Payback Period · Accounting Rate of Return · Net Present Value · Internal Rate of Return · Comparison of Methods | Cambridge A Level Accounting 9706
Investment appraisal is the process of evaluating whether a capital investment project — such as buying new machinery, building a new factory, or launching a new product — is financially worthwhile. Since capital investments involve large sums of money committed over many years, the decision requires rigorous analysis.
| Method | What it Measures | Uses Cash Flows or Profit? | Time Value of Money? |
|---|---|---|---|
| Payback Period | How quickly the initial investment is recovered | Cash flows | ❌ No |
| Accounting Rate of Return (ARR) | Average annual profit as % of investment | Accounting profit | ❌ No |
| Net Present Value (NPV) | Total value added to the business in today's money | Cash flows (discounted) | ✅ Yes |
| Internal Rate of Return (IRR) | The discount rate at which NPV = zero | Cash flows (discounted) | ✅ Yes |
Payback = Year in which cumulative cash flow turns positive (with exact months if needed)
Exact payback: Full years + (Remaining balance ÷ Next year cash flow) × 12 months
Decision rule: Accept if payback ≤ target payback period.
Between projects: choose the one with the shorter payback period.
Strengths: Simple, quick, favours liquidity, useful for risky projects.
Weaknesses: Ignores cash flows after payback, ignores time value of money,
does not measure profitability.
Lahore Industries Ltd is considering a machine costing $200,000 with the following annual net cash inflows:
| Year | Net Cash Flow ($) | Cumulative Cash Flow ($) |
|---|---|---|
| 0 (initial investment) | (200,000) | (200,000) |
| 1 | 50,000 | (150,000) |
| 2 | 70,000 | (80,000) |
| 3 | 90,000 | 10,000 |
| 4 | 80,000 | 90,000 |
| 5 | 60,000 | 150,000 |
ARR = (Average Annual Profit ÷ Initial Investment) × 100
Average Annual Profit = (Total profit over project life) ÷ Number of years
Total Profit = Total Cash Inflows − Initial Investment − Depreciation already deducted in cash flows? No — Total Profit = Total Cash Inflows − Initial Investment (if cash flows exclude depreciation)
Decision rule: Accept if ARR ≥ target/hurdle rate.
Between projects: choose higher ARR.
Strengths: Uses familiar accounting concepts (profit), easy to understand,
linked to ROCE which managers already use.
Weaknesses: Ignores time value of money, uses profit not cash flows,
average can be misleading.
Using the same machine from Example 1 (cost $200,000, no residual value).
Total cash inflows over 5 years: $50,000 + $70,000 + $90,000 + $80,000 + $60,000
= $350,000
$1 received today is worth more than $1 received in one year's time. This is because money received today can be invested to earn a return. This concept is called the time value of money and is the foundation of NPV.
PV of cash flow = Cash flow × Discount factor
Discount factor = 1 ÷ (1 + r)^n where r = discount rate, n = year number
NPV = Sum of all Present Values (including negative Year 0 investment)
Decision rule: Accept if NPV ≥ 0 (positive NPV adds value to the firm).
Between projects: choose the one with the higher positive NPV.
Strengths: Considers time value of money, uses cash flows,
gives absolute value added, theoretically the best method.
Weaknesses: Complex, sensitive to discount rate chosen,
difficult to explain to non-financial managers.
| Year | 8% factor | 10% factor | 12% factor | 15% factor | 20% factor |
|---|---|---|---|---|---|
| 0 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
| 1 | 0.926 | 0.909 | 0.893 | 0.870 | 0.833 |
| 2 | 0.857 | 0.826 | 0.797 | 0.756 | 0.694 |
| 3 | 0.794 | 0.751 | 0.712 | 0.658 | 0.579 |
| 4 | 0.735 | 0.683 | 0.636 | 0.572 | 0.482 |
| 5 | 0.681 | 0.621 | 0.567 | 0.497 | 0.402 |
Using the same machine from Example 1. Discount rate = 10%.
| Year | Cash Flow ($) | Discount Factor (10%) | Present Value ($) |
|---|---|---|---|
| 0 | (200,000) | 1.000 | (200,000) |
| 1 | 50,000 | 0.909 | 45,450 |
| 2 | 70,000 | 0.826 | 57,820 |
| 3 | 90,000 | 0.751 | 67,590 |
| 4 | 80,000 | 0.683 | 54,640 |
| 5 | 60,000 | 0.621 | 37,260 |
| NPV | 62,760 | ||
NPV = +$62,760 (positive). The investment adds $62,760 of value to the business in today's money — it earns more than the required 10% return. The project should be accepted.
