Cost of capital and capital structure

Commerce (General / Accounting and Finance / Banking and Insurance) (B.Com) · Finance and banking · free study notes for exams, placements and interviews

In short

Cost of capital is the minimum rate of return a firm must earn on its investments to keep the value of its shares unchanged — in practice the weighted average of what equity, preference and debt holders demand. Capital structure is the mix of those sources on the right-hand side of the balance sheet, and the central question is whether changing the mix changes the firm's total value and its cost of capital. The two ideas join at the hurdle rate: WACC is the discount rate used in project appraisal and in valuation, so a wrong capital structure makes every investment decision wrong. B.Com and M.Com papers, CA/CS/CMA Financial Management, the CFA Level I curriculum and placement tests for roles in corporate finance, equity research, credit rating and banking all test WACC computation, and Indian FM papers add EBIT-EPS analysis with numbers.

Explained

Cost of capital: meaning and components

Definition: the cut-off or hurdle rate — the minimum return a project must yield so that shareholder wealth is not reduced. Also read as the opportunity cost of funds to the investor.
Three ways of looking at the same number: (i) required return of suppliers of capital, (ii) minimum return on new investment, (iii) discount rate for future cash flows.
Explicit cost: the discount rate that equates cash inflow from a source with the present value of its outflows (interest, dividend, repayment). Implicit cost: opportunity cost of the forgone alternative — the relevant notion for retained earnings.
Components: cost of debt (Kd), cost of preference capital (Kp), cost of equity (Ke), cost of retained earnings (Kr) — combined into Ko or WACC.
Costs are computed on an after-tax basis because interest is deductible under the Income-tax Act, 1961 while dividends are not; this makes debt structurally cheaper. Market value weights are preferred to book value weights because they reflect current investor expectations.

Cost of debt and preference capital

Irredeemable (perpetual) debt: Kd = I(1 − t)/NP, where NP is net proceeds after discount and issue expenses — not the face value.
Redeemable debt: approximate Kd = [I(1 − t) + (RV − NP)/n] / [(RV + NP)/2]. Exact method: find the IRR of the after-tax cash flow stream (YTM approach).
Floating-rate bank term loans are usually taken at the contracted rate net of tax; in India corporate lending is largely benchmarked to MCLR or, for retail and MSME floating loans, to an external benchmark (EBLR) such as the repo rate under the RBI's framework.
Preference shares: Kp = PD/NP for irredeemable; Kp = [PD + (RV − NP)/n] / [(RV + NP)/2] for redeemable. Preference dividend is not tax-deductible, so there is no (1 − t) factor.
Post-2020, dividend distribution tax was abolished and dividends are taxed in the shareholder's hands; the company therefore bears no DDT in Kp, though students should check the rule for the assessment year in question.
Under the Companies Act, 2013 preference shares must be redeemable within 20 years (30 years for specified infrastructure projects), which is why the redeemable formula dominates in practice.

Cost of equity — four approaches

Dividend price (D/P) approach: Ke = D₁/P₀ — assumes no growth; simple but ignores retained-earnings-driven growth.
Dividend growth (Gordon) model: Ke = D₁/P₀ + g, with g estimated as retention ratio × ROE (b × r) or from historic dividend CAGR. Valid only if g < Ke and g is constant.
Earnings price approach: Ke = EPS/P₀ — the reciprocal of the P/E ratio; usable for a firm paying out all earnings, otherwise understates or overstates cost.
CAPM: Ke = Rf + β(Rm − Rf). Rf from government securities (the 10-year G-Sec yield is the Indian market convention), β from regression of the stock's returns on an index such as NIFTY 50, and (Rm − Rf) is the equity risk premium (commonly taken around 6–8% for India, but it is an estimate and varies by source and period).
Beta: measures systematic (non-diversifiable) risk. β = 1 moves with the market, β > 1 is aggressive, β < 1 defensive. Levered beta reflects both business and financial risk; Hamada: βL = βU[1 + (1 − t)D/E].
Cost of retained earnings (Kr): conceptually equals Ke because shareholders forgo dividends they could have reinvested; adjust downward for shareholder-level tax (tp) and brokerage (b): Kr = Ke(1 − tp)(1 − b). Retained earnings have no issue cost, so Kr ≤ Ke of a fresh issue.
Bond yield plus risk premium: Ke = Kd (pre-tax) + 3% to 5% — a quick cross-check used by practitioners.

