### Internal Rate of Return

The IRR is essentially the discount rate where the initial cash out (the investment) is equal to the PV of the cash in.

So, it is the discount rate where the NPV = 0

It is actual return on the investment (%).

Consequently, to work out the IRR we need to do trial and error NPV calculations, using different discount rates, to try and find the discount rate where the NPV = 0.

The good news is you only need to do 2 NPV calculations and then apply this formula:

#### Where..

L = Lower discount rate

H = Higher discount rate

NPV L = NPV @ lower rate

NPV H = NPV @ higher rate

If the IRR is higher than the cost of capital, the project should be accepted.

#### Illustration

If a project had an NPV of 50,000 when discounted at 10%, and -10,000 when discounted at 15% - what is the IRR?

**Answer**10 + (50,000/60,000) x 5% = 14.17%

If you have a positive NPV, increase the discount rate to get a smaller NPV.

If you have a negative NPV, decrease the discount rate to get a bigger NPV.

#### Little Tricks

If all the cashflows are the same

This is an annuity - simply take the Initial Cost / annual inflow - this gives you the cumulative discount factor (annuity factor).

Then go to the annuity table and look for this figure (in the row for the number of years the project is for) - the column in which the figure is found is the IRR!

If the cashflows are the same and go on forever

This is a perpetuity - simply take the Annual inflow / Initial cost and turn it into a percentage. That’s the IRR! Done.

#### Advantages of IRR

Considers the time value of money

Easily understood percentage

Uses cash not profits

Considers whole life of project

Increases shareholders wealth

#### Disadvantages of IRR

Does not produce an absolute figure (percentage only)

Interpolation of the formula means it is only an estimate

Fairly complicated to calculate

Non conventional cashflows can produce multiple IRRs

#### Interpreting the IRR

The IRR provides a decision rule for investment appraisal, but also provides information about the riskiness of a project – i.e. the sensitivity of its returns.

The project will only continue to have a positive NPV whilst the firm’s cost of capital is lower than the IRR.

A project with a positive NPV at 14% but an IRR of 15% for example, is clearly sensitive to:

- an increase in the cost of finance

- an increase in investors’ perception of the potential risks

- any alteration to the estimates used in the NPV appraisal.