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 13% per year. Determine the replacement value. Machine X Machine Y Market Value, $ ? 87,000 Annual Cost, $ per Year −63,500 −40,000 for year 1,increasing by 2000 per year thereafter. Salvage Value 14,500 23,000 Life, Years 3 5

The replacement value is $ .

Answer 1

		Machine X	Machine Y
Replacement cost		-	x
PV of annual costs		154,271.68	153,049.74
(from table below)
Life		3 years	5 years
Salvage value		14,500.00	23,000.00
PV of salvage		14500* 0.69305	23000* 0.54276
		10,049.23	12,483.48
PVIF(13%,3)		0.69305	-
PVAF (13%,3)		2.36115	-
PVIF(13%,5)		-	0.54276
PVAF(13%,5		-	3.51720
		Machine X	Machine Y
Year	PV factor	Annual costs	PV of annual costs	Annual costs	PV of annual costs
1	0.884955752	63,500.00	56,194.69	40,000.00	35,398.23
2	0.783146683	65,500.00	51,296.11	42,000.00	32,892.16
3	0.693050162	67,500.00	46,780.89	44,000.00	30,494.21
4	0.613318728	-	-	46,000.00	28,212.66
5	0.542759936	-	-	48,000.00	26,052.48
PV of annual costs			154,271.68		153,049.74
Replacement cost should be such that the Annual worth of both the machines shall be equal.
Let the replacement cost be x.
NPV X	10049.23-154271.68	equals	(144,222.46)
NPV Y	12483.48- 153049.74-x	equals	(140,566.26)
			less x
Annual worth = NPV / PVAF
so,
AW of machine X	equals	AW of machine Y
-61081.4476	equals	(140,566.26)	less x	whole divided by 3.51720
So, x = 74,253.
So, the replacement cost of the machine so that both the machines have same annual worth shall be $ 74,253.