Weighted average and marginal cost of capital

WACC steps: (1) compute each component cost after tax; (2) assign weights — book value, market value or target/marginal; (3) multiply and sum; (4) use as the discount rate for projects of average risk.
Book value weights are easy and stable but historic; market value weights are theoretically correct but fluctuate and are unavailable for unlisted debt; target weights avoid year-to-year noise and are what rating agencies and valuers typically use.
Marginal cost of capital (MCC): cost of the next rupee raised. It rises in steps as cheaper sources are exhausted — each jump is a break point = amount of cheaper source available ÷ its weight in the structure.
Plotted against the investment opportunity schedule (IOS), the intersection of MCC and IOS gives the optimum capital budget.
Divisional / risk-adjusted rates: a single WACC applied to a riskier division under-prices its risk; use a pure-play beta of comparable listed firms instead.

Capital structure: theories

Capital structure = permanent long-term financing mix (equity + preference + long-term debt + retained earnings); financial structure is wider and includes current liabilities. Capitalisation is the total par value of long-term securities.
Assumptions common to the classical theories: only debt and equity, no taxes (initially), total assets and EBIT constant, 100% payout, perpetual life, rational investors.
Net Income (NI) approach — Durand: Kd and Ke are constant and independent of leverage; more debt lowers Ko and raises value V = S + D. Optimum = maximum debt. Unrealistic because risk is ignored.
Net Operating Income (NOI) approach — Durand: Ko and Kd are constant; Ke rises exactly enough to offset the cheap debt, so V = EBIT/Ko is independent of leverage. Every structure is optimal — no optimum. Value depends only on business risk and EBIT.
Traditional (intermediate) approach: moderate debt first lowers Ko because the tax and cheapness benefit outweighs the rise in Ke; beyond a point both Ke and Kd rise and Ko turns up. Ko is saucer-shaped, giving a genuine optimum capital structure at the minimum of Ko (and maximum of value). This is the view most Indian syllabi treat as practically correct.
Modigliani–Miller (1958), no tax: by arbitrage, two firms with identical EBIT and risk must have identical value; personal (home-made) leverage lets investors replicate corporate leverage, so Vu = Vl and Ko is constant. Proposition II: Ke = Ko + (Ko − Kd)(D/S).
MM (1963), with corporate tax: interest is deductible, so Vl = Vu + t·D (the interest tax shield); value rises with debt and 100% debt would be optimal.
Miller (1977) with personal taxes and trade-off theory correct this: the tax shield is set against financial distress costs (bankruptcy, legal costs, loss of suppliers and talent) and agency costs; optimum debt is where the marginal tax shield equals marginal distress cost.
Pecking order theory (Myers–Majluf): because of asymmetric information, firms prefer retained earnings → debt → equity, so profitable firms borrow less; there is no target ratio.
Signalling theory: a debt issue signals management confidence; an equity issue signals that managers think the share is overvalued.
Agency / free cash flow theory (Jensen): debt disciplines managers by committing cash to fixed payments.

