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 $110,000 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?

Answer 1

	T=0	T=1	T=2	T=3	T=4	T=5	T=6	T=7	T=8	T=9	T=10
New Machine cost Year 2			-110000
PV of Machine at Year 0 = Machine cost/(1+ r)^2	-81747.9191
Depreciation = (New Machine cost-0)/5				22000	22000	22000	22000	22000
Depreciation Tax Shield = Deprecation* Tax rate				7040	7040	7040	7040	7040
PV of Depreciation Tax Shield At T=2(Using NPV function in Excel)			$23,051.03
PV of Depreciation Tax Benefit At T=0	$17,130.67
The Cost of Buying Machine at Year 2 including depreciation Tax shield			($86,948.97)
The Cost of Buying Machine at Year 2 including depreciation Tax shield											($86,948.97)
Opportunity Cost is difference of PV of the Cost at T=2 and PV of Cost at T=10( Same Cost -86,948.97 will be incurred both at T=2 and T=10)
PV of Machine Cost and Depreciation tax shield for T=2	($64,617.25)
PV of Machine Cost and Depreciation tax shield for T=10	-19709.9064
Opportunity Cost	($44,907.34)