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 9% per year. Determine the replacement value.

	Machine X	Machine Y
Market Value, $	?	94,000
Annual Cost, $ per Year	−57,500	−40,000 for year 1,increasing by 2000 per year thereafter.
Salvage Value	19,500	21,000
Life, Years	3	5

The replacement value is $ ________.

Answer 1

We need to calculate preset value of machine Y

Year	Cash Flow
	investment	annual cost	salvage value	net cash flow	discount factor	present worth
0	-94000			-94000	1.00000	-94,000.00
1		-40000		-40000	0.91743	-36,697.25
2		-42000		-42000	0.84168	-35,350.56
3		-44000		-44000	0.77218	-33,976.07
4		-46000		-46000	0.70843	-32,587.56
5		-48000	21000	-27000	0.64993	-17,548.15
						-250,159.59

AW of machine Y = present worth * (A/P, 9%, 5yrs = -250159.59 * 0.257092 = -64314.029

Now AW of machine X

Let market value be m then

AW of machine X = -m*(A/P, 9%, 3 yrs) - 57500 + 19500 (A/F, 9%, 3 yrs)

= -m*0.395055 -57500 + 19500 * 0.305055

= -m*0.395055 - 51551.42

To find M

AW of machine X = AW of machine Y

0.395055*m + 51551.42 =  64314.029

0.395055m = 12762.60

m = 32305.88