SingaporeAccountingSyllabus dot point

How is the accounting rate of return calculated, and what does the internal rate of return add to project appraisal?

Calculate the accounting rate of return and explain the internal rate of return as the break-even discount rate

A focused answer to the H2 Principles of Accounting outcome on ARR and IRR. The accounting rate of return on average investment, its profit basis, the internal rate of return as the rate giving zero NPV, and how to estimate IRR by interpolation.

Generated by Claude Opus 4.810 min answerUpdated 2026-06-06

Reviewed by: AI editorial process; not yet individually human-reviewed

Have a quick question? Jump to the Q&A page

Jump to a section

What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

SEAB wants you to calculate the accounting rate of return (ARR) and to explain the internal rate of return (IRR) as the break-even discount rate. These two methods sit either side of NPV: the ARR is profit-based and simple, while the IRR is a discounting method closely related to NPV. The central insight is that the ARR measures profitability against the investment but ignores timing, whereas the IRR finds the exact rate at which a project just breaks even in present-value terms.

The answer

The accounting rate of return

The ARR expresses the average annual accounting profit as a percentage of the investment. The common version uses average investment:

\text{ARR} = \frac{\text{average annual profit}}{\text{average investment}} \times 100, \qquad \text{average investment} = \frac{\text{initial cost} + \text{residual value}}{2}

Average annual profit is the total profit after depreciation divided by the number of years. The decision rule is to accept projects whose ARR exceeds a target rate and, between projects, to prefer the higher ARR.

Its strengths are simplicity and the use of familiar accounting profit. Its weaknesses are that it is based on profit rather than cash, ignores the time value of money, and depends on the chosen depreciation method.

The internal rate of return

The IRR is the discount rate at which a project's NPV is exactly zero. It is the project's own rate of return, the highest cost of capital the project can sustain and still be worthwhile. Unlike the ARR, the IRR is based on discounted cash flows, so it does account for timing.

Estimating IRR by interpolation

The IRR is found by trial: compute the NPV at two rates, one giving a positive NPV and one negative, then interpolate linearly:

\text{IRR} \approx L + \frac{\text{NPV}_L}{\text{NPV}_L - \text{NPV}_H} \times (H - L)

where $L$ and $H$ are the lower and higher rates and $\text{NPV}_L$ , $\text{NPV}_H$ the NPVs at those rates. The decision rule is to accept if the IRR exceeds the cost of capital, since then the NPV at the actual cost of capital is positive.

Worked example

A project costs $\$ 160,000 $with a residual value of$ \ $20\,000$ and generates total profit after depreciation of $\$ 90,000 $over$ 5 $years. Its NPV is$ +\ $6\,000$ at $12\%$ and $-\$ 3,000 $at$ 16%$. Find the ARR and estimate the IRR.

Step 1: Average annual profit

\frac{90\,000}{5} = \$18\,000

Step 2: Average investment and ARR

Average investment $= \dfrac{160\,000 + 20\,000}{2} = \$ 90,000$.

\text{ARR} = \frac{18\,000}{90\,000} \times 100 = 20\%

Step 3: Interpolate for the IRR

\text{IRR} \approx 12 + \frac{6\,000}{6\,000 - (-3\,000)} \times (16 - 12) = 12 + \frac{6\,000}{9\,000} \times 4 = 12 + 2.67 = 14.67\%

Step 4: Interpret

The ARR is $20\%$ , judged against the firm's target return. The IRR is about $14.7\%$ , so the project is worthwhile only if the cost of capital is below $14.7\%$ . At a $12\%$ cost of capital it is acceptable (positive NPV); at $16\%$ it is not. The two methods give complementary views: ARR on profitability, IRR on the break-even financing rate.

Examples in context

Example 1. ARR distorted by depreciation choice. Two identical projects use different depreciation methods, straight-line and reducing balance. Their cash flows are the same, but their accounting profits, and therefore their ARRs, differ because depreciation differs. This shows a key weakness of the ARR: a profit-based measure can be swayed by an accounting policy, which is why cash-based methods like NPV and IRR are more reliable for the underlying economics.

Example 2. Using IRR to set a financing ceiling. A company finds a project's IRR is $13\%$ . It can therefore accept the project only if it can finance it at less than $13\%$ . When its bank quotes a $15\%$ loan rate, the project is rejected, because the cost of capital exceeds the IRR and the NPV would be negative. The IRR translates the appraisal into a clear financing benchmark managers can act on.

Try this

Q1. Average annual profit is $\$ 24,000 $and average investment is$ \ $120\,000$ . Find the ARR. [2 marks]

Cue. $\dfrac{24\,000}{120\,000} \times 100 = 20\%$ .

Q2. A project's NPV is $+\$ 5,000 $at$ 10% $and$ -\ $5\,000$ at $20\%$ . Estimate the IRR. [3 marks]

Cue. $10 + \dfrac{5\,000}{5\,000 - (-5\,000)} \times (20 - 10) = 10 + \dfrac{5\,000}{10\,000} \times 10 = 15\%$ .

Q3. State the decision rule for the IRR and explain it. [2 marks]

Cue. Accept if the IRR exceeds the cost of capital; at that point the project's NPV at the actual cost of capital is positive, so it adds value.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original7 marksA project costs

\

200\,000

, has no residual value, and generates total accounting profit (after depreciation) of

120\,000

over

4

years. (a) Calculate the average annual profit. (b) Calculate the accounting rate of return using average investment. (c) State one weakness of the ARR.

Show worked answer →

(a) Average annual profit $= \dfrac{\text{total profit}}{\text{years}} = \dfrac{120\,000}{4} = \$ 30,000$.

(b) Average investment $= \dfrac{\text{initial cost} + \text{residual value}}{2} = \dfrac{200\,000 + 0}{2} = \$ 100,000$.

Accounting rate of return $= \dfrac{\text{average annual profit}}{\text{average investment}} \times 100 = \dfrac{30\,000}{100\,000} \times 100 = 30\%$ .

(c) A weakness: the ARR is based on accounting profit, not cash flows, and it ignores the time value of money, treating profit in year 4 as equal to profit in year 1. (It also depends on the depreciation method chosen.)

Markers reward average profit of $\$ 30,000 $, average investment of$ \ $100\,000$ , an ARR of $30\%$ , and a valid weakness (profit-based, ignores time value).

Original6 marksA project has an NPV of

+\

8\,000

at

10\%

and

2\,000

14\%

. (a) Estimate the internal rate of return by interpolation. (b) Explain what the IRR represents and the decision rule using it.

Show worked answer →

(a) The IRR is the discount rate giving an NPV of zero, between $10\%$ (positive) and $14\%$ (negative). By linear interpolation:

$\text{IRR} \approx L + \dfrac{\text{NPV}_L}{\text{NPV}_L - \text{NPV}_H} \times (H - L)$

$= 10 + \dfrac{8\,000}{8\,000 - (-2\,000)} \times (14 - 10) = 10 + \dfrac{8\,000}{10\,000} \times 4 = 10 + 3.2 = 13.2\%$ .

(b) The internal rate of return is the discount rate at which the project's NPV is exactly zero, the break-even cost of capital. It represents the maximum cost of capital the project can bear while still being worthwhile. The decision rule: accept the project if its IRR exceeds the cost of capital, and reject it if the IRR is below the cost of capital.

Markers reward the interpolation to about $13.2\%$ , the definition of IRR as the rate giving zero NPV, and the rule to accept when IRR exceeds the cost of capital.