# Internal Rate of Return method (IRR)

Sophisticated capital budgeting techniques include Net present value method (NPV), Internal Rate of Return method (IRR), Profitability index (PI) and Equivalent Annual Annuity (EAA). Internal Rate of Return method (IRR) is discussed below.

Internal Rate of Return (IRR) is a widely used technique.

It is also very easy to utilize Internal Rate of Return with the help of a financial calculator. It is much more challenging to calculate it by hand. Again, as in utilizing the NPV method, it is important to first understand the logic behind the calculation.

In simple terms, the IRR is the rate of return that would equate NPV with zero. If IRR higher than cost of capital than project should be accepted and vice versa. If IRR at least equals cost of capital than we know that business will earn at least rate equal to its cost of capital on this particular project.

Below is shown how to calculate IRR using the financial calculator.

IRR for annuity is calculated as follows:

Initial investment, minus sign – CFi

Annual cash inflow – CFi1

Number of periods – second function Ni

Second function IRR

IRR for a mixed stream is calculated as follows:

Initial investment, minus sign – CFi

Put in each cash inflow separately following with CFi1, CFi2 etc

Second function IRR

Both NPV and IRR will show whether the project is acceptable. However, the ranking of specific acceptable projects may differ between two techniques.

### Test yourself

ABC have an option to invest in project B. The initial investment for project B is \$35,000. Operating cash inflows from project B expected to be \$5,000 per year for 8 years. The cost of capital of ABC is 5%.

What is the Internal Rate of Return (IRR) for project B?

Find out if project B is acceptable based on IRR calculation.

Solution:

With the help of financial calculator, we can determine IRR of project B as follows:

CFio: -35,000

CFi1: 5,000 (annual operating cash inflow)

Second function Nj: 8 (8 years)

Second function IRR: calculate – 3.07

The IRR of project B is 3.07%. The cost of capital of ABC is 5%. Since IRR (3.07%) is below cost of capital (5%), the project is not acceptable.

### Test yourself

ABC have an option to invest in project D. The initial investment is \$300,000. The operation cash inflows are expected to be \$100,000 at the end of year 1, \$110,000 at the end of year 2 and \$130,000 at the end of year 3. The cost of capital of ABC is 10%.

1. Calculate IRR
2. Recommend if based on IRR technique project D is acceptable.

Solution:

1. With the help of financial calculator, the calculation is as follows:

Clear calculator: second function followed by C ALL

CFo: -300,000

CF1: 100,000

CF2: 110,000

CF3: 130,000

Second function IRR: calculate – 6.24%

2. Since cost of capital of ABC is 10% and IRR is only 6.24% (less than cost of capital), based on IRR technique, project D is not acceptable.

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