Question 19.5: The internal rate of return method Bruce Limited is consider...
The internal rate of return method
Bruce Limited is considering whether to invest £50,000 in a new project. The project’s expected net cash flows would be as follows:
| Year | £000 |
| 1 | 7 |
| 2 | 25 |
| 3 | 30 |
| 4 | 5 |
Required:
Calculate the internal rate of return for the proposed new project.
Bruce Ltd
Calculation of the internal rate of return:
Step 1: Select two discount factors
The first step is to select two discount factors, and then calculate the NPV of the project using both factors. The two factors usually have to be chosen quite arbitrarily but they should preferably cover a narrow range. One of the factors should produce a positive NPV, and the other factor a negative NPV. In this question factors of 10% and 15% have been chosen to illustrate the method. In practice, you may have to try various factors before you come across two that are suitable for giving a positive and a negative result.
| Year | Net cash flow |
Discount factors | Present value | ||
| (1) | (2) | (3) | (4) | (5) | (6) |
| 10% | 15% | 10% | 15% | ||
| £ | £ | £ | |||
| 1 | 7 000 | 0.9091 | 0.8696 | 6 364 | 6 087 |
| 2 | 25 000 | 0.8264 | 0.7561 | 20 660 | 18 903 |
| 3 | 30 000 | 0.7513 | 0.6575 | 22 539 | 19 725 |
| 4 | 5 000 | 0.6830 | 0.5718 | \underline{3 415} | \underline{2 859} |
| Total present values | 52 978 | 47 574 | |||
| Initial cost | \underline{50 000} | \underline{50 000} | |||
| Net present value | \underline{\underline{2 978} } | \underline{\underline{(2 426)} } | |||
Notes:
1 Column (2) has been obtained from the question.
2 Columns (3) and (4) are based on the arbitrary selection of two interest rates of 10% and 15% respectively.
The discount factors may be found in Appendix 2.
3 Column (5) has been calculated by multiplying column (2) by column (3).
4 Column (6) has been calculated by multiplying column (2) by column (4).
The project is expected to cost £50,000. If the company expects a rate of return of 10%, the project will be accepted because the NPV is positive. However, if the required rate of return is 15%, it will not be accepted because its NPV is negative. The maximum rate of return that will ensure a positive rate of return must, therefore, lie somewhere between 10% and 15%, so the next step is to calculate the rate of return at which the project would just pay for itself.
Step 2: Calculate the specific break-even rate of return
To do this, it is necessary to interpolate between the rates used in Step 1. This can be done by using the following formula:
IRR = positive rate +\left(\frac{positive NPV}{positive NPV+ negative NPV^*}\times range of rates \right)
*Ignore the negative sign and add the positive NPV to the negative NPV.
So in our example:
IRR =10\%+ \left(\frac{2978}{\left(2978+ 2426\right) }\times \left(15\%- 10\%\right) \right)
= 10% + (0.5511 × 5)
= 10% + 2.76%
=\underline{\underline{12.76\%} }
The project will be profitable provided that the company does not require a rate of return in excess of about 13%. Note that the method of calculation used above does not give the precise rate of return (because the formula is only an approximation), but it is adequate enough for decision-making purposes.