Question

A presently owned machine has the projected market value and M&O costs shown below. An outside vendor of services has offered to provide the service of the existing machine at a fixed price per year.

If the presently owned machine is replaced now, the cost of the fixed-price contract will be $315000 per year. If the presently owned machine is replaced at the end of first year, the contract price will be $292950 per year. If the presently owned machine is replaced at the end of second year, the contract price will be $277200 per year. If the presently owned machine is replaced at the end of third year, the contract price will be $267750 per year. If the presently owned machine is replaced at the end of fourth year, the contract price will be $264600 per year.

Determine the last calculated AW of the defender for which it should be replaced with the outside vendor using an interest rate of 10% per year. (If the defender is kept for 4 years, then enter 0 for AW)

Retention Year	Market Value, $	M&O Cost, $ per year
0	630,000
1	441,000	63,000
2	315,000	126,000
3	252,000	189,000
4	189,000	252,000

Answer 1

First, the annual worth (AW) of the machine is calculated beginning today (Year 0) and then this value is compared with the alternative of fixed payment.

If the the annual worth is less than the alternative fixed payment, we will not replace the machine. In that case, we will do the calculation for the next year (Year 1) and again compare it to the fixed payment alternative. We will continue this process until the Annual worth of the machine is greater than than the fixed payment alternative. At that stage, we will decide to replace the machine.

Given :

Rate of Interest = 10%

Retention Year	Market Value, $	M&O Cost, $ per year
0	630,000
1	441,000	63,000
2	315,000	126,000
3	252,000	189,000
4	189,000	252,000

Year 0

Annual Worth :

PV = A[1-(1+r)^-n/r]

where, PV = Current Market Value

r = Rate of Interest

n = Number of years {Its 5 as there are 5 payments due}

A = Annual Worth

Thus,

630000 = A [ 1 - (1.10)^-5/0.10]

A = 166,192.41

Annual Worth = $166,192.41

This amount is less than the fixed payment option of $315000. Thus, we do not replace the machine.

Year 1 :

Annual Worth :

PV = A[1-(1+r)^-n/r] * [1/1+r]

where, PV = Current Market Value

r = Rate of Interest

n = Number of years {Its 4 as there are 4 payments due}

A = Annual Worth

Thus,

441000 = A [ 1 - (1.10)^-4/0.10]

A = 139122.62

Annual Worth = Annual payment above + Annual M&O costs

Annual Worth = 139122.62 + 63000 = $ 202,122.62

This amount is less than the fixed payment option of $292,950. Thus, we do not replace the machine.

Year 2:

Annual Worth :

PV = A[1-(1+r)^-n/r] * [1/1+r]

where, PV = Current Market Value

r = Rate of Interest

n = Number of years {Its 3 as there are 3 payments due}

A = Annual Worth

Thus,

315000 = A [ 1 - (1.10)^-3/0.10]

A = 126666.16

Annual Worth = Annual payment above + Annual M&O costs

Annual Worth = 126666.16 + 126000 = $ 252,666.16

This amount is less than the fixed payment option of $277,200. Thus, we do not replace the machine.

Year 3:

Annual Worth :

PV = A[1-(1+r)^-n/r] * [1/1+r]

where, PV = Current Market Value

r = Rate of Interest

n = Number of years {Its 2 as there are 2 payments due}

A = Annual Worth

Thus,

252000 = A [ 1 - (1.10)^-2/0.10]

A = 145200

Annual Worth = Annual payment above + Annual M&O costs

Annual Worth = 145200 + 189000 = $ 334,200

This amount is more than the fixed payment option of $267750. Thus, we replace the machine.

Therefore, the last calculated AW of the defender is $334,200 when it should be replaced with the outside vendor.