Capital structure and dividend policy: formula sheet

Key formulas

Gearing (debt-to-equity)

Gearing = Debt ÷ Equity

One common form. Some definitions use Debt ÷ (Debt + Equity). State the definition you use.

Interest tax shield

Tax saved = Interest × Corporate tax rate

Applies when interest is tax deductible and the company has taxable profit to set it against.

After-tax cost of debt (simple, irredeemable)

Kd (after tax) = Interest rate × (1 − tax rate)

Applies to debt valued at its par value. For market-valued debt, use the yield instead.

Retained profit

Retained profit = Profit after tax − Dividends

This is the main internal source of long-term finance.

Interest cover

Interest cover = Profit before interest and tax ÷ Interest

A lower value means higher risk that debt cannot be serviced.

Ranking on winding up

Secured creditors > Unsecured creditors > Preference shareholders > Ordinary shareholders

A general order. Exact priority depends on the law and the terms of each instrument. Higher rank means lower risk and lower required return.

Dividend growth model (cost of equity)

Ke = D1 ÷ P0 + g, where D1 = D0 × (1 + g)

P0 is the ex-dividend price. Assumes dividends grow at a constant rate g forever.

CAPM (cost of equity)

Ke = Rf + β × (Rm − Rf)

(Rm − Rf) is the market risk premium. Use the equity beta, which reflects gearing.

Cost of irredeemable debt (after tax)

Kd = i × (1 − T) ÷ P0, where i is the annual interest per ₹100 nominal

P0 is the ex-interest market price per ₹100 nominal. T is the corporate tax rate.

Cost of redeemable debt

Find r so that P0 = Σ i(1 − T) ÷ (1 + r)^t + Redemption ÷ (1 + r)^n; then Kd = r

Use after-tax interest in the cash flows. Solve by trial and interpolation between two rates.

WACC

WACC = [E × Ke + D × Kd(1 − T)] ÷ (E + D)

If Kd is the pre-tax yield, apply (1 − T). If you already have the after-tax cost, do not apply it again. E and D are market values.

Growth from retained earnings

g = b × r

b is the retention ratio and r is the return on retained funds. A simple estimate that assumes both stay constant.

MM Proposition 1 (no tax)

VG = VU = EBIT-based cash flow ÷ ke(U)

Value is independent of gearing. For a perpetual cash flow X, VU = X ÷ ke(U), where ke(U) is the ungeared cost of equity.

MM Proposition 2 (no tax)

ke(G) = ke(U) + (ke(U) − kd) × (D ÷ E)

D and E are market values. Assumes debt is risk-free or its cost is kd with no change in risk. ke rises linearly with D ÷ E.

WACC (no tax)

WACC = ke(G) × E ÷ (D + E) + kd × D ÷ (D + E) = ke(U)

WACC is constant at all gearing levels in the no-tax case.

MM Proposition 1 (with corporate tax)

VG = VU + Tc × D

Assumes permanent debt with fixed amount D. Tc is the corporate tax rate. Tc × D is the present value of the tax shield.

MM Proposition 2 (with corporate tax)

ke(G) = ke(U) + (ke(U) − kd) × (1 − Tc) × (D ÷ E)

The (1 − Tc) factor makes the rise in ke slower than in the no-tax case.

WACC (with corporate tax)

WACC = ke(G) × E ÷ (D + E) + kd × (1 − Tc) × D ÷ (D + E) = ke(U) × (1 − Tc × D ÷ (D + E))

WACC falls as gearing rises. Use the second form for a quick check.

Ungeared value with tax

VU = X × (1 − Tc) ÷ ke(U)

X is perpetual annual pre-tax operating earnings of the ungeared firm. ke(U) is the cost of equity of the ungeared firm.

Value of geared firm (MM with tax)

V_g = V_u + T × D

Assumes permanent debt D, corporate tax rate T and no distress costs. V_u is the value of the all-equity firm.

Value with distress costs (trade-off)

V_g = V_u + PV(tax shield) − PV(expected distress and agency costs)

Optimum is where marginal tax benefit equals marginal cost of extra debt.

Annual tax shield

Tax shield = Interest × T = r_d × D × T

Use the tax rate that actually applies. It is only valuable if the firm has enough taxable profit.

Gearing ratios

Debt ÷ (Debt + Equity) or Debt ÷ Equity

State which definition you use and use market or book values consistently.

Pecking order of finance

Retained earnings → debt → new equity

Driven by information asymmetry and issue costs, not by a target ratio.

WACC

WACC = E/(D+E) × k_e + D/(D+E) × k_d × (1 − T)

The optimal structure minimises WACC. Cost of equity rises with gearing.

MM irrelevance (perfect markets)

Value of firm depends on investment policy, not on payout ratio

Needs no taxes, no transaction costs, symmetric information and fixed investment policy.

Ex-dividend price (perfect market)

Ex-dividend price ≈ cum-dividend price − dividend per share

Total shareholder wealth stays the same after the dividend.

