Investment Appraisal
Foundations of Finance
Investment Appraisal
Syllabus tag: KASNEB CPA | Intermediate Level | CA22 Financial Management | Topic 2 Investment Appraisal
Lesson objectives
By the end of this topic, you will be able to:
- Compute and interpret net present value (NPV)
- Estimate the internal rate of return (IRR) by interpolation
- Compute payback period and discounted payback period
- Compute accounting rate of return (ARR) and the profitability index
- Say which method an examiner expects and why NPV normally wins
The project used throughout
One project runs through every method below, so the results can be compared.
| Year | Cash flow (KES) |
|---|---|
| 0 | (500,000) |
| 1 | 150,000 |
| 2 | 180,000 |
| 3 | 200,000 |
| 4 | 220,000 |
Cost of capital 10%.
Words to know
- Net present value — the present value of the inflows less the initial outlay.
- Internal rate of return — the discount rate at which NPV is exactly zero.
- Payback period — how long the project takes to repay its outlay.
- Discounted payback — the same, but on discounted cash flows.
- Accounting rate of return — average profit as a percentage of investment.
- Profitability index — present value of inflows per shilling invested.
Net present value
Discount every inflow to today, then subtract the outlay.
| Year | Cash flow | Factor at 10% | Present value |
|---|---|---|---|
| 1 | 150,000 | 0.9091 | 136,364 |
| 2 | 180,000 | 0.8264 | 148,760 |
| 3 | 200,000 | 0.7513 | 150,263 |
| 4 | 220,000 | 0.6830 | 150,263 |
| Total | 585,650 |
NPV = 585,650 − 500,000 = KES 85,650
Positive, so the project adds value at a 10% cost of capital. Accept.
The decision rule is simply: accept if NPV is positive, and where projects compete, take the highest NPV.
Internal rate of return
The rate at which NPV becomes zero. At 20% the same project gives:
NPV at 20% = −KES 28,164
Positive at 10%, negative at 20%, so the IRR lies between them. Interpolate:
IRR ≈ 10% + [85,650 / (85,650 + 28,164)] × 10% = 17.5%
The exact figure is 17.19%. Interpolation always overstates slightly, because it draws a straight line through a curve. An examiner accepts the interpolated answer when the working is shown.
Decision rule: accept if IRR exceeds the cost of capital. Here 17.19% beats 10%, which agrees with the NPV.
:::checkpoint NPV and IRR agreed on this project. Describe a situation where they would disagree, and say which one you would follow. :::
Payback period
How long until the outlay is recovered, ignoring the time value of money.
| Year | Cash flow | Cumulative |
|---|---|---|
| 1 | 150,000 | 150,000 |
| 2 | 180,000 | 330,000 |
| 3 | 200,000 | 530,000 |
The 500,000 is passed during year 3. Of that year's 200,000, only 170,000 is needed:
Payback = 2 + (170,000 / 200,000) = 2.85 years
Quick to compute and easy to explain, which is why it survives in practice. But it ignores everything after the payback point and ignores discounting entirely — a project returning nothing in year 4 scores identically here.
Discounted payback
The same calculation on discounted flows, which fixes one of those two faults.
Cumulative discounted: 136,364 then 285,124 then 435,387, passing 500,000 during year 4.
Discounted payback = 3.43 years
Always longer than plain payback, because discounted inflows are smaller.
Accounting rate of return
Based on accounting profit, not cash flow.
Total inflows 750,000, less depreciation of 500,000, gives total profit of 250,000 over four years — average profit 62,500.
- On average investment (500,000 ÷ 2 = 250,000): 62,500 / 250,000 = 25%
- On initial investment (500,000): 62,500 / 500,000 = 12.5%
Both are correct; they answer different questions. State which basis you have used, because the two differ by a factor of two and an unlabelled answer looks wrong.
Profitability index
PV of inflows per shilling invested:
PI = 585,650 / 500,000 = 1.17
Above 1.0 means accept. Its real use is ranking projects when capital is rationed, since it measures value per shilling rather than total value.
Which method wins
NPV is the primary rule at this level, for three reasons: it measures value in shillings, it uses all the cash flows, and it discounts them properly. IRR is a useful cross-check but misleads on mutually exclusive projects and can give several answers where cash flows change sign more than once. Payback measures liquidity risk, not value. ARR is the only one built on accounting profit rather than cash.
:::checkpoint A project costs 500,000, returns nothing for three years, then returns 900,000 in year 4. Its payback period is 4 years — the worst of any project your company is considering. Would you reject it on that basis? Explain what payback fails to capture here. :::