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Specific Cost of Capital: Formulas and Calculation

Prerequisites

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1. Cost of Debt (Kd)

Definition: The effective rate of interest that a company pays on its borrowed funds (debentures, bonds, loans).

1.1 Formula (After-Tax Cost)

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Why (1-T)? Because interest is tax-deductible, it reduces taxable income. The actual cost to company is lower.

Tax Shield Effect:

If Interest = ₹12,000 and Tax Rate = 30%
Tax Saved = ₹12,000 × 0.30 = ₹3,600
Effective Cost = ₹12,000 - ₹3,600 = ₹8,400

1.2 Numerical Problem (Exam Format)

Problem: A company issues 10% debentures of ₹100 each at a discount of 5%. The tax rate is 30%. Calculate the cost of debt.

Given:

Face Value (FV) = ₹100
Interest Rate = 10%
Discount = 5%
Tax Rate (T) = 30% = 0.30

Formula:

Kd = [I × (1 - T)] / Net Proceeds

Solution:

Step 1: Calculate Annual Interest

Interest (I) = Face Value × Interest Rate
I = ₹100 × 10/100
I = ₹10 per debenture

Step 2: Calculate Net Proceeds

Net Proceeds = Face Value - Discount
NP = ₹100 - (5% of ₹100)
NP = ₹100 - ₹5
NP = ₹95

Step 3: Calculate After-Tax Cost of Debt

Kd = [I × (1 - T)] / NP
Kd = [₹10 × (1 - 0.30)] / ₹95
Kd = [₹10 × 0.70] / ₹95
Kd = ₹7 / ₹95
Kd = 0.0737 or 7.37%

Answer: The cost of debt is 7.37%.

2. Cost of Preference Shares (Kp)

Definition: The rate of return expected by preference shareholders, considering the fixed dividend and any discount/premium on issue.

2.1 Formula

Cost of Preference Share Formula

Kp = Preference Dividend / Net Proceeds

OR

Kp = D / NP

Where:

  • D = Annual Preference Dividend (Fixed)
  • NP = Net Proceeds after flotation costs

Note: Preference dividend is NOT tax-deductible (unlike debt interest).

2.2 Numerical Problem (Exam Format)

Problem: A company issues 12% Preference Shares of ₹100 each at par with flotation costs of ₹2 per share. Calculate the cost of preference capital.

Given:

Face Value = ₹100
Dividend Rate = 12%
Flotation Cost = ₹2 per share
Issue Price = At par = ₹100

Formula:

Kp = Annual Dividend / Net Proceeds

Solution:

Step 1: Calculate Annual Dividend

Dividend (D) = Face Value × Dividend Rate
D = ₹100 × 12/100
D = ₹12 per share

Step 2: Calculate Net Proceeds

Net Proceeds = Issue Price - Flotation Cost
NP = ₹100 - ₹2
NP = ₹98

Step 3: Calculate Cost of Preference Shares

Kp = D / NP
Kp = ₹12 / ₹98
Kp = 0.1224 or 12.24%

Answer: The cost of preference capital is 12.24%.

3. Cost of Equity (Ke)

Definition: The minimum rate of return that equity shareholders expect for providing capital to the company.

3.1 Dividend Growth Model (Gordon Model)

Dividend Growth Model Formula

Ke = (D1 / P0) + g

Where:

  • D1 = Expected Dividend next year
  • P0 = Current Market Price per share
  • g = Constant Growth Rate of dividends

Alternative: If current dividend (D0) is given:

D1 = D0 × (1 + g)
So, Ke = [D0(1+g) / P0] + g

3.2 Numerical Problem (Exam Format)

Problem: A company's equity share is currently selling at ₹50. The expected dividend is ₹5 per share, and dividends are expected to grow at 6% per annum. Calculate the cost of equity.

Given:

Current Market Price (P0) = ₹50
Expected Dividend next year (D1) = ₹5
Growth Rate (g) = 6% = 0.06

Formula:

Ke = (D1 / P0) + g

Solution:

Step 1: Apply the Formula

Ke = (D1 / P0) + g
Ke = (₹5 / ₹50) + 0.06
Ke = 0.10 + 0.06
Ke = 0.16 or 16%

Answer: The cost of equity is 16%.

3.3 CAPM Model (Capital Asset Pricing Model)

CAPM Formula

Ke = Rf + β(Rm - Rf)

Where:

  • Rf = Risk-Free Rate (e.g., Govt. bond yield)
  • β (Beta) = Systematic Risk of the stock
  • Rm = Expected Return on Market
  • (Rm - Rf) = Market Risk Premium

Problem: Calculate cost of equity if Risk-free rate is 8%, Beta is 1.2, and Market return is 14%.

Given:

Rf = 8% = 0.08
β = 1.2
Rm = 14% = 0.14

Solution:

Ke = Rf + β(Rm - Rf)
Ke = 0.08 + 1.2(0.14 - 0.08)
Ke = 0.08 + 1.2(0.06)
Ke = 0.08 + 0.072
Ke = 0.152 or 15.2%

Answer: Cost of equity = 15.2%

4. Cost of Retained Earnings (Kr)

Definition: The opportunity cost to shareholders when profit is retained instead of distributed as dividend.

4.1 Concept

Key Principle: Kr = Ke (approximately)

Reasoning:

  • Retained earnings belong to equity shareholders
  • If distributed, shareholders could invest elsewhere at Ke
  • By retaining, company must earn at least Ke
  • Opportunity Cost = Return shareholders forego = Ke

4.2 Adjusted Formula (if tax considered)

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5. Summary Comparison Table

SourceCost FormulaTax Shield?Numerical Example
DebtKd = I(1-T)/NP✓ Yes10% debt, 30% tax → 7%
PreferenceKp = D/NP✗ No12% Pref → 12%
EquityKe = D1/P0 + g✗ NoD=₹5, P=₹50, g=6% → 16%
Retained EarningsKr = Ke✗ NoSame as Equity → 16%

Exam Pattern Questions and Answers

Question 1: "Calculate the cost of debentures." (4 Marks) Given: 10% Debentures of ₹1,000, issued at 10% discount, tax rate 30%.

Solution:

Interest = ₹1,000 × 10% = ₹100
Net Proceeds = ₹1,000 - ₹100 = ₹900
Kd = [100 × (1-0.30)] / 900
Kd = 70 / 900 = 0.0778

Answer: 7.78%

Question 2: "Company issues equity at ₹100, expects ₹10 dividend growing at 5%. Find Ke." (2 Marks)

Solution:

Ke = (D1/P0) + g
Ke = (10/100) + 0.05
Ke = 0.10 + 0.05 = 0.15

Answer: 15%

Summary

Four Specific Costs:

  1. Debt: Tax-deductible, cheapest
  2. Preference: Fixed dividend, no tax benefit
  3. Equity: Highest cost, no repayment
  4. Retained Earnings: Opportunity cost = Ke

Key Formulas:

  • Kd = I(1-T) / NP
  • Kp = D / NP
  • Ke = (D1/P0) + g OR Rf + β(Rm-Rf)
  • Kr = Ke

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