Edexcel A-Level Accounting: Project appraisal (YAC11) – Revision Notes

These notes assume you have worked through the project appraisal study guide, which explains each method from scratch with a single running example.

These notes condense topic 2.6, Project appraisal (outcomes 2.6.1 and 2.6.2), of the Pearson Edexcel International Advanced Subsidiary/Advanced Level in Accounting specification (XAC11/YAC11), Issue 2, September 2018. Being part of Unit 2 (Corporate and Management Accounting), the content is Unit 2 (A2) only, and the specification lists Unit 2 as available in January, June and October. Every business and figure here is made up.

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The six methods at a glance

Outcome	Method	Discounted?	Works with	Accept when
2.6.1	Net present value (NPV)	Yes	Cash flows	NPV > 0
2.6.1	Weighted average cost of capital (WACC)	Gives the rate	Finance costs	(Used as the discount rate and IRR benchmark)
2.6.1	Profitability index (PI)	Yes	Cash flows	PI > 1
2.6.1	Internal rate of return (IRR)	Yes	Cash flows	IRR > WACC
2.6.2	Average (accounting) rate of return (ARR)	No	Profit	ARR > target return
2.6.2	Payback period	No	Cash flows	Payback ≤ maximum set by the business

Key definitions

• Net cash flow: for a single year, the project’s extra cash coming in less its extra cash going out.
• Time value of money: money received sooner is worth more, because it can be reinvested, is not eroded by inflation and carries less risk.
• Discount factor: the multiplier that turns a future amount into a present value, 1 ÷ (1 + r)ⁿ.
• Present value: what a future cash flow is worth at year 0.
• Net present value: total present value of all the project’s cash flows, including the year 0 outlay.
• Cost of capital: the return required by those who provide the business’s finance.
• WACC: the average cost of all sources of long-term finance, each weighted by its share.
• Profitability index: present value of future inflows per £1 of initial investment.
• Internal rate of return: the discount rate that makes NPV zero.
• ARR: average annual profit as a percentage of the investment.
• Payback period: time taken for net cash inflows to recover the initial outlay.

Formulae

Measure	Formula
Discount factor	1 ÷ (1 + r)ⁿ
Present value	net cash flow × discount factor
NPV	total PV of inflows − initial outlay
WACC	Σ (source ÷ total finance × cost of source)
PI	PV of future inflows ÷ initial investment
IRR (interpolation)	L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L)
Average annual profit	(total net cash inflows − total depreciation) ÷ years
ARR	average annual profit ÷ investment × 100
Average investment	(initial cost + residual value) ÷ 2
Payback, equal flows	initial outlay ÷ annual net cash inflow
Payback, part year	amount still to recover ÷ that year’s inflow × 12 months

If a question gives discount factors, copy them exactly as printed. If it does not, calculate them from the formula.

Method in steps

NPV

1. Lay out years 0 to n with net cash flows; put the residual value into the last year.
2. Multiply each year’s cash flow by its factor; year 0 uses 1.000.
3. Total the present values. Label the result NPV and say positive or negative.
4. Decide: accept if positive.

WACC

1. Total the finance.
2. Find each source’s proportion of the total.
3. Multiply each proportion by that source’s cost.
4. Add the weighted costs.

IRR

1. Find a rate with a positive NPV (L) and a rate with a negative NPV (H).
2. Put both NPVs into the interpolation formula; with NPV at H negative, the denominator is the two sizes added.
3. Compare the answer with WACC.

ARR

1. Total depreciation = cost − residual value.
2. Total profit = total net cash inflows (excluding the residual) − total depreciation.
3. Divide by the number of years.
4. Divide by initial or average investment, × 100. State the base.

Payback

1. Cumulative cash flow column.
2. Find the last full year with a negative cumulative balance.
3. Part year = balance still to recover ÷ next year’s inflow × 12.

Worked reminder: equal annual flows

Ketterick Laundry Ltd could buy a tunnel washer for £90,000 with net cash inflows of £25,000 a year for 5 years and no residual value. Its cost of capital is 12%.

