Advanced Financial Management · Discounted cash flow techniques

Adjusted Present Value (APV) for ACCA AFM

Updated 11 October 2026 · Fact-checked

Adjusted present value (APV) values a project in two parts. First, find the base-case NPV as if the project were all-equity financed, discounting at the ungeared cost of equity. Then add the present value of financing side effects: tax shields, subsidised loans and issue costs. Accept the project if APV is positive.

Understand Adjusted Present Value (APV)

A normal NPV discounts cash flows at a WACC. That WACC assumes the project has the same business risk and the same gearing as the company. When a project changes the company's financing, this assumption fails. APV avoids it by splitting the value into two parts.

Part one is the base-case NPV. Pretend the project is financed wholly by equity. Discount the project's operating cash flows at the ungeared cost of equity (Keu), which reflects business risk only. If the project's risk differs from the company's, you usually take a proxy company's equity beta and ungear it.

Part two is the financing side effects. Debt brings an interest tax shield, because interest is tax deductible. A subsidised loan (for example, a government loan below market rate) creates a saving. Issue costs reduce value. You value each one separately and add or subtract it.

The logic is value additivity: the project is worth what it is worth with no debt, plus or minus what the financing adds. This is why APV suits projects with a specific financing package, changing debt levels over time, or unusual funding. It is also easy to extend to overseas projects.

The main judgement is the discount rate for each piece. Operating cash flows use Keu. Tax shields and subsidies are usually discounted at the pre-tax cost of debt, because their risk is like that of the debt. Some questions tell you to use the risk-free rate. Follow the question.

Key rules to remember

APV: APV = Base-case NPV + PV of financing side effects; Accept the project if APV > 0. Side effects can be negative, such as issue costs.
Ungearing an equity beta: βa = βe × Ve ÷ [Ve + Vd(1 − t)]; Assumes the debt beta is zero and debt is permanent. If the question gives a debt beta, use the extended formula from the formula sheet approach: βa = [βe × Ve + βd × Vd(1 − t)] ÷ [Ve + Vd(1 − t)].
Ungeared cost of equity: Keu = Rf + βa × (Rm − Rf); Use βa from the proxy company. Use this rate for the base-case cash flows.
Annual tax shield on interest: Tax shield = Debt × interest rate × tax rate; Discount at the pre-tax cost of debt unless the question says otherwise. Match the shield's life to the debt's life.
Subsidised loan benefit: Annual benefit = Loan × (market rate − subsidised rate) × (1 − t); Discount at the market pre-tax cost of debt. The tax shield on the actual interest paid is a separate item.
Issue costs: Net issue cost = Issue cost × (1 − t) if tax-deductible; Issue costs are usually based on the gross amount raised. Check whether tax relief is allowed. Use the cost as stated if the question gives no relief.

How to solve Adjusted Present Value (APV) questions

Use this order for any APV question. Keep the base case and each financing effect in separate lines so you can pick up marks even if one part is wrong.

1Read the requirement and note the debt amount, interest rate, tax rate, loan life and any issue costs or subsidies.
2Find the ungeared cost of equity. If a proxy beta is given, ungear it with βa = βe × Ve ÷ [Ve + Vd(1 − t)], then use CAPM to get Keu.
3Calculate the project's after-tax operating cash flows, including tax on profits, capital allowances and working capital, as in a normal NPV.
4Discount those cash flows at Keu to get the base-case NPV. Show the discount factors.
5Calculate each financing side effect separately: tax shield on interest, subsidised loan benefit, and issue costs (after tax relief if allowed).
6Discount each side effect at the stated rate, usually the pre-tax cost of debt, over the correct number of years.
7Add all items: APV = base-case NPV + PV of side effects. Give a clear recommendation.
8Comment on assumptions: debt level and its link to debt capacity, tax shield being usable only if there are enough taxable profits, and the rate chosen for the shield.

Quickest way: Four-line APV layout

When to use it: Use this when time is short and the question has a single financing package.

Line 1: Base-case NPV at Keu. Compute Keu first and write it at the top of your page.
Line 2: PV of tax shield = annual shield × annuity factor at pre-tax Kd.
Line 3: PV of subsidy, if any, or issue costs as a negative figure.
Line 4: Total them for APV and write one sentence of advice. Spend leftover time on assumptions.

