Cost of capital and capital structure theories
Cost of capital is the minimum return investors require; WACC weights each source by its share. Capital structure theories differ on whether debt can raise firm value.
Cost of each source
| Source | Formula | Note |
|---|---|---|
| Irredeemable debt | Kd = I(1 − t) ÷ NP | Interest is tax-deductible |
| Redeemable debt | Kd = [I(1 − t) + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2] | Short-cut yield; RV = redemption value, NP = net proceeds, n = years |
| Preference shares | Kp = D ÷ NP; if redeemable, [D + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2] | No tax adjustment: paid from post-tax profit |
| Equity: dividend growth | Ke = D1 ÷ P0 + g, where D1 = D0(1 + g) | Use net proceeds for a new issue |
| Equity: CAPM | Ke = Rf + β(Rm − Rf) | β measures systematic risk |
| Retained earnings | Kr = Ke (opportunity cost to shareholders) | Below the cost of new equity, as there is no flotation cost |
Cost of debt and equity
(a) 10% debentures of ₹100 issued at ₹95, redeemable at par after 5 years; tax 30%. (b) Expected dividend ₹5, share price ₹50, growth 6%. (c) Risk-free rate 6%, market return 12%, beta 1.2.
- (a) After-tax interest = 10 × (1 − 0.30) = ₹7; discount spread over the life = (100 − 95) ÷ 5 = ₹1 a year
- Kd = (7 + 1) ÷ [(100 + 95) ÷ 2] = 8 ÷ 97.5 = 8.21%
- If the debentures were irredeemable: Kd = 7 ÷ 95 = 7.37%
- (b) Ke = 5 ÷ 50 + 6% = 10% + 6% = 16%
- (c) Ke = 6% + 1.2 × (12% − 6%) = 6% + 7.2% = 13.2%
Kd 8.21% (redeemable) or 7.37% (irredeemable); Ke 16% by the dividend growth model and 13.2% by CAPM. Rounded to two decimals.
Weighted average cost of capital
Equity ₹6,00,000 costing 15%; debt ₹3,00,000 with an after-tax cost of 7%; preference capital ₹1,00,000 costing 10%. Use book-value weights.
- Total capital = 6,00,000 + 3,00,000 + 1,00,000 = ₹10,00,000
- Weights: equity 0.6, debt 0.3, preference 0.1
- WACC = 0.6 × 15% + 0.3 × 7% + 0.1 × 10% = 9% + 2.1% + 1% = 12.1%
- Check in rupees: 90,000 + 21,000 + 10,000 = ₹1,21,000 on ₹10,00,000 = 12.1%
WACC = 12.1%.
WACC choices
- Weights can be book values or market values; market weights are preferred in theory.
- Marginal cost of capital is the cost of the next rupee raised.
- WACC is the hurdle (cut-off) rate for capital budgeting decisions.
Capital structure theories
| Theory | Author and year | Key claim | Optimal structure |
|---|---|---|---|
| Net income (NI) | David Durand, 1952 | Ke and Kd stay constant and Kd < Ke, so more debt lowers WACC and raises value | Maximum debt |
| Net operating income (NOI) | David Durand, 1952 | Ko and Kd constant; Ke rises with debt and offsets cheaper debt; value is independent of the mix | None: every mix is the same |
| Traditional | Intermediate view, often linked to Ezra Solomon | Moderate debt lowers WACC; beyond a point Ke and Kd rise; WACC is U-shaped | Yes, at moderate debt |
| MM without taxes | Modigliani and Miller, 1958 | Arbitrage keeps VL = VU; Ke = Ko + (Ko − Kd) × D/E | None (irrelevance) |
| MM with corporate tax | Modigliani and Miller, 1963 | Interest tax shield: VL = VU + tD | Maximum debt, in theory |
| Static trade-off | Kraus and Litzenberger, 1973 | Tax shield of debt is weighed against bankruptcy (financial distress) costs | Yes, where the marginal tax saving equals the marginal distress cost |
| Pecking order | Myers and Majluf, 1984 | Firms prefer internal funds, then debt, then equity, because of information asymmetry | No target ratio |
NI versus NOI approach
EBIT ₹2,00,000; debt ₹5,00,000 at 10%. (a) NI approach with Ke 12.5%. (b) NOI approach with Ko 12.5%.
- Interest = 10% × 5,00,000 = ₹50,000; earnings for equity = 2,00,000 − 50,000 = ₹1,50,000
- (a) NI: equity value S = 1,50,000 ÷ 0.125 = ₹12,00,000; V = 12,00,000 + 5,00,000 = ₹17,00,000; Ko = 2,00,000 ÷ 17,00,000 = 11.76%
- (b) NOI: V = 2,00,000 ÷ 0.125 = ₹16,00,000; S = 16,00,000 − 5,00,000 = ₹11,00,000
- Ke under NOI = 1,50,000 ÷ 11,00,000 = 13.64%
NI: value ₹17,00,000, Ko 11.76%. NOI: value ₹16,00,000, Ke 13.64%. Rounded to two decimals.
MM with corporate taxes
An unlevered firm is worth ₹20,00,000. An identical firm has ₹10,00,000 of debt. Corporate tax is 30%.
- Tax shield = t × D = 0.30 × 10,00,000 = ₹3,00,000
- VL = VU + tD = 20,00,000 + 3,00,000 = ₹23,00,000
The levered firm is worth ₹23,00,000. Without taxes (MM 1958) it would also be worth ₹20,00,000.
MM assumptions (1958)
- Perfect capital markets: no transaction costs; investors are rational and well informed.
- Investors can borrow and lend at the same rate as firms (home-made leverage).
- Firms fall into homogeneous risk classes.
- No corporate taxes (relaxed in 1963) and a 100% dividend payout.
- Arbitrage restores equal values when two identical firms differ only in leverage.
NET asks one-line cost of capital sums (after-tax Kd, Gordon, CAPM, WACC), matches theories with their claims and authors, and tests MM's propositions with and without taxes.
Typical MCQ: “D0 ₹2, growth 5%, price ₹42. What is the cost of equity?” D1 = ₹2.10; Ke = 2.10 ÷ 42 + 5% = 10%. Trap: using D0 gives 9.76%.
Typical MCQ: “Which theory says WACC is U-shaped and an optimal capital structure exists?” The traditional approach. NI says maximum debt; NOI and MM (1958) say capital structure is irrelevant.
Typical MCQ: “Why is the cost of preference capital not adjusted for tax?” Preference dividend is paid out of post-tax profit, so it gives no tax saving.
NI: debt is nice. NOI: no impact. Traditional: the middle is best. MM 1958: irrelevant. MM 1963: add the tax shield tD.