Financing and adjusted present value

Lesson 1 valued projects as if it did not matter how they were paid for. This lesson brings financing in. A senior adviser has to choose the sources of finance, understand how gearing changes the cost of capital and, when a project changes the company's capital structure significantly, value it in a way that keeps the investment and its financing apart: adjusted present value (APV). APV is a regular Section A and Section B calculation, usually followed by discussion of the financing choice and its effect on the reported figures. The sub-area is wide, so the lesson moves briskly through the finance options and theories, which build on area E of the HPS FM notes, and spends its time on APV.

Sources of finance: the adviser's menu

Islamic finance forbids riba (interest): returns must come from trade, leasing or sharing in a venture's profits and risks, backed by a real asset. FM covered the instruments. In AFM, discuss its role and development: sukuk issued by governments and companies, Islamic windows at conventional banks, and growth well beyond Muslim-majority countries. The rationale is access to a large pool of investors who need Sharia-compliant assets, and an ethical appeal to others. Its benefits are risk sharing (under mudaraba and musharaka, payments fall when profits fall, which lowers the risk of financial distress) and asset backing, which limits speculative lending. Its deficiencies are complex documentation and higher costs, the need for approval from Sharia scholars whose views can differ between countries, fewer standard products and less liquid markets, and criticism that some structures reproduce interest in substance.

Green finance serves organisations pursuing an environmental or sustainability agenda. With a green bond, the proceeds are earmarked for eligible environmental projects, and the issuer reports on their use and impact, often with an external review. With a sustainability-linked loan or bond, the money can be used for any purpose, but the interest rate steps up or down with the borrower's performance against stated sustainability targets. The benefits are access to investors with ESG mandates, sometimes a slightly lower cost where demand is strong, reputation, and internal discipline. The costs are reporting and verification, restrictions on the use of funds and the risk of greenwashing claims, which damage reputation and can bring legal action.

Assess any source under three headings examiners reward: its effect on the financial position (gearing, security, covenants), on financial risk (interest cover, refinancing risk, control) and on value (tax shields, issue costs, signalling and flexibility).

Capital structure and the cost of capital

FM taught the traditional view, Modigliani and Miller (M&M) and the pecking order, and how to ungear and regear a beta. AFM adds a formula and two further ideas.

M&M Proposition 2 with tax, on the formulae sheet, gives the cost of equity of a geared company: ke = ke^i + (1 − T)(ke^i − kd) × Vd ÷ Ve, where ke^i is the cost of equity of an identical ungeared company and kd the pre-tax cost of debt. With ke^i of 10%, kd of 4%, tax at 25% and Vd:Ve of 40:60, ke = 10% + 0.75 × 6% × 40 ÷ 60 = 13%. Behind it sits M&M's other result: the value of a geared company equals the value of the same company ungeared plus the present value of its tax shield. That is the foundation of APV.

The static trade-off theory says a company balances the tax benefit of more debt against the expected costs of financial distress: legal costs if it fails, and before that, lost customers, tighter supplier terms, departing staff and investment it cannot finance. Gearing is optimal where the marginal benefit equals the marginal cost, so companies with stable cash flows and tangible assets can borrow more than those with volatile cash flows and intangible assets.

The pecking order explains financing by information asymmetry: retained earnings first, then debt, then new equity, with no target gearing.

Agency effects cut both ways. Debt disciplines managers, because cash committed to interest cannot be spent on value-destroying projects. But at high gearing, shareholders may favour very risky projects (they keep the upside, lenders bear the downside) or refuse safe ones whose gains go mainly to lenders. Lenders respond with covenants, security and higher rates: the agency costs of debt.

The company's WACC is the right discount rate only for a project with the same business risk, financed without changing gearing. Otherwise use a project-specific rate from an asset beta, or APV. The cost of debt itself can be estimated from the yield curve and the company's credit spread, which lesson 4 shows.

Duration and convexity of debt

The value of fixed-rate debt falls when interest rates rise. Duration measures by how much.

• Macaulay duration is the PV-weighted average time to receive a bond's cash flows, calculated exactly like project duration in lesson 1, discounting at the bond's yield to maturity.
• Modified duration = Macaulay duration ÷ (1 + yield). The percentage change in the bond's price ≈ −modified duration × the change in yield.

Take a three-year 5% bond redeemable at par, yielding 6%:

Macaulay duration = 278.097 ÷ 97.327 = 2.857 years; modified duration = 2.857 ÷ 1.06 = 2.696. If the yield rises to 7%, duration predicts a price of 97.327 × (1 − 0.02696) = $94.70; the true price is $94.75. If it falls to 5%, duration predicts $99.95; the true price is $100.00.

