Question

A company is considering buying a CNC machine. In​ today's dollars, it is estimated that the maintenance costs for the machine​ (paid at the end of each​ year) will be

​$31,000​,

​$32,000​,

​$33,000​,

​$34,000​,

and

​$36,000

for years 1 to​ 5, respectively. The general inflation rate

​( f ​)

is estimated to be

4​%

per​ year, and the company will receive

17​%

return​ (interest) per year on its invested funds during the inflationary period. The company wants to pay for maintenance expenses in equivalent equal payments​ (in actual​ dollars) at the end of each of the five years. Find the amount of the​ company's payments.

The amount of the​ company's payments is

​$nothing

thousand. ​(

Answer 1

Real interest rate = (0.17 - 0.04)/(1+0.04) = 0.125 ~ 12.5%

Present worth in constant dollars = present worth in actual dollars

Present worth in constant dollars = 31000/(1+0.125) + 32000/(1+0.125)^2 + 33000/(1+0.125)^3 + 34000/(1+0.125)^4 + 36000/(1+0.125)^5

= 31000/(1.125) + 32000/(1.125)^2 + 33000/(1.125)^3 + 34000/(1.125)^4 + 36000/(1.125)^5

= 117219.94

Equivalent annual payment in actual dollars = 117219.94 * (A/P,17%,5)

= 117219.94*0.312564

= 36638.73 ~ 36.64 thousands (round to two decimal places) ~ 36.6 thousands (round to one decimal places)

Choose value as asked in question