Dividend payout ratio

Payout ratio = Dividends ÷ Earnings

Earnings means profit attributable to ordinary shareholders.

Dividend per share

DPS = Total ordinary dividends ÷ Number of ordinary shares

Use shares in issue that rank for the dividend.

Dividend cover

Dividend cover = Earnings ÷ Dividends

It is the reciprocal of the payout ratio.

Retention ratio

Retention ratio = 1 − Payout ratio

Retained profit funds growth without issue costs.

Theoretical ex-rights price (TERP)

TERP = (N × P₀ + n × Pᵣ) ÷ (N + n)

N = old shares in the rights ratio, n = new shares offered in that ratio, P₀ = cum-rights price, Pᵣ = issue price. Assumes the market value of the company rises by exactly the cash raised.

Value of a right (per new share)

Value of right per new share = TERP − Pᵣ

Per existing share, multiply by n ÷ N.

Ex-bonus price

Ex-bonus price = P₀ × N ÷ (N + n)

For a bonus of n shares for every N held. Total value is unchanged.

Buyback effect on shares

Shares repurchased = Cash used ÷ Buyback price

New shares = old shares − shares repurchased.

EPS after buyback

New EPS = (Earnings − after-tax earnings lost on cash used) ÷ New number of shares

If no earnings are lost on the cash, divide old earnings by the new share count.

Dividend equivalent in a perfect market

Ex-dividend price = Cum-dividend price − Dividend per share

With no taxes or costs, value falls by the cash paid out.

Scrip dividend shares

Shares received per share held = Cash dividend per share ÷ Reference share price

The reference price is set by the company. Use the price given in the question.

Quick revision

• Capital structure is the debt and equity mix; WACC is the cost of each source weighted by its proportion of total capital.
• Use market values for the weights in WACC where they are available.
• Interest is usually tax deductible, so the cost of debt after tax is the pre-tax cost × (1 − tax rate).
• Debt is cheaper than equity for the company because lenders rank first and bear less risk.
• M&M without taxes: firm value and WACC do not depend on gearing.
• M&M without taxes: the cost of equity rises as gearing rises, offsetting the cheaper debt.
• M&M with corporate tax: value rises with gearing because of the interest tax shield, so WACC falls.
• Against debt: financial distress costs, agency costs and loss of financing flexibility.
• Trade-off theory: the optimal gearing balances the tax benefit of debt against distress costs.
• Dividend irrelevance holds only under ideal assumptions, with no taxes or transaction costs and equal information.
• Dividend changes can signal management's view of future profits.
• A buyback cuts the number of shares in issue; a scrip dividend issues new shares instead of cash.

Common mistakes

• Saying retained profit is free finance. Fix: State that shareholders expect a return on retained funds. Its cost is the cost of equity, though it avoids issue costs.
• Saying debt is always better because it is cheaper. Fix: Add the risk side: fixed payments, possible distress, covenants and security. Higher gearing raises the risk to shareholders.
• Using book values as weights Fix: Use market values unless the question says otherwise. Compute shares × price and debt × market price.
• Forgetting the tax adjustment on debt, or applying it twice Fix: Write 'pre-tax' or 'post-tax' beside each debt figure. Apply (1 − T) exactly once, and only to the interest cash flows or the final yield.
• Saying that gearing has no effect on cost of equity in the no-tax case. Fix: Remember that ke rises with gearing. It is the rise in ke that keeps WACC constant.
• Using (1 − Tc) on ke(U) − kd missing in Proposition 2 with tax. Fix: Write both formulas side by side and note that the with-tax version has (1 − Tc) multiplying the D ÷ E term.
• Saying pecking order theory predicts a target gearing ratio. Fix: Remember pecking order has no optimum. Gearing is the result of the funding order.
• Using V_u + T × D when debt is not permanent or when distress costs are given. Fix: State the permanent debt assumption and subtract distress costs when the question provides them.
• Saying MM proves dividends never matter in practice. Fix: Always state the assumptions. Say it is a benchmark that shows why real-world factors matter.
• Confusing clientele effect with signalling. Fix: Clientele is about differing investor preferences, such as tax or income needs. Signalling is about information that the dividend conveys.

Exam tips

• Structure every comparison under cost, risk, control and fit. It earns marks even when you are unsure of the details.
• Use the scenario. Name the company type, the purpose and the time horizon in your answer.
• Show a short calculation when numbers are given. Gearing and interest cover are common and quick to compute.
• In MCQs, watch for words like always and never. Few statements about finance are true in every case.
• Discuss hybrids by saying which features of debt and which of equity they carry.
• Show every cost and weight separately. Method marks are given even if the final WACC is off.
• Read whether debt cost is given pre-tax or post-tax and label it on your working.
• Name your assumptions: constant growth, constant gearing, same business risk, and that the tax shield is fully used.