ACCA FM Investment Appraisal: NPV, IRR and WACC Explained

ACCA FM investment appraisal comes down to three tools you will use again and again: net present value (NPV), internal rate of return (IRR), and the weighted average cost of capital (WACC). NPV tells you whether a project adds value in today’s money. IRR tells you the project’s own percentage return. WACC tells you what discount rate to use, because it is what the company pays for its funding. In short, accept a project when its NPV is positive, when its IRR beats the cost of capital, and when you have discounted at the WACC.

ACCA FM investment appraisal: what NPV really measures

Net present value is the present value of all future cash inflows minus the initial investment. A positive NPV means the project earns more than its cost of funding and increases shareholder wealth. A negative NPV destroys value, so the project should be rejected.

How discounting turns future cash into today’s money

The logic is simple. Money received in the future is worth less than money received today, because money today can be invested and earn a return. Discounting converts every future cash flow into today’s money using a discount factor. The formula for a discount factor in year t at rate r is 1 divided by (1 + r) raised to the power t. Finally, add up the present values of the inflows, subtract the initial investment, and the result is the NPV.

The worked example, step by step

Work through this example slowly, because every step here is a step examiners expect to see. A company is considering a project that needs an initial investment of $120,000. It will generate cash inflows of $40,000 in Year 1, $50,000 in Year 2, $50,000 in Year 3, and $30,000 in Year 4. The company’s cost of capital is 10%. Using discount factors to three decimal places, as in the exam tables, the calculation is as follows.

Year	Cash flow ($)	Discount factor at 10%	Present value ($)
0	(120,000)	1.000	(120,000)
1	40,000	0.909	36,360
2	50,000	0.826	41,300
3	50,000	0.751	37,550
4	30,000	0.683	20,490
Net present value			15,700

Reading the result: accept or reject

The present value of the inflows is $135,700. Subtract the $120,000 investment and the NPV is $15,700. As a result, because the NPV is positive, the project should be accepted on NPV grounds. Note the rounding: discount factors taken to three decimal places give $15,700, while unrounded factors give $15,742. Either answer earns the method marks if your working is clear, but in the exam you should use the tables provided and show your factors, so a marker can follow every number.

As a quick cross-check on the same project, the payback period is 2.6 years. Cumulative inflows reach $90,000 by the end of Year 2, leaving $30,000 of the $120,000 investment to recover in Year 3, when the inflow is $50,000. So payback is 2 years plus 30,000 divided by 50,000, which is 2.6 years. However, payback is useful as a liquidity check, but it is not a value measure: it ignores all cash flows after payback and ignores the time value of money. Never let a short payback overrule a negative NPV. If you need a refresher on discounting itself before going further, the time value of money notes on this site walk through present value and annuities step by step: CFA Quantitative Methods: Time Value of Money and Hypothesis Testing Explained.

ACCA FM investment appraisal: finding IRR by interpolation

The internal rate of return is the discount rate at which a project’s NPV equals exactly zero. In other words, it is the project’s own break-even rate of return. For example, the decision rule is straightforward: accept the project if its IRR is greater than the cost of capital, and reject it if the IRR is lower. If the IRR equals the cost of capital, the project breaks even in present value terms and the decision is marginal.

How interpolation brackets the answer

IRR cannot usually be solved directly, so the exam method is interpolation: find two discount rates that bracket zero NPV, one giving a positive NPV and one giving a negative NPV, then estimate where NPV crosses zero. Take the same project as before. At 15%, the NPV is positive at $2,660. At 17%, the NPV is negative at $2,030. The interpolation needs a closer bracket, so try 16% as well.

Discount rate	Present value of inflows ($)	NPV ($)
15%	122,660	2,660
16%	120,240	240
17%	117,970	(2,030)

In this case, using the two closest rates, 16% and 17%, the interpolation formula is: IRR equals the lower rate plus the positive NPV divided by the sum of the two NPVs ignoring signs, multiplied by the gap between the rates. That gives 16% plus 240 divided by 2,270, multiplied by 1%, which is 16% plus 0.11%, or 16.1%. The IRR of about 16.1% is well above the 10% cost of capital, so the IRR rule agrees with the NPV rule here: accept the project.

Two warnings to carry into the exam

Two warnings belong with every IRR answer. First of all, interpolation is an estimate, not an exact solution, because NPV does not fall in a straight line between two rates. Using rates close together, as above, keeps the error small. Second, IRR can mislead when cash flows change sign more than once, for example a project with a large closure cost at the end. Such non-conventional cash flows can produce two IRRs or none at all, and in that case NPV is the reliable rule. IRR also assumes intermediate cash flows are reinvested at the IRR itself, which is often unrealistic, while NPV assumes reinvestment at the cost of capital, which is the more defensible assumption.

