Internal Rate of Return (IRR) (Cambridge International A-Level Accounting)

Spec point — how to apply the following capital investment appraisal techniques: – internal rate of return (IRR) the advantages and disadvantages of these capital investment appraisal techniques

Internal rate of return (IRR)

What is the internal rate of return (IRR)?

• The internal rate of return is the discount rate at which the NPV of a project equals zero

• It is found by interpolation between two discount rates

  • One which gives a negative NPV and one which gives a positive NPV

• Owners usually prefer investments which have a higher internal rate of return

• If the internal rate of return is higher than the cost of capital, then the project is usually accepted

• If the internal rate of return is lower than the cost of capital, then the project is usually rejected

How do I calculate the internal rate of return?

• STEP 1 Calculate the net cash flow for each year

• STEP 2 Calculate the net present values using both the lower and higher cost of capital

  • You will likely be asked to find one of these in an earlier question part
  • The NPV at the higher rate will be negative

• STEP 3 Add together the two net present values and divide the NPV at the lower cost of capital by this amount

  • $\frac{\mathrm{NPV} \mathrm{at} \mathrm{lower} \mathrm{rate}}{\mathrm{NPV} \mathrm{at} \mathrm{lower} \mathrm{rate}+\mathrm{NPV} \mathrm{at} \mathrm{higher} \mathrm{rate}}$
  • Ignore the fact that the NPV at the higher rate is negative

• STEP 4 Multiply this by the difference between the two discount rates and add this to the lower discount rate

  • $\frac{NPV \text{at} \text{lower} rate}{NPV \text{at} \text{lower} \text{rate} + \text{NPV} \text{at} \text{higher} rate} \times ( \text{higher} \text{rate} - \text{lower} \text{rate} ) + \text{lower} \text{rate}$

    • Write as a percentage

Exam Hint This formula can look confusing. Make sure the number on top of the fraction is the NPV using the lower cost of capital. It is not necessarily the smallest number. See the worked example for more help.

What are the advantages and disadvantages of the internal rate of return method?

Advantages

• It accounts for the time value of money

• It does not require a specific discount rate to be chosen in advance

• It is expressed as a percentage

  • This makes it easy to compare against the cost of capital

Disadvantages

• It requires the calculation of two net present values

• It ignores the scale of investment

  • A small project can have a high IRR

• Interpolation gives an approximation

  • It is not an exact figure

Worked Example The directors of D plc are considering the purchase of a new machine, costing $220 000, to manufacture a newly developed product, Product Omega. The directors intend to manufacture the product for only four years, after which the machine will have zero residual value.

The directors have estimated the following net cash flows arising from the project:

Year	Net cash flow ($)
1	45 000
2	60 000
3	105 000
4	30 000

Relevant discount factors are as follows:

	Discount rate
Year	3%	5%
1	0.971	0.952
2	0.943	0.907
3	0.915	0.864
4	0.888	0.823

Calculate the internal rate of return (IRR) to two decimal places.

Answer:

Calculate the NPV using the lower discount rate of 3%

Year	Net cash flow ($)**		Discounted net cash flow ($)
0	(220 000)	(220 000) × 1.000	(220 000)
1	45 000	45 000 × 0.971	43 695
2	60 000	60 000 × 0.943	56 580
3	105 000	105 000 × 0.915	96 075
4	30 000	30 000 × 0.888	26 640
			2 990

Calculate the NPV using the higher discount rate of 5%

Year	** Net cash flow ($)**		Discounted net cash flow ($)
0	(220 000)	(220 000) × 1.000	(220 000)
1	45 000	45 000 × 0.952	42 840
2	60 000	60 000 × 0.907	54 420
3	105 000	105 000 × 0.864	90 720
4	30 000	30 000 × 0.823	24 690
			(7 330)

Use the formula

• Add the two NPVs
• Divide the NPV at the lower rate by this value
• Multiply by the difference between the two rates
• Add this to the lower rate

$\frac{2 990}{2 990 + 7 330} \times ( 5 \% - 3 \% ) + 3 \% = 3.579... \%$

Round to 2 decimal places

Final answer: IRR = 3.58%