CAT / FIA FFM Syllabus E. Investment Decisions - Internal Rate of Return - Notes ^{7 / 9}

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

1. Considers the time value of money

2. Easily understood percentage

3. Uses cash not profits

4. Considers whole life of project

5. Increases shareholders wealth

Disadvantages of IRR

1. Does not produce an absolute figure (percentage only)

2. Interpolation of the formula means it is only an estimate

3. Fairly complicated to calculate

4. Non conventional cashflows can produce multiple IRRs

5. Ranking mutually exclusive projects on the basis of IRR may give misleading results

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.