Question

Here is the information about the solar energy system: Initial cost = $6,500; Initial fuel savings = $500/year; Expected life = 15 years; Value of Money = 10%; Inflation = 8%; and Incremental income tax rate = 25%. If we define the payback condition as the time required for the present worth of the accumulated benefit to equal the accumulated present worth of the system cost, what is the time required to reach the payback condition? Since the income tax benefit is related to the annual interest expense, treat it as a reduction of the annual cost.

Answer 1

We do a cash flow analysis

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Initial cost	-6,500
Fuel savings		500	540	583	630	680	735	793	857	925	1,000	1,079	1,166	1,259	1,360	1,469
Savings post tax		375	405	437	472	510	551	595	643	694	750	810	874	944	1,020	1,101
Discount factor		1.00	1.10	1.21	1.33	1.46	1.61	1.77	1.95	2.14	2.36	2.59	2.85	3.14	3.45	3.80
Fuel savings in real terms		500	491	482	473	465	456	448	440	432	424	416	409	401	394	387

The payback happens in year 14