Cambridge AS & A Level9706

Investment appraisal (A Level)

Accounting 9706 Chapter Notes

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Investment appraisal (A Level)
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In this chapter

  1. 1Introduction to Investment Appraisal
  2. 2The Payback Period Method
  3. 3Accounting Rate of Return (ARR)
  4. 4Net Present Value (NPV)
  5. 5Internal Rate of Return (IRR)
  6. 6Making the Final Decision: Financial and Non-Financial Factors

1. Introduction to Investment Appraisal

Investment appraisal is the process businesses use to evaluate the potential financial viability of long-term projects or investments. Before committing large sums of money to ventures like buying new machinery, launching a new product, or building a factory, managers need to assess whether the expected future returns justify the initial cost. These techniques use financial forecasts to help compare different investment opportunities and support rational, data-driven decision-making, reducing the risk of costly failures.

Key term

Investment Appraisal: A set of analytical techniques used to evaluate the financial costs and benefits of an investment project to decide whether it should be undertaken.

Examiner insight

Examiners look for an understanding that investment appraisal is a forward-looking process based on forecasts, which inherently involves uncertainty.

Worked example 13 marks

A bakery is considering spending $50,000 on a new, more efficient oven. What key financial questions should the owner ask before making this investment?

  1. 1
    1. What is the total initial cost of the investment? In this case, it is $50,000 plus any installation or training costs.
  2. 2
    1. What are the expected future net cash inflows from the oven? This could be from lower electricity costs, reduced labour time, or the ability to bake and sell more products.
  3. 3
    1. How long is the oven expected to last? This determines the project's lifespan over which benefits will be measured.
  4. 4
    1. By answering these, the owner can gather the necessary data to use investment appraisal techniques and assess whether the future financial benefits outweigh the initial cost.

Recap

  • Investment appraisal helps businesses decide where to allocate capital for long-term projects.
  • It involves comparing the initial cost of an investment with its expected future returns.
  • The goal is to reduce risk and make more profitable investment decisions.
  • The process is forward-looking and relies on financial forecasts, which always have a degree of uncertainty.

Quick check

  1. What is the main purpose of investment appraisal?2 marks

2. The Payback Period Method

The Payback Period is the simplest investment appraisal technique. It calculates the time it takes for a project's net cash inflows to 'pay back' the initial capital investment. It's a popular method because it's easy to understand and focuses on how quickly a firm can get its money back. A shorter payback period is generally preferred as it indicates lower risk and a faster return of cash, which can then be reinvested elsewhere. The calculation differs slightly depending on whether the annual cash inflows are constant or variable.

For constant annual cash flows: Payback Period = Initial Investment / Annual Net Cash Inflow

For variable annual cash flows: Payback Period = Full years until recovery + (Amount remaining to be paid back / Cash flow in the next year)

Key term

Payback Period: The length of time required for the cumulative net cash inflows from an investment to equal its initial cost.

Examiner insight

For variable cash flows, examiners expect to see the cumulative cash flow calculated year by year. State the final answer clearly in years and months.

Common pitfall

Simply stating the payback is 'in Year 3' instead of calculating the exact point within that year. You must calculate the months required in the final year for full marks.

Worked example 12 marks

A project requires an initial investment of $200,000 and is expected to generate net cash inflows of $50,000 per year. Calculate the payback period.

  1. 1
    1. Use the formula for constant cash flows: Payback Period = Initial Investment / Annual Net Cash Inflow.
  2. 2
    1. Substitute the values: Payback Period = $200,000 / $50,000.
  3. 3
    1. Calculate the result: Payback Period = 4 years.

Worked example 24 marks

A firm invests $150,000 in a project with the following expected net cash inflows: Year 1: $40,000, Year 2: $60,000, Year 3: $70,000, Year 4: $80,000. Calculate the payback period.

  1. 1
    1. Calculate the cumulative cash flow year by year to find the full year before recovery.
  2. 2

    End of Year 1: Cumulative cash flow = $40,000. Amount remaining = $150,000 - $40,000 = $110,000.

  3. 3

    End of Year 2: Cumulative cash flow = $40,000 + $60,000 = $100,000. Amount remaining = $150,000 - $100,000 = $50,000.

  4. 4
    1. Payback occurs during Year 3. The full years of recovery is 2 years.
  5. 5
    1. Calculate the fraction of Year 3 needed: Amount remaining / Cash flow in Year 3 = $50,000 / $70,000 = 0.714 years.
  6. 6
    1. Convert the fraction to months: 0.714 × 12 months = 8.57 months. It is conventional to round up to the next whole month.
  7. 7
    1. The total payback period is 2 years and 9 months.

