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an investment project requires an initial outlay of $2400 and can generate revenues of $2000 per...

an investment project requires an initial outlay of $2400 and can generate revenues of $2000 per year. In the first year, operating costs are $600; thereafter operating costs increase by $500 a year.

1) what is the maximum length of time for which the project should operate?

2) should it be undertaken if the interest rate is 5%?

3) should it be undertaken if the interest rate is 10%?

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Answer #1

Answer -

Initial outlay = $ 2400
revenues / year = $ 2000
Operating costs (year 1) = $ 600
Operating costs (year 2) = $ 600 + $ 500 = $ 1100
Operating costs (year 1) = $ 1100 + $ 500 = $ 1600
Operating costs (year 1) = $ 1600 + $ 500 = $ 2100
Operating costs (year 1) = $ 2100 + $ 500 = $ 2600

first year cash inflow = revenue - operating cost = $ 2000 - $ 600 = $ 1400
second year cash inflow = revenue - operating cost = $ 2000 - $ 1100 = $ 900
third year cash inflow = ​​​​​​​revenue - operating cost = $ 2000 - $1600 = $ 400
fourth year cash inflow = ​​​​​​​revenue - operating cost ​​​​​​​= $ 2000 - $ 2100 = - $ 100
fifth year cash inflow = ​​​​​​​revenue - operating cost = $ 1200 - $ 2600 = - $ 600

1) The project should operate until the overall cash inflow flow is positive

The maximum length of time that the project should operate is till one has positive cash flows = - Initial outlay + first year cash inflow + second year cash inflow + third year cash inflow

The maximum length of time that the project should operate = - $ 2400 + $ 1400 + $ 900 + $ 400
= - $ 2400 + $ 2700
​​​​​​​= $ 300

Therefore the project should operate for three years as from the fourth year the net cash inflow (- $ 100) becomes negative.


2) should it be undertaken if the interest rate is 5 %

NPV = - $ 2400 + $ 1400 / 1.05 + $ 900 / 1.052 + $ 400 / 1.053  
NPV = - $ 2400 + $ 1333.33 + $ 816.33 + $ 345.53
NPV = - $ 2400 + $ 2495.19
NPV = $ 95.19

Since the NPV is positive for an interest rate of 5 % ( $ 95.19 ) the project should be undertaken.

3) should it be undertaken if the interest rate is 10 %

NPV = - $ 2400 + $ 1400 / 1.10 + $ 900 / 1.102 + $ 400 / 1.103  
NPV = - $ 2400 + $ 1272.73 + $ 743.8 + $ 300.52
NPV = - $ 2400 + $ 2317.05
NPV = - $ 82.95

Since the NPV is negative for an interest rate of 10 % ( - $ 82.95 ) the project should not be undertaken.

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