Help with NPV question

lightspeed

Hi all im trying to prepare for a financial management exam later in the year and im trying to figure out some NPV questions.

I thought I understood it but from looking at some questions in a book im a little confused as the answers the book gives dont show the solution or how he answer was obtained.

A company has to replace a number of machines and is faced with a choice of Machine A with a lifespan of 12 years and Machine B with a life of 6 years. If Machine B is used it will be replaced at the end of 6 years by another of the same type. The pattern of maintenance and running cost differ between the two types of machine and relevant data are shown below:

Machine A
Purchase price: €19,000
Trade in value: €3000
Annual repair costs: €2000
Overhaul costs: €4000 end of year 8
Finance cost: 10% P.A

Machine B
Purchase price: €13,000
Trade in value: €3000
Annual repair costs: €2600
Overhaul costs: €2000 end of year 4
Finance cost: 10% P.A

Calculate the equivalent annual cost of using either machine and make a recommendation.

The answer given is as follows:

Year Cash flow from machine A
0 (€19000)
8 (€4000)
12 €3000
1-12 (€2000)
NPV at 10%= (€33,540)
EAC for machine A = €33,540/6.814 = €4922

The answer given is as follows:

Year Cash flow from machine A
0 (€13,000)
4 (€2000)
6 €3000
1-6 (€2600)
NPV at 10%= (€23,996)
€24,016/4.355

Can anyone explain and breakdown how the NPV of €33540 and €23996 were obtain. The above is the only info given and it does not provide a reasonable solution as to how either NPV values were obtained.

Im also not sure why for machine B the EAC is calculated using €24,016 and not €23,996. Ive also no idea where the €24,016.

Id appreciate any insight on the above as im quite lost.

johnb25

This is the NPV for Machine A.
You can follow this for B also.
Regarding the €20 differ for machine B, probably rounding or typo, cannot see any other reason to change the number.

John

Year 10% DCF
0 -19,000 1.0000 -19,000.00
1 -2,000 0.9091 -1,818.20
2 -2,000 0.8264 -1,652.80
3 -2,000 0.7513 -1,502.60
4 -2,000 0.6830 -1,366.00
5 -2,000 0.6209 -1,241.80
6 -2,000 0.5645 -1,129.00
7 -2,000 0.5132 -1,026.40
8 -2,000 0.4665 -933.00
8 -4,000 0.4665 -1,866.00
9 -2,000 0.4241 -848.20
10 -2,000 0.3855 -771.00
11 -2,000 0.3505 -701.00
12 -2,000 0.3186 -637.20
12 3,000 0.3186 955.80
-33,537.40

lightspeed

Thanks for that much appreciated. I was actually adding the €19000 figure instead of deducting it with the rest.