# A project has the following cash flows. What is the internal rate of return?

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A project has the following cash flows. What is the internal rate of return?

Year Cash Flow

0 – \$46,000

1 – 11,269

2 – 18,220

3 – 15,950

4 – 13,560

A. 10.53 percent

B. 10.58 percent

C. 10.60 percent

D. 10.67 percent

E. 11.10 percent

Internal Rate of Return
The internal rate of return (IRR) on a project is the rate of return at which the projects NPV equals zero. At this point, a project’s cash flows are equal to the project’s costs. Similar to how management must establish a maximum payback period, management must also set what is known as a “hurdle rate”, the minimum rate of return a company will accept for a project.

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When a project is reviewed with a hurdle rate in mind, the greater the IRR is above the hurdle rate, the greater the NPV, and conversely, the further the IRR is below the hurdle rate, the lower the NPV.

Look Out!
For the IRR, the decision rules are as follows:
If IRR > hurdle rate, accept the project
If IRR< hurdle rate, reject the project

For a project to be accepted, the IRR must be greater than or equal to the hurdle rate. If a company is deciding between two projects, the project with the highest IRR is the project to be accepted.

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Formula 11.12

0=( investment )+\frac{C F_{1}}{(1+I R R)^{1}}+\frac{C F_{2}}{(1+I R R)^{2}}+\sum_{(1+I R R)^{t}}

The IRR formula is quite difficult to calculate without the use of a financial calculator. Thus, a financial calculator is highly recommended to solve for a project’s IRR.

Calculation:

0 = 46,000 + [11269 / (1+r)] + [18220 / (1+r)2] + [15950 / (1+r)3 + [13560 / (1+r)4

-46000 = [11269 / (1+r)] + [18220 / (1+r)2] + [15950 / (1+r)3 + [13560 / (1+r)4

Calculating for r using excel sheets

We will get r = 10.53 %(A)