CIPFA’s Anna Howard takes a look at how Internal Rate of Return might be examined in the exams.
It is probable that Internal Rate of Return (IRR) will be assessed in the CIPFA Business Planning and Financial Management paper. After all, it may appear as an investment appraisal question, but is more likely to appear as part of a cost of capital calculation.
Many students spend the necessary time and effort to excel in this area, but some students find that because of the initial difficulties in learning IRR they decide to rely on a strategy of picking up enough marks elsewhere in the paper. This strategy is a dangerous one and will likely result in failing the exam. So what can be done if you are one of those students who struggle with IRR? Let’s consider some understanding that may help and some techniques to ensure you are able to attempt these questions in the exam.
What is IRR?
IRR is the percentage return of a particular project or investment. It is therefore the discount rate used in a net present value calculation that results in a zero NPV. In practice this can be accurately calculated using certain specific formulae. In the BPFM exam, however, students will be asked to calculate IRR using an interpolation formula that will be provided.
What is interpolation?
Interpolation is estimating outcomes between data results. For example, the average height of a newborn girl in the UK is 50 cm and at 10 years old is 138 cm. Using this data, we can estimate the height of any age between 0 and 10 using interpolation. If we take the difference of height and divide by the number of years, we can calculate the average increase in height per year. In this example it is (138 – 50)/10 = 8.8 cm increase per year.
Now use this calculation to estimate the height of a seven year old by using the height of a newborn plus seven years of average increase. That equals to 50 + (7 x 8.8) = 111.6 cm.
Using the interpolation formula
The aim of the IRR formula is to estimate what discount factor will produce a NPV of 0. Taking the example earlier, to estimate the average height of a four-year old girl we would need two data results either side of four. As the data is at 0 years and ten years, interpolation can be used.
Interpolation could not be used to estimate the height of a 15 year old because this is outside our data results and we would therefore have to use the less reliable extrapolation process. Using this reasoning, in order to estimate the discount factor that produces a zero NPV, then data results are required that produce a negative NPV and a positive NPV.
It is also important to establish a NPV calculation by interpreting the information given in a question. Students find this particularly challenging when dealing with redeemable debt whilst given the variety of information in the scenario. It may be beneficial therefore to learn the following table:
Example of an IRR question
Let’s put all this theory into practice. ABC PLC has a £600 million redeemable debenture. Its fixed coupon (interest) rate is 8%. The debenture is trading at 110% of its nominal value and will be redeemed at par in five years from today. ABC PLC pays tax on its profits at a rate of 25%.
First, we need to identify from the information what the various elements in the scenario.
- Nominal amount – £600m
- Interest Rate – 8%
- Number of years – 5
- Market Value – £600m x 110% = £660m
Now let’s produce the cashflow using the table
We need to do now produce at least two NPV calculations; one positive and one negative. Unless specific discount rates are given in the question, the interest rate itself is a good starting point. So let’s discount the cashflow using 8%.
As we now have a negative NPV, we need a positive one. In order to get a positive NPV a lower discount rate is needed. A 5% gap is a good start and so we will now use 3%.
As 3% gives a NPV of £22.68m and 8% gives a NPV of (£107.65m) then we know that a zero NPV will lie between the two. We also can expect the outcome to be nearer 3% because that NPV is nearer zero than 8%. At this point, we should be expecting an IRR around 4%. Let’s now put these figures into the formula.
3 + ((22.68/(22.68 + 107.65)) x (8-3)) = 3.87
Irregularities of IRR
When working through examples like this it may appear quite certain how things work out, but in reality this is not the case. It’s because the assumption with the interpolation formula is that data changes uniformly.
Whilst we used this method to estimate the height of a seven-year-old girl as being 111.6 cm, the actual average height is 120 cm because children do not grow uniformly between 0 and 10. The same is true with IRR and NPV. By using varying discount rates a student will get slightly different results and this can lead to uncertainty. However, for the BPFM, markers will be looking to see if students are following a process rather than focusing on the final answer. Instead, practice the questions and make sure the marker sees how you are completing the process and don’t focus on the final outcome.
- Anna Howard is head of qualifications, innovation and development at CIPFA
