A company wants to build a plant in a new industry and pay for it with a mix of new shares and a bond. Its gearing will change, its business risk will change, and it will pay issue costs. Adjusting the WACC for all of that is awkward and rests on shaky assumptions.
The adjusted present value (APV) method takes a simpler route: value the project as if it were all-equity, then add or subtract the effects of the financing one by one.
This topic covers the APV method, its decision rule, the base case NPV using an asset beta and the ungeared cost of equity, the present value of issue costs (including tax relief), the present value of the interest tax shield (including amortising loans), the reasons for preferring APV and the comparison with NPV. The previous topic covered gearing, WACC and betas.
The next covers international valuation standards. Neither the May 2014 nor the November 2014 Pathfinder sets a stand-alone question on APV.
In 30 seconds
APV = base case NPV − PV of other costs + PV of tax relief on interest. Accept if APV is positive. The base case NPV ignores the financing: discount the project’s cash flows at the ungeared cost of equity (CAPM with the asset beta of the industry). Other costs are mainly issue costs: if you need a given amount after costs, gross amount = net ÷ (1 − cost rate).
Discount them at the risk-free rate, net of any tax relief. The tax shield is the tax saved on interest (not on principal), discounted at the pre-tax cost of debt. APV does not need a new WACC, allows for the actual debt terms and shows other financing costs, so it is often preferred when the project changes risk and financing. NPV and APV can give different answers.
Key terms in plain English
| Term | What it means |
|---|---|
| Base case NPV | The NPV if the project were financed entirely by equity |
| Adjusted present value (APV) | Base case NPV plus the value of financing side effects |
| Ungeared cost of equity | The required return of an all-equity company in the same business |
| Issue costs | The costs of raising new equity or debt |
| Interest tax shield | The tax saved because interest is deductible |
| Amortising loan | A loan repaid gradually, each payment part interest and part principal |
Syllabus check
This topic is in syllabus area C (financing decisions). It covers:
- the adjusted present value method of project appraisal;
- the choice between APV and NPV.
CAMA 2020 and project finance
The Companies and Allied Matters Act 2020 (CAMA 2020) is the company law of Nigeria.
| Section | What it says | Link to this topic |
|---|---|---|
| s. 305 | A director must act in good faith in the best interests of the company | Financing side effects should be weighed for the benefit of the company |
| s. 308 | A director must use the care, diligence and skill of a reasonably prudent director | Directors should test each element of a financing plan |
| s. 377(1) and s. 378 | Directors prepare statements that follow IFRS and give a true and fair view | Decisions later affect reported assets, profit and cash |
| s. 385 | The directors’ report covers performance and risk | Major plans and risks are reported to shareholders |
The APV method and its rule
APV suits a project whose business risk and financial risk differ from the company’s current operations, for example a move into a new industry or market with new capital. It is an alternative to a new WACC from the MM formulae or the asset beta formula. Accept if APV is positive.
| Element | Amount |
|---|---|
| Base case NPV | X |
| Less: PV of other costs (mainly issue costs) | (X) |
| Add: PV of tax relief on interest | X |
| APV | X |
Base case NPV
Ignore how the project is financed. Find the asset beta for the industry (ungear a proxy equity beta), use CAPM to get the cost of equity of an ungeared company, and discount the project’s cash flows at it. ICAN’s example: an insurance company considers a transport project. The transport industry has an equity beta of 1.362 at 40 : 60 debt to equity, tax 23%.
Asset beta = 1.362 × 60 ÷ (60 + 40 × 0.77) = 0.90. With a risk-free rate of 5.3% and market return of 8.3%, keU = 5.3% + 0.90 × 3% = 8.0%. Cash flows are −₦600,000 now and ₦250,000 for three years. NPV = −600,000 + 250,000 × 2.577 = +₦44,250.
Other costs: issue costs
If the company needs a sum after paying issue costs, it must raise more: gross = net ÷ (1 − cost rate). The costs are paid out of the proceeds at the start, so their PV is the cost itself, less the PV of any tax relief. Use the risk-free rate unless told otherwise.
ICAN’s example: ₦400,000 net from equity at 5% costs, ₦200,000 net from debt at 2%, risk-free rate 5.3%, tax 23% with relief one year later. Equity gross = 400,000 ÷ 0.95 = ₦421,053 (costs ₦21,053). Debt gross = 200,000 ÷ 0.98 = ₦204,082 (costs ₦4,082). Total costs ≈ ₦25,134. Tax relief = 23% × 25,134 = ₦5,781 a year later, PV ₦5,490. PV of issue costs = 25,134 − 5,490 = ₦19,644.
The interest tax shield
Interest on debt is tax-deductible. Calculate each year’s interest, the tax saved, and discount the savings at the pre-tax cost of debt. If the debt is repaid in full at the end, interest = amount borrowed × rate. If it is an amortising loan, split each payment into interest and principal, because relief is only on interest.
