Unit 2: Cost of capital and capital structure
Corporate Finance and Policy notes · PTU syllabus (MBA 206-21)
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Unit summary
Every source of funds has a cost, and the mix of debt and equity may affect the value of the firm. This unit covers the concept and significance of cost of capital, specific costs and the weighted average cost of capital, capital structure theories — Net Income, Net Operating Income, Traditional and Modigliani–Miller (including the arbitrage process and agency costs) — the determinants of capital structure, and EBIT–EPS and ROI–ROE analysis.
After this unit you can
- Explain the concept and significance of cost of capital
- Compute specific costs and the WACC
- Explain capital structure theories, arbitrage and agency costs
- Apply EBIT–EPS and ROI–ROE analysis and identify the determinants of capital structure
PTU syllabus topics
- Concept and significance of cost of capital
- specific and weighted average cost of capital
- capital structure theories — Net Income
- Net Operating Income
- Traditional
- Modigliani-Miller (arbitrage process and agency cost)
- determinants of capital structure
- EBIT/EPS and ROI/ROE analysis
Cost of debt
Kd = I (1 − t) / net proceeds
Cost of equity (CAPM)
Ke = Rf + β (Rm − Rf)
Cost of equity (Gordon)
Ke = D1 / P0 + g
WACC
Σ wi ki
Topic 1
Cost of capital: concept, specific costs and WACC
Cost of capital is the minimum rate of return a firm must earn on its investments to maintain the market value of its shares — the hurdle rate for capital budgeting.
Cost of irredeemable debt (after tax)
Kd = I (1 − t) ÷ NP
Cost of redeemable debt
Kd = [I (1 − t) + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2]
Cost of preference shares
Kp = D ÷ NP (irredeemable); [D + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2] (redeemable)
Cost of equity — dividend growth (Gordon)
Ke = D1 ÷ P0 + g
Cost of equity — CAPM
Ke = Rf + β (Rm − Rf)
Cost of retained earnings
Kr = Ke (adjusted for personal tax and floatation, if given)
Weighted average cost of capital
WACC = Σ (Weight × Specific cost)
Example
10% debentures of ₹100 issued at ₹95, redeemable at par in 5 years, tax 30%. Kd = [10 × 0.7 + (100 − 95) ÷ 5] ÷ [(100 + 95) ÷ 2] = (7 + 1) ÷ 97.5 = 8.21%.
| Source | Amount (₹) | Weight | Cost | Weighted cost |
|---|---|---|---|---|
| Equity | 6,00,000 | 0.60 | 15% | 9.0% |
| Preference | 1,00,000 | 0.10 | 11% | 1.1% |
| Debt | 3,00,000 | 0.30 | 7% (after tax) | 2.1% |
| WACC | 10,00,000 | 1.00 | 12.2% |
- Book value weights vs market value weights — market weights are theoretically superior.
- Significance: capital budgeting cut-off, capital structure decisions, evaluating financial performance, dividend decisions.
Topic 2
Theories of capital structure
Net Income (NI) approach — Durand
Yes
Kd and Ke constant; more debt lowers WACC and raises value
Net Operating Income (NOI) approach — Durand
No
WACC constant; Ke rises with debt, offsetting cheap debt
Traditional approach
Yes, up to a point
Moderate debt lowers WACC; excessive debt raises it — optimal structure exists
Modigliani–Miller (1958, no taxes)
No
Arbitrage keeps value equal for levered and unlevered firms
MM with taxes (1963)
Yes
Interest tax shield: VL = VU + tD
Example
NI approach: EBIT ₹2,00,000; debt ₹5,00,000 at 10%; Ke 12.5%. Earnings for equity = 1,50,000; value of equity = 1,50,000 ÷ 0.125 = ₹12,00,000; value of firm = ₹17,00,000; overall cost = 2,00,000 ÷ 17,00,000 = 11.76%.
- MM assumptions: perfect capital markets, no transaction costs, homogeneous expectations, same risk class, 100% payout, no taxes (1958). Arbitrage process equalises values.
- Trade-off theory: balances tax benefits of debt against bankruptcy and agency costs. Pecking order theory: firms prefer internal funds, then debt, then equity.