• Payback: 90,000 ÷ 25,000 = 3.6 years; 0.6 × 12 = 7.2 months, so 3 years 7 months.
• NPV: with equal flows you can add the factors first. 0.893 + 0.797 + 0.712 + 0.636 + 0.567 = 3.605; 25,000 × 3.605 = 90,125; NPV = 90,125 − 90,000 = £125 positive.
• PI: 90,125 ÷ 90,000 = 1.00 (1.0014). Barely above 1.
• IRR: NPV is only just positive at 12%, so the IRR is only just above 12%.
• ARR: depreciation 90,000 ÷ 5 = £18,000 a year; profit 25,000 − 18,000 = £7,000 a year. On initial investment 7,000 ÷ 90,000 = 7.8%; on average investment (90,000 + 0) ÷ 2 = 45,000, 7,000 ÷ 45,000 = 15.6%.

A tiny NPV like this means the decision rests on how reliable the forecasts are. That is where non-financial and risk points come in.

Must-know distinctions

• Cash flow vs profit: NPV, PI, IRR and payback use cash; ARR uses profit, so only ARR charges depreciation.
• Discounted vs non-discounted: the four 2.6.1 methods allow for the time value of money; ARR and payback (2.6.2) do not.
• NPV vs PI: NPV shows the size of the gain in pounds; PI shows the gain per pound invested and ranks projects when capital is short.
• NPV vs IRR: NPV is an amount at a chosen rate; IRR is the break-even rate. When they rank mutually exclusive projects differently, NPV is preferred.
• WACC vs IRR: WACC is what finance costs the business; IRR is what the project earns. Accept when IRR is above WACC.
• Initial vs average investment in ARR: the average base gives a higher percentage for the same project.
• Payback vs NPV: payback measures speed and liquidity; NPV measures value created.

Evaluating a project (AO4)

A recommendation needs financial evidence and judgement. Useful points:

• size and sign of NPV, and how far IRR exceeds WACC;
• how quickly payback happens if cash is tight;
• reliability of forecasts, especially in later years;
• non-financial factors: staff, local community, environment, quality, supplier reliability, brand.

Finish with a clear decision and one reason that outweighs the others.

Quick self-test

1. Calculate the discount factor for year 2 at 8%, to 3 decimal places.
2. An outlay of £72,000 brings equal net cash inflows of £16,000 a year. Calculate the payback period.
3. Equity provides 60% of finance at a cost of 11% and loans 40% at 6%. Calculate WACC.
4. PV of future inflows is £138,000 and the outlay is £120,000. Calculate the PI.
5. An outlay of £50,000 brings £30,000 at the end of each of the next 2 years. Using factors 0.926 and 0.857, calculate NPV.
6. NPV is +£6,000 at 12% and −£2,000 at 20%. Estimate the IRR.
7. Average annual profit is £9,000, cost £60,000, residual value £12,000. Calculate ARR on initial and on average investment.
8. A project’s NPV at WACC is negative. Is its IRR above or below WACC?
9. Which method charges depreciation?
10. Name one cash flow that payback ignores.

Answers

1. 1 ÷ 1.08² = 0.857.
2. 72,000 ÷ 16,000 = 4.5 years (4 years 6 months).
3. 0.6 × 11% + 0.4 × 6% = 6.6% + 2.4% = 9.0%.
4. 138,000 ÷ 120,000 = 1.15.
5. 27,780 + 25,710 = 53,490; 53,490 − 50,000 = +£3,490.
6. 12 + [6,000 ÷ (6,000 + 2,000)] × 8 = 12 + 6 = 18%.
7. Initial: 9,000 ÷ 60,000 = 15%. Average investment (60,000 + 12,000) ÷ 2 = 36,000; 9,000 ÷ 36,000 = 25%.
8. Below WACC.
9. ARR, because it uses profit.
10. Any cash flow after the payback point, for example a residual value in the final year.

Where marks are usually lost

• Leaving the residual value out of the final year in NPV, or putting it into ARR profit as well as into average investment.
• Applying a discount factor to year 0.
• Averaging the costs of finance without weighting them.
• Rounding present values too early so the NPV total does not match the column.
• Writing “NPV = 34,000” without saying positive, or without a decision.
• Forgetting that the IRR denominator adds the sizes of the two NPVs.
• Not stating whether ARR is on initial or average investment.
• Giving payback as “3.4 years” when months are asked for, or converting 0.4 years to 4 months.
• A recommendation that repeats figures but never makes a decision.

Official syllabus

Pearson Edexcel International Advanced Subsidiary/Advanced Level in Accounting (XAC11/YAC11) specification, Issue 2, September 2018, first teaching September 2015 (Pearson Education Limited): Unit 2, topic 2.6 Project appraisal, outcomes 2.6.1 and 2.6.2.