A project has the following NPV at the following discount rates.
D.r (%) NPV($)
4 22800000 5 16200000
6 7200000
7 -1350000
8 - 6900000
Estimate the IRR on the project. Suppose the money could be invested elsewhere at a rate of 8%, should the project be undertaken?
To estimate the Internal Rate of Return (IRR) on the project, we need to find the discount rate at which the Net Present Value (NPV) becomes zero. In this case, we have the following NPV values at different discount rates:
D.r (%) NPV($)
4 22800000
5 16200000
6 7200000
7 -1350000
8 -6900000
To estimate the IRR, we can use a trial and error approach by checking different discount rates until we find the one where the NPV is closest to zero.
Let's start with a discount rate of 7%. At this rate, the NPV is - $1,350,000. Now let's try a discount rate of 6%. At this rate, the NPV is $7,200,000. We can continue this process until we find a discount rate that results in an NPV of zero or closest to zero.
Next, let's check at a discount rate of 4%. At this rate, the NPV is $22,800,000. Now, let's try a discount rate of 5%. At this rate, the NPV is $16,200,000. By interpolating between these two discount rates, we can estimate the discount rate at which the NPV would be zero.
Using the formula for interpolation:
IRR = Lower Discount Rate + [(NPV at Lower Discount Rate) / (NPV at Lower Discount Rate - NPV at Higher Discount Rate)] * (Higher Discount Rate - Lower Discount Rate)
IRR = 4 + [(0 - 22,800,000) / (0 - 22,800,000 + 16,200,000)] * (5 - 4)
IRR = 4 + [-22,800,000 / -6,600,000] * 1
IRR = 4 + 3.4545 * 1
IRR = 7.4545
Therefore, the estimated IRR on the project is approximately 7.45%.
To determine whether the project should be undertaken or not, we need to compare the IRR with the discount rate of 8%, which represents the rate at which money could be invested elsewhere.
Since the IRR (7.45%) is less than the discount rate (8%), it suggests that the project may not be attractive from a financial perspective. Investing the money elsewhere at 8% may provide higher returns. However, this is a simplified analysis, and other factors like project risks, strategic importance, and non-financial considerations should also be taken into account before making a final decision.