9706 · 4.4.1

Investment Appraisal — practice questions

Practice and worked examples for 9706 Investment Appraisal. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A company is considering investing in a new machine at a cost of $250,000. The machine has a five-year life and an estimated scrap value of $10,000. The forecast net cash inflows are: Year 1: $70,000 Year 2: $80,000 Year 3: $90,000 Year 4: $60,000 Year 5: $50,000

Calculate:

The Payback Period.
The Accounting Rate of Return (ARR).

Show solution outline

1. Payback Period Calculation

We track the cumulative cash flow to see when the initial investment of $250,000 is recovered.

Year	Cash Inflow ($)	Cumulative Cash Inflow ($)
1	70,000	70,000
---	---	---
2	80,000	150,000
3	90,000	240,000

At the end of Year 3, $240,000 has been recovered. Amount remaining to be recovered = $250,000 - $240,000 = $10,000.

The cash inflow in Year 4 is $60,000. Time to recover the remaining amount = ($10,000 / $60,000) * 12 months = 2 months.

Final Answer: The Payback Period is 3 years and 2 months.

2. Accounting Rate of Return (ARR) Calculation

Step 1: Calculate Total Profit Total Cash Inflows = $70,000 + $80,000 + $90,000 + $60,000 + $50,000 = $350,000 Total Depreciation = Initial Cost - Scrap Value = $250,000 - $10,000 = $240,000 Total Profit = Total Cash Inflows - Total Depreciation = $350,000 - $240,000 = $110,000

Step 2: Calculate Average Annual Profit Average Annual Profit = Total Profit / Life of Project = $110,000 / 5 years = $22,000

Step 3: Calculate Average Investment Average Investment = (Initial Cost + Scrap Value) / 2 = ($250,000 + $10,000) / 2 = $130,000

Step 4: Calculate ARR $\text{ARR} = \frac{\text{Average Annual Profit}}{\text{Average Investment}} \times 100\%$ $\text{ARR} = \frac{\text{\textdollar}22,000}{\text{\textdollar}130,000} \times 100\% = 16.92\%$

Final Answer: The Accounting Rate of Return is 16.92%.

Worked example 2

Project Alpha requires an initial investment of $500,000. It is expected to generate the following net cash inflows over four years: Year 1: $150,000 Year 2: $200,000 Year 3: $250,000 Year 4: $100,000 The company's cost of capital is 10%. The relevant discount factors are: Year 1: 0.909, Year 2: 0.826, Year 3: 0.751, Year 4: 0.683.

Calculate the Net Present Value (NPV) of Project Alpha and advise whether it should be accepted.

Show solution outline

NPV Calculation

To calculate the NPV, we find the present value (PV) of each year's cash inflow and sum them up. Then we subtract the initial investment.

Year	Net Cash Flow ($)	Discount Factor (10%)	Present Value ($)
1	150,000	0.909	136,350
---	---	---	---
2	200,000	0.826	165,200
3	250,000	0.751	187,750
4	100,000	0.683	68,300
Total			557,600

Step 1: Calculate the Total Present Value of Cash Inflows Total PV = $136,350 + $165,200 + $187,750 + $68,300 = $557,600

Step 2: Calculate the Net Present Value $\text{NPV} = \text{Total PV of Inflows} - \text{Initial Investment}$ $\text{NPV} = \text{\textdollar}557,600 - \text{\textdollar}500,000 = \text{\textdollar}57,600$

Final Answer & Advice: The Net Present Value (NPV) of Project Alpha is $57,600. Since the NPV is positive, the project is expected to generate a return greater than the company's required rate of return of 10%. Therefore, based on the NPV rule, the project should be accepted.

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