- Miller model (1977): with corporate and personal taxes, the gain from leverage = [1 − (1 − tc)(1 − tps) ÷ (1 − td)] × D; if personal tax on debt income is high enough, the advantage of corporate debt may vanish — capital structure irrelevance in equilibrium.
Topic 3
Financial distress and agency costs
- Costs of financial distress: direct (legal and administrative costs of bankruptcy) and indirect (lost sales, supplier credit withdrawn, employee exit, underinvestment).
- Agency costs of debt: asset substitution (risk shifting), underinvestment (debt overhang), claim dilution — controlled by covenants.
- Agency costs of equity: perquisites, empire-building — reduced by debt discipline (Jensen's free cash flow hypothesis).
- Trade-off theory: optimal debt balances tax shields against distress and agency costs; pecking order theory (Myers–Majluf): internal funds → debt → equity, due to information asymmetry.
Topic 4
Determinants of capital structure
Internal factors
Cash flow position, cost of capital, risk appetite, control considerations, size and age of firm, asset structure
External factors
Capital market conditions, interest rates, tax rates, regulatory norms (SEBI, RBI), lenders' policies
Business factors
Stability of sales and earnings, growth rate, nature of industry
- Stable cash flows and tangible assets support more debt (utilities, infrastructure); volatile businesses use more equity (technology start-ups).
Topic 5
EBIT–EPS analysis
EBIT–EPS analysis compares financing plans by their effect on EPS at various levels of EBIT.
EPS
[(EBIT − I)(1 − t) − Preference dividend] ÷ Number of equity shares
Indifference point (equity vs debt)
[(X − I1)(1 − t)] ÷ N1 = [(X − I2)(1 − t)] ÷ N2
Example
Need ₹10 lakh. Plan A: all equity (1,00,000 shares of ₹10). Plan B: ₹5 lakh equity (50,000 shares) + ₹5 lakh debt at 10%. Tax 30%. At EBIT ₹2,00,000: EPS A = 1,40,000 ÷ 1,00,000 = ₹1.40; EPS B = (2,00,000 − 50,000) × 0.7 ÷ 50,000 = ₹2.10. Indifference point: X ÷ 1,00,000 = (X − 50,000) ÷ 50,000 → X = ₹1,00,000. Above ₹1 lakh EBIT, debt gives higher EPS.
Topic 6
ROI–ROE analysis
ROE (after tax)
[ROI + (ROI − i) × D/E] × (1 − t)
Interpretation
If ROI > cost of debt (i), more debt raises ROE (favourable leverage)
Example
ROI 18%, interest 10%, D/E 1, tax 25%: ROE = [18 + (8 × 1)] × 0.75 = 19.5%; with D/E 0, ROE = 13.5%.
Key terms
- WACC
- Weighted average of the costs of all sources of finance
- Arbitrage
- Buying and selling to profit from price differences for identical assets
- Agency cost
- Cost arising from conflicts between managers, shareholders and lenders
- Indifference point
- EBIT at which EPS is the same under two plans
- Trading on equity
- Using debt to raise returns to equity
Quick revision
- Kd after tax; Kp; Ke (Gordon, CAPM); Kr; WACC with book or market weights.
- NI (leverage matters), NOI (irrelevant), Traditional (optimum), MM (irrelevant; with tax, debt adds value).
- Arbitrage equalises values; trade-off and pecking order theories.
- Determinants: internal and external factors.
- EBIT–EPS indifference point; ROE = [ROI + (ROI − i)D/E](1 − t).
Important exam questions
Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).
Short-answer questions
- Q1.Define cost of capital.
- Q2.Why is the cost of debt computed after tax?
- Q3.State the NI approach.
- Q4.What is the arbitrage process in MM theory?
- Q5.What is an EBIT–EPS indifference point?
- Q6.State four determinants of capital structure.
Long-answer questions
- Q1.Explain the computation of specific costs of capital and WACC.
- Q2.Critically examine the NI, NOI and Traditional approaches to capital structure.
- Q3.Explain the Modigliani–Miller theory with the arbitrage process and its criticisms.
- Q4.Explain EBIT–EPS and ROI–ROE analysis with examples.
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