Assume that Gerhardt Corporation is considering a capital investment of €50 million today with the following estimated cash flow schedule over the next five years (all amounts in millions of euros).t 0 1 2 2.5 3 4 5Cash flow –50 0 1 3 16 20 25What is the IRR of this investment, and should Gerhardt make the investment if its required rate of return is 10%?
Question
Assume that Gerhardt Corporation is considering a capital investment of €50 million today with the following estimated cash flow schedule over the next five years (all amounts in millions of euros).t 0 1 2 2.5 3 4 5Cash flow –50 0 1 3 16 20 25What is the IRR of this investment, and should Gerhardt make the investment if its required rate of return is 10%?
Solution
To calculate the Internal Rate of Return (IRR), we need to set the Net Present Value (NPV) of the cash flows equal to zero and solve for the discount rate (which is the IRR in this case). The formula for NPV is:
NPV = ∑ [Cash flow / (1 + r)^t] - Initial Investment
where:
- Cash flow is the net cash inflow during the period
- r is the discount rate or rate of return
- t is the number of time periods
Let's calculate the NPV at the required rate of return of 10%:
NPV = -50 + 0/(1+0.10)^1 + 1/(1+0.10)^2 + 3/(1+0.10)^2.5 + 16/(1+0.10)^3 + 20/(1+0.10)^4 + 25/(1+0.10)^5
If the NPV is positive, the project is considered profitable as it is expected to generate more cash than what has been invested, considering the time value of money. If the NPV is negative, the project is considered unprofitable.
However, to find the IRR, we need to find the discount rate that makes the NPV equal to zero. This is typically done through trial and error or using financial calculator or software.
If the IRR is greater than the required rate of return (10% in this case), then the project is considered a good investment. If the IRR is less than the required rate of return, then the project is not considered a good investment.
Without the exact calculations, we cannot definitively say whether Gerhardt Corporation should make the investment or not.
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