Key Idea: Topic 3.8 is about comparing investment appraisal methods and then justifying a recommendation using both numbers and business context. At HL, this includes payback period, ARR and NPV, so students are expected to be disciplined with method, comparison and evaluation — not just the final number.
⏱️ Payback: **Payback period —** time to recover initial investment. **Focus —** speed and risk. **Shorter payback —** preferred. **Best for —** cash-sensitive or risk-averse businesses.
📊 ARR: **ARR —** average annual profit ÷ investment × 100. **Focus —** profitability. **Higher ARR —** preferred. **Best for —** judging long-term return.
💰 NPV: **NPV —** discounted future cash flows minus initial cost. **Focus —** value created after allowing for time value of money. **Positive NPV —** accept. **Negative NPV —** reject.
🧠 Why HL students must know it: **Main HL advantage —** considers time value of money. **Discount factors —** will be given in the exam. **Decision rule —** positive = worthwhile, negative = not worthwhile. **Best for —** deeper long-term investment judgement.
🤔 Trade-offs: **Short payback, low ARR —** safer but less profitable. **Long payback, high ARR —** more profitable but riskier. **Positive NPV but long payback —** attractive long-term but weaker short-term cash recovery. **Start-ups or weak liquidity —** often prefer payback.
⚠️ Limitations: **Payback —** ignores profits after payback. **ARR —** ignores timing of cash flows. **NPV —** relies on estimated cash flows and chosen discount rate. **All methods —** should still be supported by qualitative factors.
HL exam tip: Always show full working in calculations. Even when the final answer is wrong, method marks can still be earned if the process is clear.
Past-paper tip: For payback, use a cumulative cash-flow column for uneven flows. For ARR, do not forget to subtract the initial investment before finding total profit. For NPV, multiply each year's cash flow by the given discount factor carefully and then subtract the initial cost at the end.
NPV tip: Discount factors will be provided in the exam. You do not need to calculate them — just apply them accurately and interpret the final NPV correctly.
Recommendation tip: A top-band answer does not just say which project is better. It explains why one method matters more for this business at this time, and acknowledges at least one limitation or uncertainty.
Example: A strong answer: Project A has a shorter payback so is less risky and better for cash flow, while Project B has a higher ARR and a positive NPV, suggesting stronger long-term profitability and value creation. The better choice depends on whether the business prioritises fast cash recovery or long-term return.
Important: Common triggers: calculate payback, calculate ARR, calculate NPV, compare options, evaluate the methods, and recommend an investment using both quantitative and qualitative evidence.
- Calculate with full working
- State results clearly
- Compare the options
- Explain what each result means
- Include qualitative factors
- Make a justified recommendation with one limitation or caveat