Question

A piece of onboard equipment has a first cost of $600,000, an annual cost of $92,000, and a salvage value that decreases to zero by $150,000 each year of the equipment’s maximum useful life of 5 years. Assume the company’s MARR is 10% per year.

(a) Determine the ESL by hand.

(b) Use a spreadsheet with a graph indicating the capital recovery, AOC, and total AW per year to determine the ESL.

Answer 1

Here is the stesps to solve such problem with taxes.

Given probme is the simple one without taxes.

Steps:

1. You have MV and BV

2. After-tax MV = MV – (MV – BV) * Tax

3. Capital recovery = (MV_k-1 – MV_k) + r*MV_k-1

4. Depreciation: D = BV_k-1 - BV_k

5. You have O&M

6. Taxable Income: TI = -O&M – Depreciation

7. Tax = TI*0.40

8. MC = Capital recovery + O&M + Tax

9. Convert it into EUAC: PMT (r%, k, NPV(r%, 1 to k^th MC), 0) for k^th year

	Book Value	Depreciation	Capital Recovery	AOC	Marginal Cost	EUAC
0	600,000
1	450,000	150,000	210,000	92,000	302,000	302,000.00
2	300,000	150,000	195,000	92,000	287,000	294,857.14
3	150,000	150,000	180,000	92,000	272,000	195,308.16
4	0	150,000	165,000	92,000	257,000	145,012.28
5	0	0	0	92,000	92,000	81,690.01

Given the data in problem, economic service life is 5 years.

Generally EUAC decreases and increases. Economic service life is at minimum EUAC.