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In: Economics

3. A French company is planning to replace the old machine for a new one. The...

3. A French company is planning to replace the old machine for a new one. The new machine will cost Euro 4 million, the old one can not be sold. The new machine will be used for 20 years, then it can be sold for 25% of the purchase price. Each year the company will save Euro 450,000 on the production costs, but the maintenance costs will be higher too: Euro 40,000 per year. The MARR of this company is 9% annual nominal, compounded annually.

Calculate the discounted Payback period

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Expert Solution

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Answer

Discounted payback period refers to the time taken by the project to recovers its initial investment by calculating the present value of the cash inflows.
We have to calculate cumulative cash flows .

Net cash inflow per year = 450,000-40,000
=410,000 Euros

Discounted at 9 %
In year 20 the cash inflows will be = 25% of 4 million + 410000
= 1410000

Year Cash flows PV Cumulative cash flows
0 -40,00,000 -4000000 -4000000
1 410000 376146.8 -3623853
2 410000 345088.8 -3278764
3 410000 316595.2 -2962169
4 410000 290454.3 -2671715
5 410000 266471.9 -2405243
6 410000 244469.6 -2160773
7 410000 224284 -1936489
8 410000 205765.2 -1730724
9 410000 188775.4 -1541949
10 410000 173188.4 -1368760
11 410000 158888.5 -1209872
12 410000 145769.2 -1064103
13 410000 133733.2 -930369
14 410000 122691.1 -807678
15 410000 112560.6 -695118
16 410000 103266.6 -591851
17 410000 94740 -497111
18 410000 86917.43 -410194
19 410000 79740.76 -330453
20 1410000 251587.6 -78865.4
21 410000 67116.21 -11749.2
22 410000 61574.5 49825.32

The payback period of this project is greater than the life of the project . THe payback period lies betwen 21 to 22 years. he project should not be taken .


THe payback period is imaginary
= 21+ 11749/61574.5
= 21 + .19
= 21.2 years

Rahul Sunny answered 2 years ago
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