• # Internal Rate of Return (IRR)

Internal rate of return is another widely used evaluation method for capital budgeting process which calculates the rate of return from the new project and compares it with the cost of capital to take the capital budgeting decision.

Internal rate of return or IRR is the discount rate which makes the present value of project’s total cash inflow equal to the total value of project’s cash outflow. Mathematically IRR is the discount rate which make PV (Cash inflows) = PV (Cash outflows) relationship hold for any project.

As the NPV is calculated as PV (Cash inflows) – PV (Cash outflows), IRR will make NPV = 0.

The IRR method considers the same rules to calculate the cash inflows and outflows as NPV method. The difference is only with the process as NPV method calculates the net present value on a given discount rate while IRR method calculates the discount  for NPV as 0.

Mathematically the following equation should hold

NPV = CF0 + CF1 /((1+IRR)^1) + CF2 /((1+ IRR)^2) + ….. + CFn/((1+ IRR)^n) = 0

Where:

CFo = after tax Cash inflow at the beginning of the project (For cash inflow the sign will be positive and for cash outflow or initial capital investment it will negative)

CFn = after tax cash inflow at the end of n-th year (here year is considered as the period interval of receiving cash inflow, it can be months, weeks as well).

IRR = Internal Rate of Return

Use of IRR in capital budgeting decision making

• If IRR > Required rate of return or cost of capital then the project should be accepted as it offers more return than the market return. Company should be able to create more money if it accepts this project.
• If IRR < Required rate of return or cost of capital then the project should be rejected as it offers lower return than the market return. Company should not go ahead with this project.
• If IRR = Required rate of return or cost of capital then the decision will be indifferent. In this case, other evaluation methods should be used and project can be accepted if there is any strategic business advantage.

Example of IRR

Let us consider two example projects X and Y to calculate the IRR for the same with the below information

• For project X, the initial investment or cash outflow is 1000 USD, for project Y it is 1000 USD.
• Both the projects are for 5 years and will generate cash inflow for next 5 years. The cash inflows for project X are 400 USD, 350 USD, 300 USD, 250 USD and 200 USD respectively. Total Cash inflow will be 1500 USD over the next 5 years.
• The cash inflows for project Y are 200 USD, 250 USD, 300 USD, 350 USD and 400 USD respectively. Total Cash inflow will be 1500 USD over the next 5 years, same as project X.
• If the IRR of project X is IRRx, then use the below equation to calculate the value of IRRx.

– 1000 + (400/(1+ IRRx)^1) +  (350/(1+ IRRx)^2) + (300/(1+ IRRx)^3) + (250/(1+ IRRx)^4) + (200/(1+ IRRx)^5) = 0

Financial calculator or excel sheet formula can be used to calculate the IRR for the same. Here IRRx is calculated as 17.466 %

• And If the IRR of project Y is IRRy, then use the below equation to calculate the value of IRRx.

– 1000 + (200/(1+ IRRy)^1) +  (250/(1+ IRRy)^2) + (300/(1+ IRRy)^3) + (350/(1+ IRRy)^4) + (400/(1+ IRRy)^5) = 0

Financial calculator or excel sheet formula can be used to calculate the IRR for the same. Here IRR7 is calculated as 13.453%

If we check the IRR data closely IRR for project X is much higher than the IRR of project Y. This is mainly because of receiving more money at the earlier stage of the project. If the required rate of return or the cost of capital is 15%, then project X will be accepted and project Y will be rejected based on the IRR.

Post Tagged with ,