Capital structure theories and practical considerations: formula sheet

Key formulas

Cost of equity (dividend valuation model with growth)

Ke = [D0 × (1 + g) ÷ P0] + g

D0 is the dividend just paid. P0 is the ex-dividend share price. g is the constant annual dividend growth rate.

Cost of equity (CAPM)

Ke = Rf + β × (Rm − Rf)

Rf is the risk-free rate. Rm − Rf is the equity risk premium. β measures systematic risk.

Cost of irredeemable debt (after tax)

Kd = i × (1 − T) ÷ P0

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

Cost of redeemable debt

Kd = IRR of: − market price now, + interest × (1 − T) each year, + redemption value at the end

Find it by interpolation between two discount rates. Use the post-tax interest cash flows.

Cost of preference shares

Kp = Preference dividend ÷ Market price

No tax adjustment, because preference dividends are not tax deductible.

Weighted average cost of capital

WACC = [Ve × Ke + Vd × Kd + Vp × Kp] ÷ (Ve + Vd + Vp)

V is the total market value of each source. Use the after-tax Kd.

Weighted average cost of capital

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

E and D are market values of equity and debt. Kd(1 − T) is the after-tax cost of debt. Use the version that matches the data given.

Value of the company at a given WACC

Value = Annual cash flows to all providers of finance ÷ WACC

Applies when cash flows are constant in perpetuity. A lower WACC gives a higher value.

Optimal capital structure rule

Optimal gearing = the gearing level with the lowest WACC (and so highest value)

Under the traditional view this is an interior point, not zero debt and not maximum debt.

Proposition 1 (value)

Vg = Vu = Earnings before interest ÷ Keu

Valid with no tax and constant earnings. Vg is geared value, Vu is ungeared value, Keu is the cost of equity of the ungeared firm.

Proposition 2 (cost of equity)

Keg = Keu + (Keu − Kd) × (Vd ÷ Ve)

Vd and Ve are market values of debt and equity. Kd is the pre-tax cost of debt. No tax term appears because there is no tax.

WACC under MM without tax

WACC = Keu at every level of gearing

Check: WACC = Keg × Ve/(Ve+Vd) + Kd × Vd/(Ve+Vd) gives Keu.

Value of the geared firm

Vg = Ve + Vd

So Ve = Vu − Vd if you are asked for the equity value after debt is introduced.

Value of geared company

Vg = Vu + D × t

Assumes permanent debt D and tax rate t. Dt is the present value of the tax shield.

Value of ungeared company

Vu = Earnings before interest and tax × (1 − t) ÷ Keu

Keu is the cost of equity of the ungeared company. Assumes constant perpetual earnings.

Annual tax shield

Annual tax saving = D × Kd × t

Interest is D × Kd. Discounting this perpetuity at Kd gives D × t.

Cost of equity of geared company

Keg = Keu + (Keu − Kd) × (1 − t) × D ÷ E

E is the market value of equity of the geared company. Kd is the pre-tax cost of debt.

WACC of geared company

WACC = Keu × (1 − D × t ÷ (D + E))

Here D + E = Vg. WACC is below Keu whenever there is debt and tax.

Market value of equity

E = Vg − D

Use after finding Vg.

Pecking order of finance

Retained earnings → Debt → New equity

Use this as a ranking rule, not a calculation. Firms move down only when the previous source is exhausted or insufficient.

Funding gap

External funding needed = Investment required − Internal funds available

If the gap is zero or negative, the theory predicts no external finance. If positive, borrow first, then issue shares if needed.

Gearing (debt/equity)

Debt ÷ Equity (market or book values)

Say which basis you use. Market values are better for valuation; book values are common in loan covenants.

Gearing (debt/total capital)

Debt ÷ (Debt + Equity)

Use the same basis for debt and equity. Check the definition the question gives.

Interest cover

Profit before interest and tax ÷ Interest

Low cover means higher risk of default and less debt capacity. Lenders often set a minimum in covenants.

Value of geared firm (M&M with tax)

Vg = Vu + (Debt × Tax rate)

This is the theory. Practical factors explain why firms do not reach the extreme this implies.

Quick revision

• WACC is weighted using market values of equity and debt, with debt cost taken after tax.
• Traditional view: WACC falls as cheap debt is added, then rises as financial risk grows; there is an optimal gearing level.
• M&M without tax: value and WACC are unaffected by gearing.
• M&M without tax: the cost of equity rises linearly with gearing, which offsets the cheaper debt.
• M&M with tax: debt gives a tax shield, so WACC falls and value rises as gearing increases.
• M&M with tax and permanent debt: value geared = value ungeared + tax rate × debt.
• M&M theory in its pure form implies near 100% debt, which ignores bankruptcy costs and other real-world limits.
• Pecking order: retained earnings first, then debt, then new equity.
• Pecking order is about managers' preferences, not about finding an optimal gearing level.
• Practical factors: business risk, cash flow stability, security available, covenants, issue costs, tax position and the company's existing gearing.
• Financial risk is the extra variability in returns to shareholders caused by fixed interest payments.
• In written answers, link each point to the scenario instead of listing theory.

Common mistakes

• Using book values for weights. Fix: Use market values whenever they are given. Use book values only if the question gives no market values.
• Forgetting to adjust the cost of debt for tax. Fix: Multiply interest by (1 − T) before finding the cost. Do not tax-adjust preference share dividends.
• Saying the traditional view claims more debt always lowers WACC. Fix: Always describe both phases: WACC falls at low gearing, then rises at high gearing, giving a U-shape.
• Confusing the traditional view with Modigliani and Miller. Fix: Traditional: an optimal gearing exists. M&M without tax: WACC is constant, so gearing is irrelevant. Write this contrast in one line.
• Saying WACC falls as debt is added because debt is cheaper. Fix: Add the second half: Ke rises to compensate for financial risk. Under MM without tax the two effects cancel and WACC is flat.
• Using book values of debt and equity in the Ke formula. Fix: Use market values. MM works with market values of Vd and Ve.
• Using Vg = Vu + D instead of Vu + Dt. Fix: Always multiply the debt by the tax rate. Write t next to D before calculating.
• Forgetting to deduct tax when finding Vu. Fix: Use EBIT × (1 − t) ÷ Keu in a tax question. The earnings must be after tax.
• Putting new equity before debt in the order. Fix: Remember the theory is about cost, effort and signals, not risk. Debt is cheaper to raise and sends a weaker negative signal than new shares.
• Saying pecking order theory gives an optimal gearing ratio. Fix: State that pecking order has no target gearing. Gearing is the by-product of financing choices over time.

Exam tips

• In objective questions, check the units. Market value may be given per share or per ₹100 nominal, and you must scale it correctly.
• Always read whether the share price is cum-div or ex-div, and whether the dividend given is D0 or D1.
• In a constructed response question, lay out the WACC in a table with value, cost and weighted cost. Markers can then award marks for each step.
• Add a short comment on limits: WACC assumes constant risk and capital structure, and market values change daily. These points often earn marks.
• If the question asks for the cost of debt, show the interpolation for redeemable debt in full. Marks are given for both discount rates tried.
• In written parts, draw or describe the U-shaped WACC curve and say what happens to Ke, Kd and WACC in each phase.
• Always link the lowest WACC to the highest company value. Markers look for this link.
• Add a one-line comparison with Modigliani and Miller. It earns easy marks in Section C.