ICAN’s example: ₦204,081 borrowed over three years at 5.3% (annuity factor 2.708). Payment = 204,081 ÷ 2.708 = ₦75,362. Interest: ₦10,816, ₦7,395, ₦3,793. Tax relief at 23% one year in arrears: ₦2,488, ₦1,701, ₦872 in years 2, 3 and 4. PV at 5.3% = ₦4,409.
ICAN’s APV. Taking the three parts together:
- Base case NPV = +₦44,250.
- PV of issue costs = −₦19,644.
- PV of the tax shield = +₦4,409. APV = +₦29,015, so the project is worthwhile on financial grounds.
Why use APV
- It does not need assumptions about the new WACC after the project.
- It uses the actual tax relief on the actual debt and does not assume permanent debt.
- It shows other financing costs such as issue costs.
It is arguably the best way to measure the effect on shareholders’ wealth. NPV and APV may disagree, because they treat the financing differently.
ICAN’s conflict. A ₦9m project funded ₦4.5m equity and ₦4.5m debt, with issue costs of ₦300k, operating cash flows after tax and allowances, equity beta 1.25 and a 9% WACC.
- NPV at 9% = −₦53k: reject.
- APV.
asset beta = 1.25 × 4,500 ÷ 7,650 = 0.735
keU = about 8%.
Base NPV = ₦490k; issue costs −₦300k; tax shield (₦315k interest, 30%, 4 years at 7%) = +₦320k.
APV = +₦510k: accept. - The methods conflict, which is why the financing effects need separate treatment.
The rules in more depth
Why value the project all-equity first
It separates the business risk, which the asset beta captures, from the financing, which is valued separately.
Why the tax shield is discounted at the cost of debt
The tax saving depends on interest payments, which are as certain as the debt, so the debt rate is the suitable rate.
Why issue costs use the risk-free rate
They are known costs paid at the start, so their risk is low.
Why only interest gets tax relief
Repaying principal is not an expense. This is why amortising loans need a split of each payment.
Effect on analysis
Show the three parts separately, state your discount rates and conclude with the sign of the APV.
Worked examples
Example 1: base case. A project costs ₦100m and returns ₦40m a year for four years. The ungeared cost of equity is 12% (annuity factor 3.037).
- PV of inflows.
40 × 3.037 = ₦121.5m. - Base case NPV.
121.5 − 100 = +₦21.5m. - This ignores the financing.
Example 2: issue costs. The company needs ₦60m net from a share issue with costs of 4% of the amount raised, with no tax relief.
- Gross = 60 ÷ 0.96 = ₦62.5m.
- Issue costs = ₦2.5m, all at time 0.
- PV of other costs = ₦2.5m.
Example 3: the tax shield. ₦40m of debt at 8% is repaid in full after four years. Tax is 30%, paid in the year of the interest.
- Interest = ₦3.2m a year. Tax saved = ₦0.96m a year.
- Discount at 8% (annuity factor 3.312): 0.96 × 3.312 = ₦3.18m.
- The principal repayment gets no relief.
Example 4: the APV. Combine Examples 1 to 3.
- APV = 21.5 − 2.5 + 3.18.
- APV = +₦22.2m.
- Positive, so accept.
How to score full marks
- Ungear the proxy beta to an asset beta and compute the ungeared cost of equity.
- Present the base case NPV with the financing excluded.
- Gross up issue costs correctly and net the tax relief.
- Split loan payments into interest and principal.
- Discount each element at its own rate.
- State the decision and why APV may differ from NPV.
Common mistakes in the exam
- Discounting the base case at the WACC.
- Including interest or issue costs in the base case flows.
- Dividing issue costs by the wrong base.
- Giving tax relief on loan principal.
- Discounting the tax shield at the cost of equity.
- Forgetting the timing of tax relief.
Quick revision
- APV = base NPV − other costs + tax shield.
- Base: asset beta, CAPM, ungeared rate, no financing.
- Issue costs: gross = net ÷ (1 − rate); risk-free rate.
- Tax shield: interest only; pre-tax cost of debt.
- APV does not need a new WACC.
- CAMA 2020: ss. 305, 308, 377(1), 378, 385.
Practice questions
These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer. Full model answers follow the written questions.
Recall check: multiple choice
Recent ICAN papers are written, although older papers such as May 2014 included multiple-choice questions. These questions are for quick recall. The written questions that follow are closer to the exam.
