Welcome to 3.8 Investment appraisal
This interactive workbook focuses on the syllabus methods for assessing investment proposals: payback period, ARR, and NPV (HL only).
What you should be able to do
- Use the formula to calculate each method from a contextual data set.
- Interpret the result and decide if the investment should go ahead.
- Explain why the decision makes sense (and what the limitations are).
How the practices work
- Read the scenario and extract the relevant numbers.
- Enter your calculation(s).
- Choose a decision: accept or reject.
- Click Check to get feedback on both the calculation and the reasoning.
Learning – the three methods
What each method measures, how to calculate it, and what “good” typically looks like.
Payback period
Payback = time until cumulative cash inflows = initial investmentIf the final year is partial:
fractional year = (amount remaining ÷ cash inflow in that year)
Shorter payback is usually preferred (less risk, faster liquidity).
ARR (Average rate of return)
ARR = (Average annual profit ÷ Initial investment) × 100where
Average annual profit = Total profit over life ÷ number of years
Higher ARR is better, but remember it uses accounting profit (not cash flow).
NPV (HL only)
NPV = Σ (Discounted net cash flows) − Initial investmentIf NPV is positive, the investment may be worthwhile.
Quick interpretations
- Payback: if it recovers quickly (and within a target period), it’s usually attractive.
- ARR: if ARR is above a required return / alternative, it’s attractive.
- NPV (HL): positive NPV suggests value added at the discount rate used.
Quick check – method matching
1. Which method focuses mainly on speed of recovering the initial cost?
2. Which method uses accounting profit rather than cash flow?
3. Which method applies a discount factor to future cash flows? (HL)
Learning – choosing between methods
Strengths and limitations you can use in evaluation.
Strengths
- Payback: simple, focuses on liquidity and risk.
- ARR: simple percentage return, easy to compare with targets.
- NPV (HL): accounts for the time value of money and uses discounted cash flows.
Limitations
- Payback: ignores cash flows after payback; ignores profitability in later years.
- ARR: uses profit (not cash); ignores timing; can be affected by accounting policies.
- NPV (HL): requires a discount rate (assumption); more complex; forecasts can be uncertain.
Quick check – evaluation thinking
1. A method that ignores cash flows after payback might lead to a poor decision because…
2. If forecast data is unreliable, which is the most sensible point to make?
Practice – Payback period (3 cases)
Use cash flow data to calculate payback and decide whether to accept the proposal.
How we mark
Enter payback as a decimal year (e.g. 3.5 years). If payback happens exactly at the end of a year, enter a whole number.
Scenario – Riverside Café (new oven)
The café is considering a new oven costing $24 000. Forecast net cash inflows are: Year 1: $8 000, Year 2: $10 000, Year 3: $9 000, Year 4: $7 000. The owner’s target payback period is 3 years.
| Task | Your answer | Hint |
|---|---|---|
| Payback period (years) | Use cumulative cash inflows and fraction of the final year. |
Should the café accept the investment based on payback?
Scenario – QuickDrop Couriers (delivery van)
A van costs $30 000. Forecast net cash inflows are: Year 1: $9 000, Year 2: $9 000, Year 3: $9 000, Year 4: $6 000. The company wants a payback of 3 years or less.
| Task | Your answer | Hint |
|---|---|---|
| Payback period (years) | After 3 years, compare cumulative inflow with $30 000. |
Should the firm accept the investment based on payback?
Scenario – BrightFit Gym (solar panels)
Solar panels cost $20 000. Forecast net cash inflows from energy savings are: Year 1: $4 000, Year 2: $5 000, Year 3: $5 000, Year 4: $6 000. The gym’s maximum acceptable payback is 4 years.
| Task | Your answer | Hint |
|---|---|---|
| Payback period (years) | Check if cumulative inflows hit $20 000 exactly. |
Should the gym accept the investment based on payback?
Practice – ARR (Average rate of return) (3 cases)
Use profit forecasts to calculate ARR and decide whether to accept the investment.
How we mark
Enter ARR as a percentage (e.g. 18.5). Use the syllabus-friendly formula: ARR = (Average annual profit ÷ Initial investment) × 100.
