Advanced Financial Management · Impact of financing on investment decisions and adjusted present values

Adjusted Present Value (APV) Method for ACCA AFM

Updated 11 October 2026 · Fact-checked

APV values a project in two parts. First, discount the base-case cash flows as if the project were all-equity financed, using the ungeared cost of equity. Then add the present value of financing side effects, mainly the interest tax shield, and subtract issue costs. If APV is positive, accept the project.

Understand Adjusted Present Value (APV) Method

Normal NPV uses one discount rate, usually a WACC, which blends the cost of debt and equity. That rate bakes the financing mix into the discount rate. It works only if the project has the same business risk and the same gearing as the firm. In real questions, the project often has different risk, or it is funded in a special way.

APV separates the two questions. Question one: is the project worth doing on its own, ignoring how it is paid for? Question two: does the way we finance it add or destroy value?

For question one, you discount the base-case cash flows at the ungeared cost of equity. This is the return shareholders would need if the firm had no debt and the project carried this business risk. The result is the base-case NPV.

For question two, you list each financing side effect and value it separately. The main ones are the tax shield on debt interest, issue costs, and the benefit of subsidised loans. You add the present values to the base-case NPV.

APV is most useful when gearing changes because of the project, when debt is raised for the project alone, or when side effects are unusual. The price is that you must estimate the debt level and each side effect with care.

Key rules to remember

APV: APV = Base-case NPV + PV of financing side effects; Side effects include the tax shield, subsidised loan benefit and, as a negative, issue costs. Accept if APV > 0.
Asset (ungeared) beta: βa = βe × E ÷ [E + D(1 − T)] (debt beta = 0); Use market values of E and D. If a debt beta is given, use the full weighted version: βa = βe × E ÷ [E + D(1 − T)] + βd × D(1 − T) ÷ [E + D(1 − T)].
Ungeared cost of equity (CAPM): Keu = Rf + βa × (Rm − Rf); This is the base-case discount rate.
Ungeared cost of equity (Modigliani and Miller with tax): Keg = Keu + (Keu − Kd)(1 − T) × D ÷ E; Rearrange to find Keu from an observed geared cost of equity. Check which form your formula sheet gives.
Annual tax shield: Tax shield = Interest × T; Only count interest on debt the project supports, and only while the tax relief is available.
Tax shield on permanent debt: PV of tax shield = D × T; Valid when debt is perpetual and discounted at the pre-tax cost of debt.
Discount rate for tax shield: Use the pre-tax cost of debt (Kd); The tax shield has the risk of the debt. State this assumption in your answer.

How to solve Adjusted Present Value (APV) Method questions

Use this order for any APV question. Keep base case and financing in separate working blocks so a marker can follow each part.

1Identify the base-case cash flows. Include only relevant, incremental, after-tax operating flows and any working capital. Leave out interest and financing flows.
2Find the ungeared cost of equity. If you are given a proxy firm's equity beta, ungear it with the asset beta formula, then use CAPM. If a Keu is given, use it.
3Discount the base-case cash flows at Keu. Subtract the initial investment to get the base-case NPV.
4Work out how much debt the project supports. Use the amount stated, or debt capacity such as a percentage of project value or of the asset cost.
5Calculate the annual interest and the tax saving (interest × T). Discount at the pre-tax cost of debt for the period the debt is outstanding.
6Deal with other side effects: issue costs (subtract, and note whether they are tax deductible), subsidised loan benefit (interest saved after tax, discounted at the market Kd), and any other financing item in the question.
7Add everything to get the APV. State the decision and say which assumptions drive the answer.
8Add a short comment: the sensitivity of APV to the debt assumption, and how much of the value comes from financing rather than operations.

Quickest way: Three-line APV in exam time

When to use it: Use this when the question gives you a clear debt amount and rate, and you need a fast, reliable layout for a 10 to 15 mark requirement.

Write three headings: Base-case NPV, Financing effects, APV. Fill in the base-case block first, because that earns the most marks.
For a fixed term, use annuity factors at Keu for operating flows and at Kd for the tax shield. For permanent debt, shortcut the shield to D × T.
Put issue costs at time 0 as a negative. Then add the three lines and write one sentence: accept or reject, and why.

Common mistakes in Adjusted Present Value (APV) Method

Discounting base-case cash flows at WACC instead of the ungeared cost of equity.
Students are used to NPV with WACC and reach for it by habit.
Fix: Remember the first stage has no financing in it. Use Keu only. WACC does not appear in APV.
Forgetting to ungear the proxy firm's beta, or ungearing it without the (1 − T) term.
The equity beta is given, so students plug it straight into CAPM.
Fix: Always ask whether the beta reflects the proxy firm's gearing. If so, convert it to βa with E ÷ [E + D(1 − T)] before applying CAPM.
Including interest payments in the base-case cash flows.
Students treat the debt as part of the project's cash flows.
Fix: Keep interest out of the base case. Its only role is to create the tax shield in the financing block.
Discounting the tax shield at Keu or at the after-tax cost of debt.
Students are unsure what risk the shield carries.
Fix: Use the pre-tax cost of debt unless the question says otherwise, and state it as an assumption.
Applying the tax shield to the wrong debt amount, such as all firm debt rather than the debt raised for the project.
The question mentions the firm's capital structure, and students mix it up with the project's financing.
Fix: Underline the debt the project actually supports. Compute interest and tax relief on that amount only.
Treating issue costs as an after-tax figure, or adding them instead of subtracting them.
Students rush the signs and skip the tax relief check.
Fix: Issue costs reduce value, so subtract. Apply tax relief only if the question says the costs are deductible.