IRR = Lower rate + [(NPV at lower rate ÷ (NPV at lower rate − NPV at higher rate)) × (Higher rate − Lower rate)]
The IRR is the discount rate at which NPV = 0. It is found by
interpolation — calculating NPV at two different rates (one giving
positive NPV, one giving negative NPV) and interpolating between them.
Decision rule: Accept if IRR ≥ cost of capital (hurdle rate).
Between projects: choose the one with higher IRR.
Strengths: Gives a percentage return — easy to compare with cost of capital.
Considers time value of money.
Weaknesses: Can give multiple IRRs, assumes reinvestment at IRR rate,
does not show absolute value added (unlike NPV).
Using the same machine. We already know NPV at 10% = +$62,760. Now calculate NPV at 25% to find a negative NPV.
| Year | Cash Flow ($) | Discount Factor (25%) | Present Value ($) |
|---|---|---|---|
| 0 | (200,000) | 1.000 | (200,000) |
| 1 | 50,000 | 0.800 | 40,000 |
| 2 | 70,000 | 0.640 | 44,800 |
| 3 | 90,000 | 0.512 | 46,080 |
| 4 | 80,000 | 0.410 | 32,800 |
| 5 | 60,000 | 0.328 | 19,680 |
| NPV at 25% | (16,640) | ||
IRR by interpolation:
IRR of 21.86% exceeds the 10% cost of capital — the project generates a higher return than the minimum required. Accept the project.
| Feature | Payback | ARR | NPV | IRR |
|---|---|---|---|---|
| Basis | Cash flows | Accounting profit | Discounted cash flows | Discounted cash flows |
| Time value of money | No | No | Yes ✅ | Yes ✅ |
| Result expressed as | Years / months | Percentage (%) | Absolute $ amount | Percentage (%) |
| Decision rule | Shorter is better | Higher % is better | Positive NPV = accept | IRR > cost of capital = accept |
| Considers all cash flows? | No — ignores post-payback | Yes — uses total profit | Yes ✅ | Yes ✅ |
| Theoretically superior? | No | No | Yes — preferred by academics | Good but NPV preferred |
| Ease of use | Very simple | Simple | Complex | Most complex |
| Best for | Liquidity focus, risky projects | Comparing % return to ROCE | Maximising shareholder wealth | Comparing % with hurdle rate |
Two items often appear in investment appraisal questions that students frequently mishandle — residual (scrap) value and working capital.
The expected sale proceeds of the asset at the end of its useful life. It is treated as a cash inflow in the final year of the project.
Year 5 cash flow = Annual operating cash flow + Residual value
Also affects ARR calculation — total profit = total cash inflows − (initial investment − residual value)
Many projects require an initial injection of working capital (e.g. extra inventory, receivables). This is a cash outflow at the start of the project and is recovered (inflow) at the end.
Year 0: Working capital outflow (negative)
Final year: Working capital released (positive)
Machine cost: $150,000 | Residual value Year 5:
$20,000 | Working capital required: $15,000
Annual cash inflows: Years 1–5: $50,000 per year.
Discount rate: 10%.
| Year | Cash Flow ($) | Discount Factor (10%) | Present Value ($) |
|---|---|---|---|
| 0 — Machine | (150,000) | 1.000 | (150,000) |
| 0 — Working capital | (15,000) | 1.000 | (15,000) |
| 1 | 50,000 | 0.909 | 45,450 |
| 2 | 50,000 | 0.826 | 41,300 |
| 3 | 50,000 | 0.751 | 37,550 |
| 4 | 50,000 | 0.683 | 34,150 |
| 5 — Operating | 50,000 | 0.621 | 31,050 |
| 5 — Residual value | 20,000 | 0.621 | 12,420 |
| 5 — Working capital released | 15,000 | 0.621 | 9,315 |
| NPV | 46,235 | ||
Positive NPV confirms the project exceeds the 10% required return and should be accepted.
P-A-N-I
Payback — simplest, no time value
ARR — uses profit not cash, no time value
NPV — best method, discounts cash flows, gives $ value
IRR — discounts cash flows, gives % return
NPV is theoretically superior — always recommend NPV unless the
question asks you to evaluate all methods.
Positive NPV → Accept (project earns more than cost of capital)
Negative NPV → Reject (project earns less than cost of capital)
Zero NPV → Indifferent (project earns exactly the cost of capital)
Between two projects: always choose the higher positive NPV —
it adds more value to shareholders.