Leverage, EBIT-EPS analysis and practical determinants

Operating leverage = contribution/EBIT (business risk); financial leverage = EBIT/(EBIT − I − Dp/(1 − t)) (financial risk); combined leverage = DOL × DFL = contribution/(EBIT − I − Dp/(1 − t)), which reduces to contribution/PBT when there is no preference dividend.
Trading on equity: using fixed-cost funds to raise EPS — profitable only when ROI (ROCE) exceeds the interest rate on debt, both measured pre-tax (equivalently, after-tax ROI above after-tax Kd); otherwise leverage works in reverse and magnifies losses.
Indifference point (EBIT level): the EBIT at which EPS is identical under two financing plans. Above it, the more debt-heavy plan gives higher EPS; below it, equity is better.
Financial break-even: the EBIT at which EPS = 0, i.e. EBIT = I + Dp/(1 − t).
Determinants of capital structure in practice: stability of EBIT, asset tangibility (collateral), growth stage, cost and ease of issue, control dilution (promoter-held Indian firms resist equity), lender covenants, interest coverage, industry norms, tax position (a firm with carried-forward losses gets no shield), flexibility to raise future funds, and market conditions.
Indian regulatory context: debenture issues and debt listing are governed by SEBI's NCS Regulations, 2021; the Companies Act, 2013 requires a debenture redemption reserve for specified issues and permits buy-backs (section 68) subject to a post-buy-back debt-to-capital-plus-free-reserves limit of 2:1; thin capitalisation under section 94B of the Income-tax Act caps deductible interest to associated enterprises at 30% of EBITDA, limiting the tax shield; the IBC, 2016 has made distress costs far more real for over-levered Indian companies. Large listed entities also face SEBI's framework encouraging a share of incremental borrowing through the bond market — the specifics have been revised more than once, so verify the current circular.

Key points

Cost of capital - minimum return that leaves shareholder wealth unchanged; the hurdle rate for appraisal.
After-tax basis - interest is tax-deductible, dividends are not, so Kd(after tax) = Kd(1 − t).
Net proceeds, not face value - always divide by money actually received after discount and issue cost.
Kp has no tax adjustment - preference dividend is paid from post-tax profit.
Ke is the highest component cost - equity bears residual risk and has no contractual claim.
CAPM - Ke = Rf + β(Rm − Rf); β measures systematic risk only, diversifiable risk is unpriced.
Kr ≈ Ke - retained earnings are not free; they carry an opportunity cost, less issue expense.
WACC - Σ(weight × after-tax component cost); market value weights preferred to book value.
Marginal cost of capital - cost of the next rupee; rises in steps at break points.
NI approach - value rises continuously with debt; optimum is maximum debt.
NOI approach - value is independent of leverage; no optimum structure.
Traditional approach - saucer-shaped Ko gives one optimum point.
MM without tax - arbitrage and home-made leverage make Vu = Vl; Ke = Ko + (Ko − Kd)D/S.
MM with tax - Vl = Vu + tD; the tax shield is the only source of gain from leverage.
Trade-off theory - optimum debt balances tax shield against financial distress and agency costs.
Pecking order - retained earnings first, then debt, then equity; no target ratio.
Trading on equity - leverage raises EPS only while ROCE exceeds the pre-tax interest rate on debt.
Indifference point - EBIT where two plans give equal EPS; a key decision tool in exams and interviews.

Formulas and examples

Kd (irredeemable) = I(1 − t) / NP — I = annual interest (₹), t = tax rate (decimal), NP = net proceeds (₹)
Kd (redeemable, approx.) = [I(1 − t) + (RV − NP)/n] / [(RV + NP)/2] — RV = redemption value, n = years to maturity
Kp (irredeemable) = PD / NP; Kp (redeemable) = [PD + (RV − NP)/n] / [(RV + NP)/2] — PD = preference dividend (₹)
Ke (D/P) = D₁ / P₀; Ke (growth) = D₁/P₀ + g — D₁ = next year's dividend, P₀ = current (or net issue) price, g = growth rate
Ke (CAPM) = Rf + β(Rm − Rf) — Rf = risk-free rate, Rm = expected market return, β = beta (dimensionless)
g = b × r — b = retention ratio, r = return on equity
Kr = Ke(1 − tp)(1 − b) — tp = shareholder's tax rate, b = brokerage/transaction cost rate
WACC (Ko) = (E/V)Ke + (P/V)Kp + (D/V)Kd(1 − t) — E, P, D = market values of equity, preference, debt; V = E + P + D
Break point = amount of cheaper source available / its weight in the capital structure
MM Prop. II (no tax): Ke = Ko + (Ko − Kd)(D/S); MM with tax: Vl = Vu + t·D
Value (NOI / MM): V = EBIT / Ko; Equity value S = (EBIT − I)/Ke
DFL = EBIT / [EBIT − I − Dp/(1 − t)]; DOL = Contribution / EBIT; DCL = DOL × DFL
EPS = [(EBIT − I)(1 − t) − Dp] / N — N = number of equity shares
Indifference EBIT: [(EBIT − I₁)(1 − t) − Dp₁]/N₁ = [(EBIT − I₂)(1 − t) − Dp₂]/N₂
Hamada: βL = βU[1 + (1 − t)D/E]