Recap

  • The payback period measures how long it takes to recover an investment's cost.
  • A shorter payback period is generally preferred as it means lower risk and better liquidity.
  • It is simple to calculate and understand, but it ignores all cash flows after the payback period.
  • A key weakness is that it completely ignores the time value of money.

Quick check

  1. State two disadvantages of using the payback method.2 marks

3. Accounting Rate of Return (ARR)

The Accounting Rate of Return (ARR) measures the expected profitability of an investment. Unlike payback, which uses cash flows, ARR uses accounting profit. It calculates the average annual profit a project will generate as a percentage of the initial investment. The decision rule is to accept projects where the ARR is higher than a pre-set target rate set by the business (often related to the cost of capital or the ARR of other projects). It provides a clear percentage return which is easily comparable with other business performance metrics like Return on Capital Employed (ROCE).

Annual Depreciation = (Initial Cost - Residual Value) / Lifespan of Project

Average Annual Profit = (Total Net Profit over project's life) / Lifespan of project

ARR (%) = (Average Annual Profit / Initial Investment) × 100

Key term

Accounting Rate of Return (ARR): A measure of the average annual profitability of an investment, expressed as a percentage of the initial investment cost.

Examiner insight

Candidates who compare the calculated ARR to a pre-set target rate or the company's cost of capital demonstrate better application skills.

Common pitfall

Using cash flow figures directly instead of calculating profit. Remember, profit = cash flow - non-cash expenses, and depreciation is a key non-cash expense that must be accounted for in ARR calculations.

Worked example 15 marks

A machine costs $180,000 and will have a 5-year life with no residual value. It is expected to generate total net cash flows of $250,000 over the 5 years. Calculate the ARR.

  1. 1
    1. Calculate total profit. First, find total depreciation over the 5 years: Total Depreciation = Initial Cost - Residual Value = $180,000 - $0 = $180,000.
  2. 2
    1. Total Profit = Total Net Cash Flow - Total Depreciation = $250,000 - $180,000 = $70,000.
  3. 3
    1. Calculate Average Annual Profit: Average Annual Profit = Total Profit / Lifespan = $70,000 / 5 years = $14,000 per year.
  4. 4
    1. Calculate ARR using the initial investment: ARR = (Average Annual Profit / Initial Investment) × 100.
  5. 5
    1. ARR = ($14,000 / $180,000) × 100 = 7.78%.

Recap

  • ARR measures the average annual profit as a percentage of the initial investment.
  • The formula is (Average Annual Profit / Initial Investment) x 100.
  • To find profit from cash flow, you must subtract the non-cash expense of depreciation.
  • The decision rule is to accept projects with an ARR above a target rate.
  • ARR is useful for assessing profitability but, like payback, it ignores the timing of profits (time value of money).

Quick check

  1. Why must depreciation be subtracted from cash flow when calculating ARR?2 marks

4. Net Present Value (NPV)

Net Present Value (NPV) is a sophisticated investment appraisal method that accounts for the 'time value of money'. The core idea is that money received today is worth more than the same amount received in the future, because today's money can be invested to earn a return. NPV works by 'discounting' all expected future cash flows back to their current value (Present Value) and then subtracting the initial investment. The rate used for discounting is typically the company's cost of capital. A positive NPV means the project is expected to generate a return greater than the cost of capital, adding value to the business.

Present Value (PV) = Net Cash Flow × Discount Factor

Discount Factor = 1 / (1 + r)^n (where r = discount rate, n = year)

NPV = (Sum of all Present Values of future cash flows) - Initial Investment

Key term

Time Value of Money: The concept that a sum of money is worth more now than the same sum will be at a future date due to its potential earning capacity.

Examiner insight

Examiners reward clear working, especially the use of a table to show the discounting process for each year's cash flow. Always state a clear decision based on the NPV result.

Common pitfall

Forgetting that the initial investment (Year 0) is already a present value and does not need to be discounted. It is always a negative figure in the final NPV calculation.

Fun fact

The concept of present value dates back to at least the 13th century, used by merchants in Genoa to value future deliveries of goods, showing that accounting for time and risk is an age-old problem.

Worked example 15 marks

A project costs $100,000. Expected net cash inflows are $40,000 for 3 years. The cost of capital is 10%. Discount factors for 10% are: Year 1=0.909, Year 2=0.826, Year 3=0.751. Calculate the NPV and advise whether the project should be accepted.

  1. 1
    1. Set up a table to calculate the Present Value (PV) of each year's cash flow.
  2. 2

    Year 1: PV = $40,000 × 0.909 = $36,360.

