Cost of capital: debt, preference, equity and short-term borrowing

1. Meaning

The cost of capital is the minimum rate of return a firm must earn on its investments so that the market value of its shares does not fall. It is the rate the suppliers of funds expect, given the risk they bear. Seen from the investment side it is the cut-off or hurdle rate: a project that earns less than it reduces the value of the firm. Each source has a specific cost (k_d, k_p, k_e, k_r); their weighted average is the overall cost (WACC, next note).

2. Importance (benefits)

• Capital budgeting: it is the discount rate for NPV and the cut-off for IRR.
• Capital structure: the firm mixes sources so as to lower the overall cost.
• Choice of source: it shows which source is cheapest after tax.
• Performance evaluation: the return actually earned is judged against it.
• Dividend and working-capital decisions: retention is justified only if retained funds earn more than the shareholders’ required rate; the cost of short-term funds guides working-capital financing.

3. Cost of debt

Irredeemable debt: k_d = I(1 − t) ÷ NP, where I is the annual interest, t the tax rate and NP the net proceeds. Interest is tax-deductible, which is why debt is the cheapest source.

Redeemable debt (approximation method):

k_d (after tax) = [I(1 − t) + (RV − NP)/n] ÷ [(RV + NP)/2]
k_d (before tax) = [I + (RV − NP)/n] ÷ [(RV + NP)/2]

RV is the redemption value, NP the net amount realised, n the years to maturity.

Worked problem (January 2026). 10% debentures of Rs. 10,00,000 realise Rs. 9,00,000 after a 10% discount; redeemable at a 10% premium after 5 years; tax 50%.

Before tax: (1,00,000 + 40,000) ÷ 10,00,000 = 14%.
After tax: (1,00,000 × 0.5 + 40,000) ÷ 10,00,000 = 90,000 ÷ 10,00,000 = 9%.

Worked problem (August 2024, part i). A 5-year Rs. 100 debenture sells for a net Rs. 96.50; coupon 14%; redeemable at a 5% premium; tax 40%.

k_d = [14 × 0.6 + (105 − 96.50)/5] ÷ [(105 + 96.50)/2] = (8.40 + 1.70) ÷ 100.75 = 10.02% after tax (before tax: 15.70 ÷ 100.75 = 15.58%).

4. Cost of preference capital

Irredeemable: k_p = D ÷ NP. Redeemable: k_p = [D + (RV − NP)/n] ÷ [(RV + NP)/2]. No tax adjustment: preference dividend is paid out of after-tax profit.

Worked problem (August 2024, part ii). Face value Rs. 50, 14% dividend, realises Rs. 42, repayable at par after 12 years. D = Rs. 7.

k_p = [7 + (50 − 42)/12] ÷ [(50 + 42)/2] = (7 + 0.667) ÷ 46 = 16.67%.

5. Cost of equity

• Dividend yield method: k_e = D₁ ÷ P₀ (no growth).
• Dividend growth (Gordon) model: k_e = D₁ ÷ P₀ + g. A share at Rs. 20 expected to pay Rs. 2 growing at 7% has k_e = 10% + 7% = 17% (February 2025).
• Earnings-price method: k_e = EPS ÷ MPS.
• CAPM: k_e = R_f + β(R_m − R_f) (separate note on Sharpe–Lintner).

For a new issue, use the net proceeds after flotation cost in place of the market price. Equity has no fixed charge, yet it is the dearest source, because the shareholder bears the highest risk.

Retained earnings are not free. They belong to the shareholders, who could have invested the dividend elsewhere. Their cost (k_r) equals k_e, or slightly less where the shareholder would have paid personal tax and brokerage: k_r = k_e(1 − t_p)(1 − f), where t_p is the personal tax rate and f the brokerage.

6. Cost of short-term borrowing

Trade credit. It looks free, but giving up a cash discount has a cost. On terms “2/10, net 30” the buyer who pays on day 30 instead of day 10 pays Rs. 2 extra on Rs. 98 for 20 days: annual cost = 2/98 × 365/20 = 37.24%.

Bank loans. Effective cost = interest paid ÷ usable funds. If a bank lends Rs. 1,00,000 at 12% but deducts the interest in advance (a discounted loan), the firm has Rs. 88,000 and pays Rs. 12,000: 13.64%. A compensating balance has the same effect. Commercial paper and bank overdraft are costed the same way, after tax where the interest is deductible.

How this is examined

January 2026 set the debenture problem in section 3 (10 marks) and the benefits of cost of capital (6 marks); August 2024 set the debenture and preference pair (10 marks) and the importance of cost of capital (6 marks); February 2025 asked a short note on cost of capital. In every problem, state the formula, the symbols and the figures before the answer; most of the marks are for the layout.