Question

Assume you have been hired to evaluate an investment required by EPA for a waste management system for a nearby hog operation. The system will cost $350,000 and will last 30 years but only depreciated for 10 years. Assuming straight line depreciation, the salvage value is zero fro depreciation. The actual expected terminal value is %50,000 which will be received in 30 years time. The system has a $3,250 annual maintenance cost. The marginal tax rate is 28% and the after-tax cost of capital is 8.25%. The production of hog will require feed at $23,000 per year and the operation will produce $60,000 in income each year. What is the annualized capital recovery cost in pre-tax terms for this $300,000 investment?

Answer 1

Given
Cost of investment	350,000
Life	30
Depreciable year	10
Salvage value for depreciation	0
Actual terminal value	50,000
Annual maintenance cost	3,250
Marginal tax rate	28%
After tax cost of capital	8.25%
Production cost	23,000
Revenue	60,000

Answer

Annualized pre-tax capital recovery cost
Cost of investment	350,000
Marginal tax rate	28.00%
After tax cost of capital	8.25%
Pre tax cost of capital 8.3%/(1-28%)	11.46%
Present value of salvage value 50,000/(1.1146^30)	1,930
Net value of investment Cost of investment - PV of salvage value	348,070

Let pre-tax annualized capital recovery cost be X, then

XPVIFA11.46%,30 years = 348,070

Where PVIFA can be calculated as:

Where PMT = X, r = 11.46% and n = 30

[X/1.1146]*[1-{1/(1.1146^30)}} = X*8.3904

X*8.3904 = 348,070

X=41,484

Therefore, the annualized capital recovery cost is equal to 41,484

The actual annualized pre-tax capital recovery before depreciation is as follows

Revenue	60,000
Less: Production cost	23,000
Less: Maintenance cost	3,250
Actual pre-tax income before depreciation	33,750

Given that the actual capital recovery of 33,750 is lesser than the cost of 41,484, the project of implemented will give return lower than pre-tax cost of capital.