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

As Marginal Tax Rate = 8.25 is currently after tax it means tax impact is already taken into impact
In order to keep the Rate pre tax as per question requirement divide the 8.25 / 0.72= 11.46 approx
It is divided by 0.72 because as 8,25 is given after tax and tax rate is 28% 1-0.28 = 0.72 and rate is reflected at 0.72 hence divided by 0.72
All values are in $
Cost Incurred	350000
Salvage Value is	50000		Receivable at 30th Year
Cash Outflows
Annual Maintenance Cost	3250
Production Cost		23000
Revenue Earned		60000
Depreciation		35000*
* Salvage value is Zero for calculating Depreciation for 10 years on SLM
	Reveue	AMC	ProductionCost	Depreciation	Salvage inflow	Net Income	Tax	Net Inflow	PV Factor @ 11.46%	PV Factor @ 5%	PV Factor @ 1%
Year 1	60000	3250	23000	35000	0	-1250	NIL	33750	0.897	30274	0.952	32130	0.99	33413
Year 2	60000	3250	23000	35000	0	-1250	NIL	33750	0.804	27135	0.907	30611	0.98	33075
Year 3	60000	3250	23000	35000	0	-1250	NIL	33750	0.722	24368	0.863	29126	0.97	32738
Year 4	60000	3250	23000	35000	0	-1250	NIL	33750	0.647	21836	0.822	27743	0.96	32400
Year 5	60000	3250	23000	35000	0	-1250	NIL	33750	0.581	19609	0.783	26426	0.951	32096
Year 6	60000	3250	23000	35000	0	-1250	NIL	33750	0.521	17584	0.746	25178	0.942	31793
Year 7	60000	3250	23000	35000	0	-1250	NIL	33750	0.467	15761	0.71	23963	0.932	31455
Year 8	60000	3250	23000	35000	0	-1250	NIL	33750	0.419	14141	0.676	22815	0.923	31151
Year 9	60000	3250	23000	35000	0	-1250	NIL	33750	0.376	12690	0.644	21735	0.914	30848
Year 10	60000	3250	23000	35000	0	-1250	NIL	33750	0.337	11374	0.613	20689	0.905	30544
Year 30th	0	0	0	0	30000	8400	21600	21600	0.038	821	0.231	4990	0.741	16006

Applying Interpolation and Expolation:

Total PV at 1% 335517

Total PV at 5% 265405

We want value for 300000$

Difference between 1% and 5% value = 70112

Difference between 1% and 0% = 35517

hence 4%X 35517 / 70112 = 2.02%