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, $	?	92,000
Annual Cost, $ per Year	?60,000	?40,000 for year 1,increasing by 2000 per year thereafter.
Salvage Value	11,500	16,000
Life, Years	3	5

The replacement value is $  .

Answer 1

• First let us find the Annual worth of Machine Y

AW = Initial Inflow today(Replacement Value) + Present Value of Salvage Value - Present Value of Annual Costs

Present Value Interest Factor Annuity @ 11%

Net Worth of Machine Y (Amount in $)

Year	Cash Inflow/(Outflow)	Present Value Factors	Present Value
0	92000	1	92000
1	(40000)	0.9009	(36036)
2	(42000)	0.8116	(34087.2)
3	(44000)	0.7312	(32172.8)
4	(46000)	0.6587	(30300.2)
5	(48000)	0.5934	(28483.2)
	Salvage Value - 16000	0.5934	9494.4
		Present Value	(59585)

Annual Worth (Cost) = $59585 / 3.6959

= $ 16121.9189

• For Machine X, AW should be ($16121.9189)

AW = Initial Replacement Value - P.V. of Annual Cost + P.V. of Salvage Value

Present Value Interest Factor Annuity for 3 years@11%

1. Finding the present value of Annual Cost of Machine X

= Annual Cost * Present Value Interest Factor Annuity for 3 years @ 11%

= $60000 * 2.4437

= $146622

2.Present Value of Salvage Value

= Salvage Value * Present Value Factor for 3rd year @ 11%

=$11500 * 0.7312

= $ 8408.8

Now,

AW * Present Value Interest Factor Annuity for 3 years@11% = Initial Replacement Value - P.V. of Annual Cost + P.V. of Salvage Value

that is ($16121.9189) * 2.4437 = Initial Replacement Value - $146622 + $8408.8

($39397.1332) = Initial Replacement Value - $138213.2

So, ($39397.1332) + $ 138213.2 = Initial Replacement Value

that is $ 98816 = Initial Replacement Value

Therefore the replacement value is $ 98816