Scenario – Station Coffee (new coffee cart)
The business is considering a coffee cart costing $30 000. Forecast accounting profit over 4 years is: Year 1: $5 000, Year 2: $6 000, Year 3: $7 000, Year 4: $6 000. The owners require an ARR of at least 15%.
| Task | Your answer | Hint |
|---|---|---|
| Average annual profit ($) | Total profit ÷ 4 years. | |
| ARR (%) | (Average annual profit ÷ 30 000) × 100 |
Should the business accept the investment based on ARR?
Scenario – FreshWrap Foods (new packaging line)
A new packaging line costs $80 000. Forecast accounting profits over 5 years are: $10 000, $7 000, $9 000, $6 000, $8 000. The company requires an ARR of at least 12%.
| Task | Your answer | Hint |
|---|---|---|
| Average annual profit ($) | Total profit ÷ 5 years. | |
| ARR (%) | (Average annual profit ÷ 80 000) × 100 |
Should the business accept the investment based on ARR?
Scenario – Seaview Hotel (renovation)
The hotel is considering a renovation costing $75 000. Forecast accounting profits over 3 years are: Year 1: $9 000, Year 2: $12 000, Year 3: $15 000. The target ARR is 14%.
| Task | Your answer | Hint |
|---|---|---|
| Average annual profit ($) | Total profit ÷ 3 years. | |
| ARR (%) | (Average annual profit ÷ 75 000) × 100 |
Should the business accept the investment based on ARR?
Practice – NPV (HL only) (3 cases)
Use discount factors to calculate present values and decide whether to accept the investment.
How we mark
Enter total discounted cash flows and then NPV. Decision rule: if NPV > 0 accept; if NPV < 0 reject (based on NPV).
Scenario – BeanCraft (coffee roaster)
Initial investment: $40 000. Discount rate: 8%. Net cash flows and discount factors:
| Year | Net cash flow ($) | Discount factor | Your discounted cash flow ($) |
|---|---|---|---|
| 1 | 15 000 | 0.926 | |
| 2 | 16 000 | 0.857 | |
| 3 | 17 000 | 0.794 |
| Task | Your answer | Hint |
|---|---|---|
| Total discounted cash flows ($) | Add your discounted cash flows. | |
| NPV ($) | Total discounted cash flows − 40 000 |
Based on NPV, should the firm accept the investment?
Scenario – PulseFit (new studio)
Initial investment: $50 000. Discount rate: 10%. Net cash flows and discount factors:
| Year | Net cash flow ($) | Discount factor | Your discounted cash flow ($) |
|---|---|---|---|
| 1 | 18 000 | 0.909 | |
| 2 | 19 000 | 0.826 | |
| 3 | 20 000 | 0.751 | |
| 4 | 2 000 | 0.683 |
| Task | Your answer | Hint |
|---|---|---|
| Total discounted cash flows ($) | Add your discounted cash flows. | |
| NPV ($) | Total discounted cash flows − 50 000 |
Based on NPV, should the firm accept the investment?
Scenario – GreenFields Farm (equipment upgrade)
Initial investment: $60 000. Discount rate: 6%. Net cash flows and discount factors:
| Year | Net cash flow ($) | Discount factor | Your discounted cash flow ($) |
|---|---|---|---|
| 1 | 18 000 | 0.943 | |
| 2 | 18 000 | 0.890 | |
| 3 | 18 000 | 0.840 | |
| 4 | 18 000 | 0.792 | |
| 5 | 3 000 | 0.747 |
| Task | Your answer | Hint |
|---|---|---|
| Total discounted cash flows ($) | Add your discounted cash flows. | |
| NPV ($) | Total discounted cash flows − 60 000 |
Based on NPV, should the firm accept the investment?
Flashcard studio – 3.8 key terms
Secure the language of investment appraisal.
Deck
Click a term in the list to jump straight to that card.
End-of-topic quiz – 3.8 investment appraisal (20 Qs)
Increasing difficulty: definitions → calculations → interpretation and evaluation.