That gap is convexity: the price–yield relationship is a curve, and duration is a straight-line approximation to it. Duration therefore overstates the fall in price when yields rise and understates the gain when they fall, and the error grows with the size of the change. Duration's benefits are a single measure that compares the interest rate risk of debts with different coupons and maturities, and a way to match the durations of assets and liabilities. Its limitations are that it assumes a flat yield curve that moves in parallel, it is accurate only for small changes, it must be recalculated as time passes and yields move, and it ignores credit risk.

Adjusted present value

Discounting at the WACC assumes the project leaves business risk and gearing unchanged. When a project is financed in a way that changes the capital structure significantly, or comes with a subsidised loan or large issue costs, APV is more reliable. It values the project as if it were financed entirely by equity, then adds the value of each financing effect separately.

On step 5, some answers take the interest saved after tax and base the tax shield on interest at the normal rate; the total is the same. If a question specifies a method, such as a tax shield based on the project's debt capacity, follow it.

APV's strength is transparency: the board sees how much value the investment itself creates and how much the financing adds. Its weaknesses come from M&M's assumptions: it ignores the costs of financial distress and agency costs, the right discount rate for tax shields is debatable, tax shields are worth something only if the company pays tax, and the base case depends on a proxy beta.

Reported financial position and performance

Boards and markets also watch the reported figures: earnings per share, gearing, interest cover and covenants. A project with a positive APV may still depress EPS for several years if early profits are low; debt finance raises gearing and reduces interest cover; an equity issue dilutes EPS. A question may ask you to forecast profit, EPS, gearing and interest cover under alternative financing and comment on the likely market reaction. Compare each measure with any covenant limit and with the levels investors are used to.

Worked example

Kubwa Ceramics Co, a fictional company, is considering a four-year project.

• The investment is $40m at T0. After-tax operating cash flows, including tax savings on tax-allowable depreciation but before any financing effects, are $11m, $13m, $14m and $12m in years 1 to 4.
• A proxy company in the same industry has an equity beta of 1.50 and equity and debt in the ratio 60:40 by market value. Debt betas are nil. Tax is 25%, paid in the year profits arise. The risk-free rate is 4% and the market return 10%.
• A regional development agency will lend $16m at a subsidised 2%, repayable at the end of year 4. The rest will be raised by a four-year bond at Kubwa's normal pre-tax borrowing rate of 6%, issued at par. Bond issue costs are 2% of the gross amount raised, paid from the proceeds, and are not tax-deductible.
• Financing effects are discounted at 6%.

Step 1: the ungeared cost of equity. βa = 1.50 × 60 ÷ (60 + 40 × 0.75) = 1.50 × 60 ÷ 90 = 1.00. ke^i = 4% + 1.00 × (10% − 4%) = 10%.

Step 2: the base-case NPV.

Base-case NPV = −$0.553m. Financed entirely by equity, the project would destroy value.

Step 3: issue costs. The bond must provide $24m net. Gross amount = 24 ÷ 0.98 = $24.490m, so issue costs are $0.490m.

Step 4: the bond's tax shield. Interest = 24.490 × 6% = $1.469m a year; tax saved = 1.469 × 25% = $0.3673m a year. The four-year annuity factor at 6% is 3.465, so the PV is 0.3673 × 3.465 = $1.273m.

Step 5: the subsidised loan. Interest saved = 16 × (6% − 2%) = $0.640m a year, with a PV of 0.640 × 3.465 = $2.218m. The tax shield on the interest actually paid is 16 × 2% × 25% = $0.080m a year, with a PV of 0.080 × 3.465 = $0.277m. To check the subsidy from first principles, value the loan's own cash flows at 6%: Kubwa receives $16m, pays interest of $0.32m a year (PV 0.32 × 3.465 = $1.109m) and repays $16m at T4 (PV 16 × 0.792 = $12.672m), a net benefit of 16 − 1.109 − 12.672 = $2.219m, the same as the subsidy apart from rounding. ACCA's model answers often set the same figures out in three lines instead: the tax shield on the whole loan at the normal rate (16 × 6% × 25% = $0.240m a year, PV $0.832m), plus the interest saved before tax ($2.218m), minus the tax shield lost on that saving (16 × 4% × 25% = $0.160m a year, PV $0.554m). That totals $2.496m, exactly the $2.218m + $0.277m above apart from rounding, so use whichever layout the question suggests.

Step 6: the APV.