Example 1 — Component costs and WACC (book value weights). A company's capital: Equity ₹50,00,000 (5,00,000 shares of ₹10), 9% Preference ₹10,00,000, 12% Debentures ₹40,00,000. Tax 30%. Current market price ₹25, next year's dividend ₹2.00, expected growth 8%.

Kd = 12% × (1 − 0.30) = 8.40%
Kp = 9% (issued at par, irredeemable) = 9.00%
Ke = 2.00/25 + 0.08 = 0.08 + 0.08 = 16.00%
Weights (book): Equity 50/100 = 0.50, Preference 0.10, Debt 0.40
WACC = 0.50(16.00) + 0.10(9.00) + 0.40(8.40) = 8.00 + 0.90 + 3.36 = 12.26%

Source	Book value (₹)	Weight	After-tax cost	Weighted
Equity	50,00,000	0.50	16.00%	8.000%
Preference	10,00,000	0.10	9.00%	0.900%
Debentures	40,00,000	0.40	8.40%	3.360%
Total	1,00,00,000	1.00		12.26%

Using market value weights (equity 5,00,000 × ₹25 = ₹1,25,00,000; preference and debt at book): V = 1,25,00,000 + 10,00,000 + 40,00,000 = ₹1,75,00,000 → WACC = (125/175)16 + (10/175)9 + (40/175)8.40 = 11.4286 + 0.5143 + 1.9200 = 13.86%. Market weights raise WACC because the high-cost equity carries a bigger weight.

Example 2 — Redeemable debentures. A ₹100 debenture carrying 11% interest is issued at a 4% discount, with ₹2 issue expenses, redeemable at par in 5 years. Tax 30%.

NP = 100 − 4 − 2 = ₹94; RV = ₹100; I = ₹11; I(1 − t) = ₹7.70
Amortised discount per year = (100 − 94)/5 = ₹1.20
Average funds = (100 + 94)/2 = ₹97
Kd = (7.70 + 1.20)/97 = 8.90/97 = 9.18%

(Ignoring the tax shield on the written-off discount; some texts apply (1 − t) to it, giving (7.70 + 0.84)/97 = 8.80% — state the assumption.)

Example 3 — EBIT-EPS indifference point. A firm needs ₹40,00,000. Plan A: all equity, 4,00,000 shares at ₹10. Plan B: ₹20,00,000 equity (2,00,000 shares) + ₹20,00,000 of 12% debt. Tax 30%.

Plan A: I₁ = 0, N₁ = 4,00,000. Plan B: I₂ = ₹2,40,000, N₂ = 2,00,000.
Indifference: EBIT(0.7)/4,00,000 = (EBIT − 2,40,000)(0.7)/2,00,000
Multiply out: 0.7·EBIT × 2,00,000 = (EBIT − 2,40,000) × 0.7 × 4,00,000 → EBIT = 2(EBIT − 2,40,000) → EBIT = ₹4,80,000
Check at EBIT = ₹4,80,000: A → 4,80,000 × 0.7/4,00,000 = ₹0.84; B → (4,80,000 − 2,40,000) × 0.7/2,00,000 = 1,68,000/2,00,000 = ₹0.84. Equal.
At EBIT ₹8,00,000: A = 5,60,000/4,00,000 = ₹1.40; B = (8,00,000 − 2,40,000)0.7/2,00,000 = 3,92,000/2,00,000 = ₹1.96 → debt plan wins above the indifference EBIT.
At EBIT ₹3,00,000: A = 2,10,000/4,00,000 = ₹0.525; B = (60,000 × 0.7)/2,00,000 = ₹0.21 → equity plan wins below it.
Note ROI at indifference = 4,80,000/40,00,000 = 12% = the pre-tax cost of debt — the general result that the indifference ROI equals the interest rate.