Common mistakes in Adjusted Present Value (APV)

Discounting the operating cash flows at WACC instead of Keu.
Students are used to NPV and reach for WACC out of habit.
Fix: In APV the base case is all-equity. Always discount operating cash flows at the ungeared cost of equity.
Forgetting to ungear the proxy beta, or ungearing it with the wrong debt value.
The beta given looks ready to use, and students mix up book and market values.
Fix: If the beta comes from a geared company, ungear it using market values of equity and debt, with Vd(1 − t) in the denominator.
Calculating the tax shield on the whole debt balance for the wrong number of years.
Students ignore the loan term or use the project life by default.
Fix: Count the shield only for years in which the debt exists and the interest is paid. Check whether debt is repaid early.
Mistaking the subsidised loan benefit for the full interest saving without tax adjustment.
Students forget that the saving is taxable, or omit the tax shield on the actual interest.
Fix: Benefit = loan × rate difference × (1 − t). Then add the tax shield on the actual (subsidised) interest as a separate line if the question includes tax.
Treating issue costs as a cash flow in the base case, or ignoring them.
Issue costs feel like a project cost rather than a financing cost.
Fix: Put issue costs in the financing section. Base them on the gross amount raised and deduct them from APV, with tax relief only if the question allows it.
Stopping at the number without a recommendation or comment.
Students run out of time or forget the professional skills marks.
Fix: State accept or reject based on APV, say which part drives the result, and mention one or two limits of the method.

Worked examples

Example 1

A company is considering a project costing $2,000,000 now. It will produce after-tax operating cash flows of $700,000 a year for 4 years. The ungeared cost of equity is 10%. The project will be partly financed by a $1,000,000 four-year loan at 6% interest, which is also the company's pre-tax cost of debt. Tax is 25%. Issue costs on the loan are $30,000, with no tax relief. Calculate the APV. Annuity factors for 4 years: 10% = 3.170; 6% = 3.465.

Show the solution

Base-case NPV: PV of cash flows = 700,000 × 3.170 = $2,219,000.
Base-case NPV = 2,219,000 − 2,000,000 = $219,000.
Annual tax shield = 1,000,000 × 6% × 25% = $15,000.
PV of tax shield = 15,000 × 3.465 = $51,975, discounted at 6%.
Issue costs = $30,000 (no tax relief), so deduct 30,000.
APV = 219,000 + 51,975 − 30,000 = $240,975.

Answer: APV = $240,975. It is positive, so the project should be accepted. Most of the value comes from the operating cash flows. The tax shield adds $51,975 and the issue costs reduce value by $30,000.

Example 2

A company wants to value a project in a new industry. A proxy company has an equity beta of 1.2 and a debt-to-equity ratio of 0.4 (market values). Tax is 20% and the debt beta is zero. The risk-free rate is 4% and the market risk premium (Rm − Rf) is 6%. The project will be funded partly by a $500,000 five-year loan at 3% fixed, where the market pre-tax rate for similar debt is 7%. Calculate (a) the ungeared cost of equity and (b) the present value of the subsidised loan benefit, discounting at 7%. Annuity factor, 5 years at 7% = 4.100.

Show the solution

(a) Ungear: βa = 1.2 ÷ [1 + 0.4 × (1 − 0.20)] = 1.2 ÷ 1.32 = 0.909.
Keu = 4% + 0.909 × 6% = 4% + 5.45% = 9.45%.
(b) Annual benefit before tax = 500,000 × (7% − 3%) = $20,000.
After tax: 20,000 × (1 − 0.20) = $16,000 a year.
PV = 16,000 × 4.100 = $65,600.

Answer: (a) The ungeared cost of equity is about 9.45%. (b) The subsidised loan is worth $65,600 in present value terms. Add this to the base-case NPV, along with the tax shield on the actual interest paid at 3%, to reach the APV.

Exam tips

Show Keu on its own line with the beta workings. Markers give marks for each step, even if the final number is wrong.
Label each financing effect clearly. Section A cases often have several, such as a tax shield, a subsidy and issue costs.
Use the discount rate the question specifies for the tax shield. If it is not stated, use the pre-tax cost of debt and say so.
Always finish with a recommendation and one or two assumptions or limits. This earns professional skills marks for analysis and commercial judgement.
Know when APV is better than NPV: financing changes the capital structure, the subsidy is project-specific, or debt levels change over time.

Practice questions from Discounted cash flow techniques

Adjusted Present Value (APV) 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): frequently asked questions

What is the difference between APV and NPV?

NPV discounts all cash flows at one WACC, which bakes the financing into the rate. APV values the project as if all-equity financed, then adds the financing effects separately. APV is more flexible when gearing or financing differs from the company's usual pattern.

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

The usual choice is the pre-tax cost of debt, because the shield is about as risky as the debt itself. Some questions say to use the risk-free rate. Follow the instruction in the question and state your choice if none is given.

How do I ungear a beta in ACCA AFM?

Use βa = βe × Ve ÷ [Ve + Vd(1 − t)] with market values and a zero debt beta. Then put βa into CAPM to find the ungeared cost of equity. If a debt beta is given, include it in the formula.

How are issue costs treated in APV?

They are a financing side effect, so they are deducted from the base-case NPV. They are normally based on the gross amount raised. If the question says they are tax-deductible, deduct the after-tax amount.

When is APV better than NPV?

APV suits projects with a specific financing package, such as subsidised loans, changing debt levels, or issue costs. It also suits projects whose risk is different from the company's normal business. NPV at WACC is acceptable when gearing and risk stay the same.