A firm expects to install smog control equipment on the exhaust of a gasoline en

Question

A firm expects to install smog control equipment on the exhaust of a gasoline engine. The local smog control district has agreed to pay to the firm a lump sum of money to provide for the first cost of the equipment and maintenance during its 10 year useful life. At the end of 10 years the equipment, which initially cost $10,000, is valueless. The firm and the smog control district have agreed the following are reasonable estimates of the end of year maintenance costs: Assuming interest at 6% per year, how much should the smog control district pay to the firm now to provide for the first cost of the equipment and its maintenance for 10 years?

Explanation / Answer

If we split the cash flow 500 in period 1 into 75+ 425, then the upper cash flow is equivalent to a uniform series of A = 75 for 10 years, an arithmetic series of G= 25 for 10 years, a single cash flow of $10,000 in the year 0, and another single period cash flow of $425 in year 1. So the present worth of the above cash flow is P = 10,000 + 425(P/F,6%,1) + 75(P/A,6%,10) + 25(P/G,6%,10) P = 10,000+425(.9434)+75(7.360)+25(29.602) = 11693

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