Worked examples

Example 1

Kora plc is considering a 4-year project costing $10m now. It will give after-tax operating cash flows of $3.5m at the end of each of years 1 to 4. The ungeared cost of equity is 10%. The project will be financed by $4m of 6% debt, outstanding for the four years and then repaid. The tax rate is 25%. Issue costs on the debt are 2% of the amount raised, are paid at time 0 and are not tax deductible. Calculate the APV and advise whether to accept.

Show the solution

Base case: the 4-year annuity factor at 10% is 3.170. PV of operating flows = 3.5 × 3.170 = $11.095m.
Base-case NPV = 11.095 − 10.000 = $1.095m.
Annual interest = 4 × 6% = $0.24m. Annual tax saving = 0.24 × 25% = $0.06m.
Discount the tax shield at the pre-tax cost of debt of 6%. The 4-year annuity factor at 6% is 3.465. PV = 0.06 × 3.465 = $0.208m.
Issue costs = 4 × 2% = $0.08m, at time 0, no tax relief.
APV = 1.095 + 0.208 − 0.080 = $1.223m.

Answer: APV is about $1.22m, which is positive, so accept. The project is worthwhile on its own (base-case NPV $1.095m), and the financing adds a small net benefit of about $0.13m after issue costs.

Example 2

Zeta Ltd is appraising a project costing $6m. It will produce after-tax operating cash flows of $0.63m a year in perpetuity. A listed proxy company in the same business has an equity beta of 1.25 and a debt-to-equity ratio of 1:3 by market value. Assume its debt beta is zero. The tax rate is 25%, the risk-free rate is 4% and the market return is 9%. Zeta will raise permanent debt of $3m at 5% pre-tax, with issue costs of 1.5% of the debt, not tax deductible. Calculate the APV.

Show the solution

Ungear the proxy beta. With D ÷ E = 1 ÷ 3, take E = 3 and D = 1. βa = 1.25 × 3 ÷ [3 + 1 × (1 − 0.25)] = 1.25 × 3 ÷ 3.75 = 1.0.
Ungeared cost of equity = 4% + 1.0 × (9% − 4%) = 9%.
PV of operating flows in perpetuity = 0.63 ÷ 0.09 = $7.0m.
Base-case NPV = 7.0 − 6.0 = $1.0m.
Permanent debt, so PV of tax shield = D × T = 3 × 25% = $0.75m. Check: interest 3 × 5% = 0.15, tax saving 0.0375 a year, divided by 5% = 0.75.
Issue costs = 3 × 1.5% = $0.045m.
APV = 1.0 + 0.75 − 0.045 = $1.705m.

Answer: APV is $1.705m, which is positive, so accept. About 44% of the value comes from the tax shield, so the decision is reasonably safe on operating grounds but the gain is boosted by the permanent debt assumption.

Exam tips

Show the base-case NPV and the financing effects as separate sub-totals. Marks are given for each, so a wrong tax shield will not cost you the base case.
State your assumptions in a line each: debt amount, discount rate for the tax shield, and tax deductibility of issue costs. Examiners reward clear, sensible assumptions.
In the discussion part, compare APV with NPV using WACC. Say APV copes better with changing gearing and special financing, but needs reliable estimates of debt and side effects.
Use the professional skills marks. Give a clear recommendation, say which numbers it depends on, and comment on the risk that the tax shield may not be fully usable if profits are too low.
Check the time frame of debt. If debt is repaid at the end of year 4, the shield stops at year 4. If it is permanent, use D × T.

Practice questions from Impact of financing on investment decisions and adjusted present values

Adjusted Present Value (APV) Method in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Adjusted Present Value (APV) Method: frequently asked questions

What is the difference between APV and NPV in ACCA AFM?

Standard NPV discounts all cash flows at one rate, usually WACC, which already includes the effect of debt. APV discounts the base-case flows at the ungeared cost of equity and then adds the value of financing side effects separately. APV is better when gearing or financing differs from the firm's usual pattern.

Which discount rate do I use for the tax shield in APV?

Usually the pre-tax cost of debt, because the tax saving is about as risky as the debt interest that creates it. Some questions specify a different rate, so always follow the question. State your choice as an assumption.

How do I find the ungeared cost of equity?

Take the equity beta of a similar company, convert it to an asset beta with βa = βe × E ÷ [E + D(1 − T)] when the debt beta is zero, and then use CAPM. If the question gives a geared cost of equity instead, use the Modigliani and Miller with tax relationship to find Keu.

Are issue costs tax deductible in APV questions?

Only if the question says so. Without that information, treat issue costs as a time-0 outflow with no tax relief and say that you have done so. If they are deductible, reduce the cost by the tax saving and show the timing.