  3. 3

    Year 2: PV = $40,000 × 0.826 = $33,040.

  4. 4

    Year 3: PV = $40,000 × 0.751 = $30,040.

  5. 5
    1. Sum the Present Values of the inflows: Total PV = $36,360 + $33,040 + $30,040 = $99,440.
  6. 6
    1. Calculate NPV by subtracting the initial investment (which is in Year 0, so its PV is its actual value): NPV = Total PV - Initial Investment.
  7. 7
    1. NPV = $99,440 - $100,000 = -$560.
  8. 8
    1. Conclusion: Since the NPV is negative, the project should be rejected. It is expected to generate a return less than the 10% cost of capital, meaning it would destroy shareholder value.

Recap

  • NPV accounts for the time value of money by discounting future cash flows.
  • The decision rule is to accept projects with a positive NPV and reject those with a negative NPV.
  • A positive NPV represents the surplus value the project adds to the business.
  • NPV considers all cash flows over the project's entire life, making it a comprehensive measure.
  • Its main drawback is its heavy reliance on an accurate forecast of the discount rate and future cash flows.

Quick check

  1. If a project has an NPV of $25,000, what does this figure represent?2 marks

5. Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is another discounted cash flow technique. It is defined as the specific discount rate at which a project's Net Present Value (NPV) becomes exactly zero. In simpler terms, it's the true underlying percentage rate of return that a project is expected to generate. To find the IRR, we use a trial-and-error approach: we calculate the NPV using two different discount rates, aiming for one positive NPV and one negative NPV. The IRR must lie between these two rates. We can then estimate the IRR more precisely using an interpolation formula. The decision rule is to accept a project if its IRR is greater than the company's cost of capital.

IRR ≈ r_a + [ NPV_a / (NPV_a - NPV_b) ] × (r_b - r_a)

Where: r_a = lower discount rate, r_b = higher discount rate, NPV_a = NPV at rate r_a (the positive one), NPV_b = NPV at rate r_b (the negative one)

Key term

Internal Rate of Return (IRR): The discount rate that makes the Net Present Value (NPV) of all cash flows from a particular project equal to zero.

Examiner insight

Students who can clearly explain the decision rule for IRR (accept if IRR > cost of capital) and use the interpolation formula accurately score highly.

Common pitfall

Making a mistake with the signs in the interpolation formula. Remember that (NPV_a - NPV_b) where NPV_b is negative becomes a sum (NPV_a + absolute value of NPV_b), which is a common source of error.

Worked example 15 marks

A project costs $220,000 and generates net cash flows of $80,000 per year for 4 years. At a discount rate of 10%, the NPV is +$33,520. At a discount rate of 20%, the NPV is -$11,680. Estimate the IRR.

  1. 1
    1. Identify the components for the IRR formula: r_a = 10%, r_b = 20%, NPV_a = +$33,520, NPV_b = -$11,680.
  2. 2
    1. Write down the interpolation formula: IRR ≈ r_a + [ NPV_a / (NPV_a - NPV_b) ] × (r_b - r_a).
  3. 3
    1. Substitute the values: IRR ≈ 10% + [ $33,520 / ($33,520 - (-$11,680)) ] × (20% - 10%).
  4. 4
    1. Simplify the denominator: $33,520 - (-$11,680) = $33,520 + $11,680 = $45,200.
  5. 5
    1. Simplify the rest of the calculation: IRR ≈ 10% + ($33,520 / $45,200) × 10%.
  6. 6
    1. IRR ≈ 10% + (0.7416) × 10% = 10% + 7.416%.
  7. 7
    1. The estimated IRR is 17.42%.

Recap

  • IRR is the discount rate at which NPV equals zero.
  • It represents the project's true percentage rate of return.
  • The decision rule is: accept the project if its IRR is greater than the cost of capital.
  • IRR is found by testing two discount rates (one giving a positive NPV, one giving a negative NPV) and then using the interpolation formula.
  • It is an intuitive measure but can be more complex to calculate than NPV.

Quick check

  1. A project's IRR is 14%. The firm can borrow money at 11%. Should the project be accepted? Why?2 marks

6. Making the Final Decision: Financial and Non-Financial Factors

No single investment appraisal method is perfect. A thorough analysis uses several techniques to build a complete picture. For example, a project might have a quick Payback (good for cash flow) but a low ARR (poor profitability). NPV is often considered the most reliable method as it uses all cash flows and accounts for the time value of money, giving a clear indication of value added. However, investment decisions are not made in a vacuum. Managers must also consider non-financial factors – qualitative aspects that cannot be easily measured in monetary terms but are crucial for long-term success. These can include the impact on employee morale, the firm's brand image, environmental considerations, and alignment with the company's overall strategy.

