Question

Internal Rate of Return (IRR)

IRR

Project L costs $48,422.38, its expected cash inflows are $10,000 per year for 10 years, and its WACC is 13%. What is the project's IRR? Round your answer to two decimal places.

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Answer 1

To calculate the Internal rate of return, first let's understand the meaning of it. It is basically that discount rate of a project which makes the Net present value from a project equal to zero. This means that the cash outflow of the project must equate the present value of cash inflows from a project.

Here, we use trial and error method to compute the IRR.

Since cash inflows are same throughout the life of a project so to compute the present value of cash inflows we use the present value of an ordinary annuity factor that can be calculated s follows:

Cash outflow = $48,422.38

First, let us see the Present value of Cash flows at 13% = 10,000 x Present value of an ordinary annuity factor_(13%,10)

= (10,000 x 5.4262) = $54,262

This is greater than our cash outflow. So, we have to increase our discount rate to get a closer value remember the aim is to equate cash inflows and outflow. And the greater the discount factor, the lower shall be the cash inflows.

Present Value of Cash Flows:

At 15% discount rate = 10,000 x Present value of an ordinary annuity factor_(15%,10)

  = 10,000 x 5.0188 = $50,188

That's pretty close so let's take 1% higher discount rate.

At 16% discount rate = 10,000 x Present value of an ordinary annuity factor_(16%,10)

= 10,000 x 4.8332 = $48,332

Now, this value is pretty close again to the value of outflow so our desired Internal rate of return will lie somewhere between 15% and 16%. To find out, we use interpolation:

Desired Rate = Lower Rate + [(Cash inflows at lower rate - Cash inflows at WACC)/ (Cash inflows at lower rate - Cash inflows at higher rate)]

= 15 + [(50,188 - 48,422.38) / (50,188 - 48,332)] = 15 + (1765.62 / 1856) = 15.95 %

Hence, IRR of the project is 15.95%

  

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