Question

4-55 A firm expects to install smog control equipment on the exhaust of a gasoline engine. The local smog con- trol district has agreed to pay to the firm a lump sunm of money to provide for the first cost of the equip- ment 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 that the following are reasonable estimates of the end-of-year maintenance costs: Year 1 $75 Year 6 $200 225 250 9 275 300 2 100 3 125 4 150 5 175 10 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?

Answer 1

Initial cost(P) = $10,000

Present value of maintainance cost:

A = A₁ + G(A/G,i,n)

   = 75 + 25(A/G, 6%, 10)

   = 75 + 25(4.022)

   = 75 + 100.55

= $175.55

P = $175.55(P/A, 6%, 10)

= $175.55(7.3601)

= $1292

Therefore, the total amount that the smog control district pay to the firm = $10,000 + $1292 = $11.292