Project L has an IRR of approximately 4.90%. This means that the project is expected to generate a return of 4.90% per year on the initial investment of $77,263.
Project L requires an initial outlay of $77,263. Its expected cash inflows are $14,000 per year for 9 years. Its WACC is 10%.
The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of all the project's cash flows equal to zero.
In other words, it is the return that the project is expected to generate on the initial investment.
To calculate the IRR of Project L, we can use the following steps:
Calculate the net present value (NPV) of the project for a range of discount rates.
Find the discount rate where the NPV is closest to zero. This is the IRR.
Here is a table showing the NPV of Project L for different discount rates:
Discount Rate NPV
0% $77,263
1% $56,563
2% $36,629
3% $17,462
4% -$1,840
5% -$11,283
6% -$20,867
7% -$30,591
8% -$40,457
9% -$50,464
10% -$60,613
As you can see from the table, the NPV is positive for discount rates below 4% and negative for discount rates above 4%.
This means that the IRR of Project L is between 4% and 5%.
To find the exact IRR, we can use interpolation. Here is the formula for linear interpolation:
IRR = r1 + (NPV1 / (NPV1 - NPV2)) * (r2 - r1)
where:
r1 is the lower discount rate
r2 is the higher discount rate
NPV1 is the NPV at the lower discount rate
NPV2 is the NPV at the higher discount rate
In this case, we can use r1 = 4%, r2 = 5%, NPV1 = -$1,840, and NPV2 = -$11,283. Plugging these values into the formula, we get:
IRR = 4% + (-$1,840 / (-$1,840 - -$11,283)) * (5% - 4%)
IRR ≈ 4.90%
Therefore, the IRR of Project L is approximately 4.90%.
Project L has an IRR of approximately 4.90%.
This means that the project is expected to generate a return of 4.90% per year on the initial investment of $77,263.