Suppose that a project has the following costs and bene ts over the rst three ye

Question

Suppose that a project has the following costs and bene ts over the rst three years of its lifespan:
Year Benefits Costs
0 170 0
1 90 150
2 56 200
a) If the interest rate is 20% per year, what is the net present value of the project? What is the bene t-cost
ratio? Is the project worth it"?
b) How are your answers different if the interest rate is 10%? 30%?

Explanation / Answer

Year   PV Factor @20% Benefit Cost PV of Benefits PV of Costs Year 0                   1.000                170                  -          170.00                      -   Year 1                   0.833                   90              150          75.00                   125 Year 2                   0.694                   56              200          38.89                   139 Total        283.89             263.89 a NPV of project =                   20.00 Benefit /cost Ratio=                     1.08 As the NPV is positive and benefit cost ratio> 1, the project is acceptable. b when interest is 10% Year   PV Factor @10% Benefit Cost PV of Benefits PV of Costs Year 0                   1.000                170                  -          170.00                      -   Year 1                   0.909                   90              150          81.82                   136 Year 2                   0.826                   56              200          46.28                   165 Total        298.10             301.65 NPV of project =                   (3.55) Benefit /cost Ratio=                     0.99 As the NPV is negative and benefit cost ratio 1, the project is acceptable.

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