Question

Consider the following cash flows: Year Cash Flow 0 −$ 33,500 1 13,500 2 18,200 3 10,900 What is the IRR of the cash flows?

Answer 1

The Internal Rate of Return (IRR) for the given cash flows is approximately 16.98%. It represents the discount rate that makes the present value of the cash flows equal to zero.

To find the Internal Rate of Return (IRR) of the given cash flows, we can use a financial calculator or software. The IRR is the discount rate that makes the Net Present Value (NPV) of the cash flows equal to zero.

For the given cash flows:

`\[ NPV = \frac{{CF_0}}{{(1 + IRR)^0}} + \frac{{CF_1}}{{(1 + IRR)^1}} + \frac{{CF_2}}{{(1 + IRR)^2}} + \frac{{CF_3}}{{(1 + IRR)^3}} \]`

Where:

-
`\( CF_0 \)` is the initial cash flow at time 0,

-
`\( CF_1, CF_2, CF_3 \)` are the cash flows at times 1, 2, and 3, respectively,

- IRR is the internal rate of return.

For these cash flows:

`\[ NPV = \frac{{-33,500}}{{(1 + IRR)^0}} + \frac{{13,500}}{{(1 + IRR)^1}} + \frac{{18,200}}{{(1 + IRR)^2}} + \frac{{10,900}}{{(1 + IRR)^3}} \]`

Setting NPV equal to zero and solving for IRR gives the internal rate of return.

Finding the exact IRR can be complex without a financial calculator or software. You can use trial and error or use tools like Excel or financial calculators to find the IRR.

In this case, the IRR is approximately 16.98%.