Question 1. APV equals:
- Base case NPV − other costs + PV of tax relief on interest
- Base case NPV + other costs
- NPV at the WACC
- Interest − tax
Show the answer
A. Accept if positive.
Question 2. The base case NPV discounts at:
- The ungeared cost of equity
- The WACC
- The cost of debt
- Zero
Show the answer
A. Financing is ignored.
Question 3. Gross amount to raise with 5% issue costs on a net need of ₦400,000 is:
- ₦421,053
- ₦420,000
- ₦380,000
- ₦400,000
Show the answer
A. 400,000 ÷ 0.95.
Question 4. Issue costs are usually discounted at:
- The risk-free rate
- The cost of equity
- The WACC
- The market return
Show the answer
A. They are paid at the start.
Question 5. Tax relief on loans is given on:
- Interest only
- Principal only
- Both
- Neither
Show the answer
A. Principal repayment is not an expense.
Question 6. The tax shield is discounted at the:
- Pre-tax cost of debt
- Cost of equity
- WACC
- Risk-free rate only
Show the answer
A. As ICAN does.
Question 7. APV is preferred when:
- The project changes risk and financing
- The project is tiny
- There is no tax
- Debt is zero
Show the answer
A. No new WACC is needed.
Question 8. NPV and APV:
- Can give different answers
- Always agree
- Are the same
- Ignore tax
Show the answer
A. They treat financing differently.
Question 9. The base case asset beta comes from:
- Ungearing the industry equity beta
- The company’s own beta
- The debt beta only
- The market return
Show the answer
A. It shows business risk.
Question 10. Which section of CAMA 2020 sets the director’s duty of care and skill?
- Section 308
- Section 400
- Section 405
- Section 409
Show the answer
A. Directors should test the assumptions behind a decision.
Written questions
Question 11 (10 marks). (a) Explain the three elements of APV. (6 marks) (b) State two reasons for using APV instead of adjusting WACC. (4 marks)
Question 12 (20 marks). Obi Plc will spend ₦90m on a project in a new industry, returning ₦30m a year for five years. The ungeared cost of equity for the industry is 10% (annuity factor 3.791). It will raise ₦40m of new debt at 6%, repaid at the end of year 5, and the rest from equity. Issue costs total ₦2.5m with no tax relief.
Tax is 25%, paid in the year of the interest (annuity factor at 6% for five years 4.212). Ignore tax on operating cash flows. (a) Calculate the base case NPV. (5 marks) (b) State the PV of the issue costs. (2 marks) (c) Calculate the PV of the interest tax shield. (6 marks) (d) Calculate the APV and advise. (3 marks) (e) Explain why the tax shield is discounted at the cost of debt. (4 marks)
Question 13 (10 marks). (a) A company needs ₦500m net from a share issue with costs of 4%. Calculate the amount to raise and the issue costs. (4 marks) (b) Explain how an amortising loan affects the calculation of the tax shield. (3 marks) (c) Explain why NPV and APV may give different decisions. (3 marks)
Model answers
Show the model answer to Question 11
(a) Elements (6 marks). Base case NPV: the NPV if the project were all-equity financed, at the ungeared cost of equity. (2) PV of other costs: mainly issue costs, net of any tax relief, discounted at the risk-free rate. (2) PV of tax relief on interest: the tax saved on the interest of the project debt, discounted at the pre-tax cost of debt. (2)
(b) Reasons (4 marks). It does not need a new WACC based on assumptions about the capital structure. (2) It allows for the actual debt terms and tax relief and for other financing costs such as issue costs. (2)
Show the model answer to Question 12
(a) Base case (5 marks).
- PV of inflows.
30 × 3.791 = ₦113.7m. (3) - NPV = 113.7 − 90 = +₦23.7m. (2)
(b) Issue costs (2 marks). There is no tax relief, so the PV is ₦2.5m. (2)
(c) Tax shield (6 marks).
- Interest = 40 × 6% = ₦2.4m a year. (2)
- Tax saved.
25% × 2.4 = ₦0.6m a year. (2) - PV = 0.6 × 4.212 = ₦2.53m. (2)
(d) APV (3 marks).
- APV = 23.7 − 2.5 + 2.53 = +₦23.7m. (2)
- Positive, so accept. (1)
(e) Cost of debt (4 marks). The tax saving depends on interest payments, which are about as certain as the debt itself. (2) The debt rate therefore reflects the risk of the tax saving, whereas the cost of equity would overstate it. (2)
Show the model answer to Question 13
(a) Issue (4 marks).
- Gross = 500 ÷ 0.96 = ₦520.8m. (2)
- Costs = 520.8 − 500 = ₦20.8m. (2)
(b) Amortising loan (3 marks). Each payment must be split into interest and principal, because only interest gets tax relief. (1.5) Interest falls each year as the balance falls, so the tax shield falls. (1.5)
(c) Different decisions (3 marks). NPV discounts all cash flows at one WACC and so treats the financing in a single rate. (1.5) APV values the business risk and the financing effects separately, so it can give a different sign. (1.5)
Pathfinder on APV: base case NPV, issue costs and the interest tax shield
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
Neither the May 2014 nor the November 2014 Pathfinder sets a stand-alone question on this topic. APV can follow the project-specific beta steps in a question like November 2014 question 1. Worked examples 1 to 4 show the three parts of APV.
Revise first: Worked examples
Questions ask for the base case NPV, the issue costs and the tax shield. See the section on the APV method.
Revise first: The APV method and its rule
Source: ICAN Pathfinder, Strategic Financial Management. Diets covered: No stand-alone question in the May 2014 or November 2014 Pathfinder.
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