Question

With the estimates shown below, Sarah needs to determine the trade-in (replacement) value of machine X that will render its AW equal to that of machine Y at an interest rate of 11% per year. Determine the replacement value.

	Machine X	Machine Y
Market Value, $	?	86,000
Annual Cost, $ per Year	−57,500	−40,000 for year 1,increasing by 2000 per year thereafter.
Salvage Value	15,500	20,000
Life, Years	3	5

The replacement value is ________$  .

Answer 1

AW of machine Y = -86000*(A/P,11%,5) - 40000 - 2000*(A/G,11%,5) + 20000*(A/F,11%,5)

= -86000*0.270570 - 40000 - 2000*1.792259 + 20000*0.160570

= -63642.14

Let trade in value be P, then

AW of X = -P*(A/P,11%,3) - 57500 + 15500*(A/F,11%,3)

= -P*0.409213 - 57500 + 15500*0.299213

As per given condition

-P*0.409213 - 57500 + 15500*0.299213 = -63642.14

P = (63642.14 - 57500 + 15500*0.299213) / 0.409213 = 26343.11