Key term

Non-Financial Factors: Qualitative considerations that can influence an investment decision but are not included in quantitative appraisal techniques.

Examiner insight

Top-level answers provide a balanced conclusion that justifies a decision by weighing both quantitative (NPV, IRR etc.) and qualitative (non-financial) factors, rather than just relying on one number.

Common pitfall

Simply listing non-financial factors without explaining *how* they would specifically influence the investment decision in the context of the question.

Worked example 16 marks

A fashion retailer is choosing between two projects. Project A: Invest in a new IT system to improve stock control. NPV = +$50,000, Payback = 4 years. Project B: Invest in using sustainable, ethically sourced materials for its clothing line. NPV = +$20,000, Payback = 6 years. Advise the retailer which project to choose.

  1. 1
    1. Financial Analysis: Project A is financially superior based on the data provided. It has a higher NPV ($50k vs $20k), meaning it adds more value to the business, and a shorter payback period (4 years vs 6 years), meaning it returns the initial investment faster.
  2. 2
    1. Non-Financial Analysis: Project B, despite being financially weaker, has significant non-financial benefits. Using sustainable and ethical materials can greatly enhance the company's brand image, attract environmentally and socially conscious customers, and boost employee morale. This could lead to higher sales and brand loyalty in the long run, which are not captured by the initial NPV calculation.
  3. 3
    1. Recommendation: If the company is focused purely on short-term profit and cash flow, Project A is the clear choice. However, if the company's strategic goal is to build a strong, ethical brand for the future, Project B may be the better long-term investment. The decision depends on the company's priorities. A good recommendation would be to choose Project B, accepting the lower initial financial return for the strategic and marketing benefits it will bring.

Recap

  • NPV is theoretically the best method as it measures absolute value added and uses all cash flows.
  • Payback is good for assessing risk and liquidity, while ARR is good for assessing profitability.
  • A comprehensive analysis should use a combination of these methods to get a full picture.
  • Non-financial factors, such as brand image, employee relations, and environmental impact, are also critical.
  • The final decision involves balancing quantitative financial data with qualitative non-financial factors.

Quick check

  1. Name two non-financial factors a car manufacturer might consider when investing in a new electric vehicle plant.2 marks

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Define the term 'Accounting Rate of Return' (ARR).2 marks
  2. A project has an initial cost of $300,000. It is expected to have a 5-year life and generate a total profit of $150,000 over this period. Calculate the ARR.3 marks
  3. A project requires an initial outlay of $250,000. The expected net cash inflows are: Year 1: $70,000; Year 2: $90,000; Year 3: $100,000; Year 4: $100,000. Calculate the payback period for this project.4 marks
  4. A company is considering an investment of $500,000. The project is expected to generate net cash flows of $180,000 per year for 4 years. The company's cost of capital is 12%. The relevant discount factors are: Year 1: 0.893, Year 2: 0.797, Year 3: 0.712, Year 4: 0.636. Calculate the Net Present Value (NPV) of the project and state whether it should be accepted.5 marks
  5. Explain two advantages and two disadvantages of using the Net Present Value (NPV) method for investment appraisal.4 marks
  6. A firm is appraising a project and has calculated its Internal Rate of Return (IRR) to be 13.5%. The firm's bank offers loans at an interest rate of 9%, and the firm has a target rate of return for all new projects of 15%. Advise the firm whether to proceed with the project. Justify your answer.3 marks
  7. An investment has an initial cost of $80,000. Using a discount rate of 10%, its NPV is calculated as +$4,100. Using a discount rate of 15%, its NPV is calculated as -$5,200. Estimate the Internal Rate of Return (IRR) for this investment.5 marks
  8. Compare and contrast the Payback method with the Net Present Value (NPV) method for investment appraisal.6 marks
  9. A company must choose between two mutually exclusive projects. Project Alpha requires an investment of $400,000 and will generate net cash flows of $120,000 for 5 years. Project Beta requires an investment of $400,000 and will generate net cash flows of $150,000 for 4 years. The cost of capital is 10%. The discount factors are: Y1=0.909, Y2=0.826, Y3=0.751, Y4=0.683, Y5=0.621. Calculate the Payback Period and NPV for both projects and recommend which project should be chosen, justifying your answer.8 marks
  10. 'Financial methods of investment appraisal are the only things that matter when making a large investment decision.' To what extent do you agree with this statement?7 marks

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