# IRR vs Cost of Capital

soleadea

5 years 3 weeks 1 day

## How CFA® exam questions can fool you

Very often in questions related to capital budgeting (both in the QM and CF sections of the CFA exam) the cost of capital is given, even though you are only asked to __compute the IRR__. In such questions the cost of capital is a distractor.

However, in questions that require decision-making __based on the IRR criterion__ (i.e. whether a company should undertake a project or not), the cost of capital has to be taken into consideration. Namely, we need to compare it with the calculated IRR.

__Remember__: The IRR is one of the possible discount rates (the one for which the NPV is 0). It does not depend on any other discount rate (like the cost of capital) and no other discount rate is needed to compute it.

### Cost of capital as a distractor

Have a look at two examples illustrating the problem of cost of capital distractor.

__Example 1__:

Mark, a financial manager, gathered the following data about a project:

The opportunity cost of capital is equal to 20%. Mark would like to evaluate the profitability of the project using the internal rate of return rule. What is the value of the IRR?

- A. 20.00%
- B. 21.85%
- C. 39.22%

__Answer__: B is correct.

Calculator CF and IRR worksheets:

Press [CF] to access the Cash Flow worksheet

Press [2ND] [CLR WORK] to clear the CF wotksheet

CF0=-50,000

C01=-15,000

F01=1

C02=13,000

F02=1

C03=42,500

F03=1

C04=40,000

F04=1

C05=32,000

F05=1

Then, press [IRR] and [CPT].

B is correct because IRR = 21.85%.

### Cost of capital as a necessity

__Example 2__:

Mark, a financial manager, gathered the following data about a project:

The opportunity cost of capital is equal to 20%. Mark would like to evaluate the profitability of the project using the internal rate of return rule. Which of the following statements is most likely correct?

- A. The financial manager should accept the project.
- B. The financial manager should not accept the project.
- C. Given the cash flows of the project, it is impossible to compute the internal rate of return explicitly.

__Answer__: A is correct.

To make the decision, we have to compute the internal rate of return (we have done it in Example 1) and __compare it with the cost of capital (20%)__. So, answer A is correct because IRR equals 21.85% and it is higher than the cost of capital.

As you can see, even though the cost of capital is superfluous in Example 1 (and its presence can be somehow misleading), it is essential to do Example 2 correctly.

BTW, do you know how one can get at the incorrect answer C (39.22%) of Example 1? If yes, please share it with others in the comments below :)