year	Depreciation Tax shield	PV Factor 16%	PV
1	3450	0.862069	2974.138
2	6900	0.743163	5127.824
3	6900	0.640658	4420.538
4	6900	0.552291	3810.809
5	6900	0.476113	3285.18
6	3450	0.410442	1416.026
			21034.51

Total PV of tax shield = $25,288.35.

Net Cost = -115,000 +21034.51

               = -$93,965.50

The opportunity cost the difference in PV due to the difference in the investment time.

Opportunity cost = -$93,965.50/ (1+0.16)^2 – (-$93,965.50/ (1+0.16)^10)

                               = -48531.2282

Therefore, opportunity cost would be $48,531.23.