Question 1 Application — 6 marks Paper 3
Karachi Plastics Ltd is considering purchasing a machine costing $180,000. Expected net cash inflows:
| Year | Cash Inflow ($) |
|---|---|
| 1 | 40,000 |
| 2 | 60,000 |
| 3 | 70,000 |
| 4 | 50,000 |
| 5 | 40,000 |
Calculate: (a) Payback period (in years and months) (b) ARR based on initial investment (c) NPV at 10% discount rate
Discount factors at 10%: Year 1: 0.909, Year 2: 0.826, Year 3: 0.751, Year 4: 0.683, Year 5: 0.621
(a) Payback Period:
| Year | Cash Flow ($) | Cumulative ($) |
|---|---|---|
| 0 | (180,000) | (180,000) |
| 1 | 40,000 | (140,000) |
| 2 | 60,000 | (80,000) |
| 3 | 70,000 | (10,000) |
| 4 | 50,000 | 40,000 |
Payback = 3 years + ($10,000 ÷ $50,000) × 12 = 3 years + 2.4 months ≈ 3 years 2 months (2 marks)
(b) ARR:
Total cash inflows = $260,000 | Less investment = $180,000
Total profit = $80,000 | Average annual profit = $80,000 ÷ 5 = $16,000
ARR = ($16,000 ÷ $180,000) × 100 = 8.9% (2 marks)
(c) NPV at 10%:
| Year | Cash Flow ($) | DF (10%) | PV ($) |
|---|---|---|---|
| 0 | (180,000) | 1.000 | (180,000) |
| 1 | 40,000 | 0.909 | 36,360 |
| 2 | 60,000 | 0.826 | 49,560 |
| 3 | 70,000 | 0.751 | 52,570 |
| 4 | 50,000 | 0.683 | 34,150 |
| 5 | 40,000 | 0.621 | 24,840 |
| NPV | 17,480 | ||
NPV = +$17,480 → Accept (positive NPV) (2 marks)
Question 2 Analysis — 4 marks Paper 3
A company calculates the NPV of a project as +$28,000 at 12% and −$14,000 at 20%. Calculate the IRR and state whether the project should be accepted if the company's cost of capital is 15%.
IRR interpolation:
IRR = 12% + [28,000 ÷ (28,000 + 14,000)] × (20% − 12%)
IRR = 12% + [28,000 ÷ 42,000] × 8%
IRR = 12% + 0.6667 × 8%
IRR = 12% + 5.33% = 17.33% (2 marks)
Decision: The IRR of 17.33% exceeds the cost of capital of 15% — the project generates a higher return than the minimum required. The project should be accepted. (2 marks)
Question 3 Analysis — 4 marks Paper 1
Explain two advantages and two disadvantages of using the Net Present Value method for investment appraisal.
Advantage 1: NPV considers the time value of money — cash flows received in later years are discounted to their present value, recognising that money received sooner is worth more than money received later. This produces a more accurate assessment of a project's true value. (1 mark)
Advantage 2: NPV considers all cash flows over the entire project life — unlike Payback which ignores cash flows after the payback point. It gives an absolute measure of value added (in $) which directly shows the impact on shareholder wealth. (1 mark)
Disadvantage 1: NPV is sensitive to the discount rate chosen — a different rate can change the decision from accept to reject. Selecting the appropriate discount rate is subjective and can significantly affect the outcome. (1 mark)
Disadvantage 2: NPV is more complex to calculate and understand than simpler methods like Payback. Non-financial managers may find it difficult to interpret, reducing its practical usefulness in communication and decision making. (1 mark)
Question 4 Application — 5 marks Paper 3
Punjab Textiles Ltd is considering a project requiring an initial investment of $120,000 and working capital of $10,000. Annual cash inflows of $40,000 for 4 years. Residual value at end of Year 4: $15,000. Working capital is released at the end of Year 4. Discount rate: 12%.
Discount factors at 12%: Year 1: 0.893, Year 2: 0.797, Year 3: 0.712, Year 4: 0.636.
Calculate the NPV and state the investment decision.
| Year | Cash Flow ($) | DF (12%) | PV ($) |
|---|---|---|---|
| 0 — Machine | (120,000) | 1.000 | (120,000) |
| 0 — Working capital | (10,000) | 1.000 | (10,000) |
| 1 | 40,000 | 0.893 | 35,720 |
| 2 | 40,000 | 0.797 | 31,880 |
| 3 | 40,000 | 0.712 | 28,480 |
| 4 — Operating | 40,000 | 0.636 | 25,440 |
| 4 — Residual value | 15,000 | 0.636 | 9,540 |
| 4 — Working capital | 10,000 | 0.636 | 6,360 |
| NPV | 7,420 | ||
NPV = +$7,420 — Accept the project. The positive NPV indicates the project generates a return above the 12% cost of capital and adds $7,420 of value to the business. (5 marks — 1 per correct PV line + decision)
Question 5 Analysis — 3 marks Paper 1
A company uses Payback Period as its primary method of investment appraisal. Discuss three limitations of this approach.
Any three of the following (1 mark each):