Example 4 — MM with and without tax. Firm U is unlevered; Firm L has ₹30,00,000 of 10% debt. Both have EBIT ₹12,00,000. Unlevered cost of equity (Ko) = 15%.

No tax: Vu = 12,00,000/0.15 = ₹80,00,000. By MM, Vl = ₹80,00,000 too, so S = 80,00,000 − 30,00,000 = ₹50,00,000.
- Ke of L = (12,00,000 − 3,00,000)/50,00,000 = 9,00,000/50,00,000 = 18%.
- Check Prop. II: 15 + (15 − 10)(30/50) = 15 + 3 = 18%. WACC of L = (50/80)18 + (30/80)10 = 11.25 + 3.75 = 15% — unchanged.
With 30% tax: Vu = 12,00,000(0.70)/0.15 = 8,40,000/0.15 = ₹56,00,000; Vl = 56,00,000 + 0.30 × 30,00,000 = 56,00,000 + 9,00,000 = ₹65,00,000. The ₹9,00,000 gain is the present value of the interest tax shield.

Example 5 — Marginal cost of capital and break point. Target structure: 60% equity, 40% debt. Retained earnings available ₹18,00,000 (Kr = 15%); fresh equity would cost 17%. Debt up to ₹10,00,000 at 10% pre-tax, beyond that 13%; tax 30%.

Break point (equity) = 18,00,000/0.60 = ₹30,00,000; break point (debt) = 10,00,000/0.40 = ₹25,00,000.
Up to ₹25,00,000 raised: WACC = 0.60(15) + 0.40(10 × 0.7) = 9.00 + 2.80 = 11.80%
₹25,00,000 to ₹30,00,000: WACC = 0.60(15) + 0.40(13 × 0.7) = 9.00 + 3.64 = 12.64%
Above ₹30,00,000: WACC = 0.60(17) + 0.40(9.10) = 10.20 + 3.64 = 13.84% — accept only projects returning more than the MCC at that level.

Approach	Ke as debt rises	Kd	Ko (WACC)	Optimum structure
Net Income	Constant	Constant	Falls	Maximum debt
Net Operating Income	Rises	Constant	Constant	None (indifferent)
Traditional	Rises slowly, then sharply	Rises after a point	Saucer-shaped	At minimum Ko
MM (no tax)	Rises linearly	Constant	Constant	None
MM (with tax)	Rises	Constant	Falls	100% debt (theoretical)
Trade-off	Rises with distress risk	Rises with risk	U-shaped	Tax shield = distress cost

Where it is used

Corporate finance and treasury teams (Reliance, Tata Steel, L&T, Infosys): setting the internal hurdle rate, deciding between an NCD issue, an ECB, a QIP or a rights issue, and tracking the target debt-equity ratio against covenants.
Equity research and investment banking: WACC is the discount rate in DCF valuation; analysts build it from a G-Sec risk-free rate, a regression beta against NIFTY and an equity risk premium, then re-lever beta for the target structure.
Credit rating and lending: CRISIL, ICRA and CARE and bank credit teams judge gearing, interest coverage and debt-service capacity — the practical limits on leverage; capital structure drives the rating, and the rating drives Kd, a visible feedback loop.
Infrastructure and project finance: NHAI/HAM road projects, renewable SPVs and power plants are structured to a target debt-equity (commonly around 70:30 or 75:25) because the tax shield and lower Kd make long-tenor debt essential to the bid price.
Regulated utilities: tariff orders by CERC and state electricity regulatory commissions allow a specified return on equity on a normative debt-equity mix, making the cost of capital a regulatory variable rather than a market one.
Exams and roles: CA/CS/CMA Financial Management papers, CFA Level I, MBA finance entrance and campus tests for analyst roles at Deloitte, KPMG, EY, Nomura, HSBC and corporate FP&A teams.

