Question

A self-employed worker operates a firewood-splitting service. He purchased a commercial-grade wood splitter for $5800. He used $400 of business capital and financed the balance at 5% per year for 3 years. The estimated values of the splitter for the next 6 years are $2200 after the first year of ownership, decreasing by $400 per year to year 5, after which the resale value remains at $600. Annual operating costs are expected to be $1000 the first year, increasing by 10% each year thereafter. He considers keeping the splitter at least 6 years. If money is worth 7% per year, for how many years should the splitter be retained? (Perform the Economic Minimum Life analysis for at least 12 years.) Spreadsheet solution required with a summary of what is being analyzed.

Answer 1

Finance splitter through   

Business capital	loan
400	5400

Economic Life Analysis

	1	2	3	4	5	6	7	8	9	10	11	12
Value of splitter	5800	2200	1800	1400	1000	600	200
Depreciation	3600	400	400	400	400	400
Annual cost	1000	1100	1210	1331	1464.1	1610.51	1771.561	1948.717	2143.589	2357.948	2593.742	2853.117
Interest on loan	270	270	270
Opportunity cost of capital	28	28	28	28	28	28	28	28	28	28	28	28
total cost	4898	1798	1908	1759	1892.1	2038.51	1799.561	1976.717	2171.589	2385.948	2621.742	2881.117
discount @ 7%	0.934579	0.8734	0.81629	0.76289	0.71298	0.66634	0.62274	0.582	0.54393	0.50834	0.475	0.444
NPV	4577.57	1570.373	1557.481	1341.924	1349.029	1358.341	1120.659	1150.449	1181.192	1212.873	1245.328	1279.216

NPV increases till 7th year after which it increases. If splitter is retained for 6 years and sold for $600 then NPV of cost will be 1358.341-600=$758.341.

Hence, to incur minimum cost, splitter should be retained for 6 Years.