Advice to the board. On an APV basis the project adds about $2.7m to shareholder wealth and should go ahead, but the board should see where the value comes from: the project itself loses $0.55m, and the financing package, chiefly the agency's subsidy, more than makes up for it. That raises three questions. Is the subsidy available only for this project? If so, it belongs in the appraisal; if Kubwa could use it for another investment, it does not. Will Kubwa have enough taxable profits to use the tax shields? If not, about $1.5m of the value is at risk. And can the business carry $40.5m of new debt? APV ignores the costs of financial distress, so check the effect on interest cover, gearing and existing covenants, and any conditions the agency attaches to its loan, before committing.

Common mistakes

• Discounting the base case at the WACC or the geared cost of equity instead of the ungeared cost of equity.
• Taking issue costs as a percentage of the net amount needed when they are charged on the gross amount raised.
• Discounting tax shields at the ungeared cost of equity instead of the cost of debt.
• Basing the subsidised loan's tax shield on interest at the normal rate and then adding the pre-tax subsidy as well, which claims tax relief on interest that is never paid.
• Using the proxy's gearing to regear in an APV: the base case needs the ungeared figure only.
• Applying modified duration without dividing Macaulay duration by (1 + yield), or forgetting the minus sign.

Exam technique

Set APV out in three blocks a marker can follow: the ungeared cost of equity, the base-case NPV table, then a schedule of financing effects with a line for each and a total, as in the example. Put each financing working (the gross-up, the interest, the annuity factor) beside its line. State assumptions you make, such as the discount rate for tax shields. The discussion marks usually go to explaining why APV suits this financing, where the value comes from, and what APV leaves out. For a sources-of-finance requirement, use the three headings of financial position, financial risk and value, applied to the scenario's own numbers.

Study with AI

I am studying ACCA Advanced Financial Management (AFM), adjusted present value.
Set me a project with an investment, four or five years of after-tax operating
cash flows, a proxy equity beta and gearing, the risk-free rate and market return,
and a financing package that includes a subsidised loan, a bond with issue costs
charged on the gross amount, and a tax rate. Ask me for the ungeared cost of
equity, the base-case NPV, each financing effect and the APV, one step at a time.
Mark each step with workings, then ask me two questions a sceptical board member
would raise.

AI assistants can make arithmetic mistakes and can misstate the rules: check every answer against these notes and the ACCA formulae sheet before you rely on it.

Lecturer's note: APV is easiest to remember as two questions asked one after the other. First: if this project were paid for entirely by shareholders, would it be worth doing? That is the base case, at the ungeared cost of equity. Second: what does the way we are actually paying for it add or take away? That is every financing effect, each valued on its own. Keep the two questions apart and APV is never confusing, and the discussion writes itself, because the board can see whether it is buying a good project or a good financing deal.

Key points

• Assess a source of finance by its effect on the financial position, on financial risk and on value; know the features of hybrids, private equity, securitisation, Islamic finance, green finance and security token offerings.
• M&M with tax: ke = ke^i + (1 − T)(ke^i − kd) × Vd ÷ Ve, and geared value = ungeared value + PV of the tax shield; the static trade-off theory adds distress costs, and agency effects add covenants and conflicts.
• Modified duration = Macaulay duration ÷ (1 + yield) and gives the approximate percentage price change for a change in yield; convexity makes the approximation less accurate for large changes.
• APV = base-case NPV at the ungeared cost of equity + PV of tax shields − issue costs + PV of any subsidy.
• APV suits projects that change the capital structure significantly, but it ignores distress costs and assumes the tax shields can be used.

Quick check

1. A company receives a five-year subsidised loan of $10m at 3% when its normal pre-tax borrowing rate is 7%. Tax is 30%, paid in the same year. What is the present value of the subsidy and of the tax shield on the loan, at 7%?
2. A company needs $20m from a share issue whose costs are 3% of the gross amount raised. What are the issue costs?
3. A bond has a Macaulay duration of 4.2 years and a yield of 5%. What is its modified duration, and roughly how much will its price change if yields rise by 0.5 percentage points?

Answers

1. Subsidy: 10 × (7% − 3%) = $0.40m a year × 4.100 = $1.640m. Tax shield: 10 × 3% × 30% = $0.09m a year × 4.100 = $0.369m. Together $2.009m.
2. Gross amount = 20 ÷ 0.97 = $20.619m, so issue costs are $0.619m (not 3% × $20m = $0.600m).
3. Modified duration = 4.2 ÷ 1.05 = 4.0. Price change ≈ −4.0 × 0.5% = −2.0%.