ACCA FM investment appraisal: WACC and the discount rate

Every NPV in this post so far used a given discount rate of 10%. In practice, that rate is the company’s weighted average cost of capital, the average of what the company pays for each source of long-term finance, weighted by market value. The formula is the weight of equity multiplied by the cost of equity, plus the weight of debt multiplied by the after-tax cost of debt.

Cost of equity from the capital asset pricing model

Start with the cost of equity. The capital asset pricing model gives it as the risk-free rate plus beta multiplied by the market risk premium, where the market risk premium is the expected market return minus the risk-free rate. To see how this works, suppose the risk-free rate is 4%, the company’s equity beta is 1.2, and the expected market return is 11%. The market risk premium is 11% minus 4%, which is 7%. The cost of equity is therefore 4% plus 1.2 multiplied by 7%, which is 4% plus 8.4%, or 12.4%. A beta above 1.0 means the share moves more than the market, so investors demand a return above the market average, and the model captures exactly that.

Cost of debt after tax, weighted by market value

Next, the cost of debt. Interest is tax deductible, so the relevant cost is after tax. If the pre-tax cost of debt is 8% and the tax rate is 25%, the after-tax cost of debt is 8% multiplied by 1 minus 0.25, which is 6.0%. Now weight the two sources by market value, not book value, because market values show what the finance is actually worth today. Suppose equity has a market value of $600,000 and debt has a market value of $400,000, giving total capital of $1,000,000. Equity is 60% of the total and debt is 40%.

Source	Market value ($)	Weight	Cost after tax	Weighted cost
Equity	600,000	60%	12.4%	7.44%
Debt	400,000	40%	6.0%	2.40%
WACC				9.84%

Using the WACC for projects of average risk

The WACC is 9.84%. That is the discount rate the company should use for a project of average risk, meaning a project with the same risk as the company’s existing operations. A project that is riskier than the company’s normal business needs a higher, risk-adjusted discount rate, and a safer project can use a lower one. Using the WACC blindly for a project in a completely different risk class is one of the classic FM errors.

NPV versus IRR: when they disagree

Similarly, for a single standalone project, NPV and IRR usually agree, as they did in the example above. For mutually exclusive projects, where accepting one means rejecting the other, they can disagree, and NPV wins. Three causes explain most conflicts.

• Scale. A small project can show a high IRR on a small investment while a larger project creates far more value in cash terms. NPV measures value in dollars, so it ranks the larger value creator first.
• Timing. A project with early cash flows can show a strong IRR even when a later-heavy project has the higher NPV at the company’s cost of capital. The ranking flips as the discount rate changes, which is why the NPV profiles cross.
• Reinvestment assumption. IRR assumes cash flows are reinvested at the IRR itself, which flatters high-IRR projects. NPV assumes reinvestment at the cost of capital, which is what the company can actually earn on average.

Therefore, the exam tip follows directly: when NPV and IRR rank two mutually exclusive projects differently, recommend the project with the higher NPV and explain the conflict in one sentence, naming its cause. A recommendation without the explanation loses the discussion marks.

Exam pitfalls that cost marks

• Using profit instead of cash flow. Appraisal uses incremental cash flows, not accounting profit. Add back non-cash items such as depreciation, and strip out allocated overheads that will be incurred whether or not the project goes ahead.
• Counting sunk costs. Money already spent, such as past market research, is irrelevant to the decision and must be excluded, however large it was.
• Forgetting working capital. An increase in inventory and receivables at the start of a project is a cash outflow, and its release at the end is a cash inflow. Missing either leg distorts the NPV.
• Mixing financing flows into project cash flows. Loan drawdowns, interest payments, and dividends are financing, not project operating flows. They are already reflected in the discount rate through the WACC, so including them again double counts.
• Ignoring tax. Tax on operating cash flows, and tax relief on capital allowances, both belong in the cash flows, with the correct timing. The discount rate must then be consistent: a nominal rate discounts nominal, inflation-inclusive cash flows, and a real rate discounts real cash flows. Mixing the two is a common error.
• Discounting with book values. WACC weights must use market values. Book values are historic accounting numbers and will give the wrong discount rate.
• Rounding too early. Keep full precision through the working and round only the final NPV and IRR. Early rounding is how a correct method ends with a wrong answer.

Quick revision checklist

Before you close this topic, make sure you can do each of the following without looking back: state the NPV decision rule and compute an NPV from a discount table; find an IRR by interpolation between two bracketing rates; compute a cost of equity with the capital asset pricing model; convert a pre-tax cost of debt to an after-tax cost; weight equity and debt by market value to get the WACC; explain why NPV outranks IRR for mutually exclusive projects; and list the cash flows that must be excluded from a project appraisal. On the other hand, if any one of those is shaky, rework the examples above with the figures covered, then uncover them and try again. That active rework is what turns a read-through into exam-ready knowledge.