Interview questions

Q: What exactly does WACC mean, and why do we use it as a discount rate? A: It is the blended minimum return demanded by all suppliers of capital, weighted by their share; a project earning more than WACC adds value, so it is the correct discount rate for projects of average risk.
Q: Why is debt cheaper than equity? A: Lenders bear less risk (fixed contractual claim, prior charge, often secured) and interest is tax-deductible, so the after-tax cost to the firm is Kd(1 − t).
Q: If debt is cheaper, why not fund entirely with debt? A: Rising leverage raises financial risk, so Ke and eventually Kd rise, and expected financial distress and agency costs plus covenant and IBC consequences outweigh the tax shield past some point.
Q: Are retained earnings free of cost? A: No — they carry the opportunity cost of what shareholders could have earned, so Kr is roughly Ke, lower only by issue costs and shareholder-level tax.
Q: Should we use book value or market value weights? A: Market value weights, because they reflect today's required returns and the actual proportions investors hold; book weights are used when market values are unavailable, and target weights for long-run planning.
Q: What is the MM arbitrage argument in one line? A: An investor can replicate or undo corporate leverage with personal borrowing, so two firms with the same EBIT and business risk cannot sell at different values in equilibrium.
Q: How does MM change when corporate tax is introduced? A: The deductibility of interest creates a tax shield worth t×D, so Vl = Vu + tD and value rises with debt — the result that trade-off theory then tempers with distress costs.
Q: What is the EBIT indifference point and how do you use it? A: The EBIT at which EPS is the same under two financing plans; if expected EBIT is comfortably above it, the debt plan raises EPS, and the margin of safety tells you how much EBIT volatility the leverage can absorb.
Q: When does trading on equity backfire? A: When return on capital employed falls below the interest rate on debt (compared on the same pre-tax basis) — leverage then magnifies the fall in EPS and can wipe out equity earnings.
Q: How would you estimate the cost of equity for an unlisted Indian company? A: Take an average unlevered beta of comparable listed firms, re-lever it to the target D/E using the Hamada relation, apply CAPM with a G-Sec risk-free rate, and add a size or company-specific risk premium.
Q: Two divisions, one steel and one software, in the same group — same hurdle rate? A: No; a single corporate WACC subsidises the riskier division and penalises the safer one, so use risk-adjusted divisional rates built from pure-play betas.
Q: What does pecking order theory predict about highly profitable firms? A: That they carry less debt, because internal accruals are the preferred and cheapest source and they need external funding less — the opposite of what trade-off theory alone would suggest.

Common mistakes

Dividing by face value instead of net proceeds when computing Kd, Kp or Ke of a fresh issue.
Applying (1 − t) to preference dividends, or forgetting it for interest.
Using D₀ instead of D₁ in the Gordon model — D₁ = D₀(1 + g).
Mixing weights and costs: using market value weights with historic book-based costs, or quoting some costs pre-tax and others post-tax in the same WACC.
Treating retained earnings as costless, which understates WACC and makes bad projects look acceptable.
Confusing the NI and NOI approaches, or stating MM's conclusion without its assumptions (no taxes, perfect markets, no bankruptcy cost, homogeneous risk classes).
Comparing a pre-tax ROCE with an after-tax Kd when judging whether leverage pays — the two sides must be on the same tax basis.
In EBIT-EPS problems, forgetting preference dividend is not tax-deductible — it must be subtracted after tax, so the financial break-even uses Dp/(1 − t).