Understanding Cost of Capital, Risk, and Return in Finance
Chapter 11: Rates of Return and Risk
Calculating Rates of Return
Percentage Return = (Capital Gain + Dividend) / Initial Share Price
Dividend Yield = Dividend / Initial Share Price
Capital Gain Yield = Capital Gain / Initial Share Price
Real Rate of Return: 1 + Real Rate of Return = (1 + Nominal Rate of Return) / (1 + Inflation Rate)
Example:
Assume you bought a stock for $75.06 and received $1.37 in dividends. The stock’s year-end price is $93.29, and inflation was 4.1%.
Percentage Return = (18.23 + 1.37) / 75.06 = 26.1%
Dividend Yield = 1.37 / 75.06 = 1.8%
Capital Gain Yield = 18.23 / 75.06 = 24.3%
Real Rate of Return = (1 + 0.261) / (1 + 0.041) = 21.1%
Average Rates of Return and Risk
Average Return = (R1 + R2 + … + RT) / T
Variance = [(R1 – Average Return)^2 + (R2 – Average Return)^2 + … + (RT – Average Return)^2] / T
Standard Deviation = Square Root of Variance
Portfolio Risk and Diversification
Portfolio Expected Return: E(r) = Σ [p(s) * r(s)]
Portfolio Variance: σ^2 = Σ [p(s) * (r(s) – E(r))^2]
Diversification is investing in various assets to reduce risk. Owning assets across different industries is more effective than owning many assets within the same industry.
Principles of Diversification:
- Combining uncorrelated assets reduces portfolio variability.
- Diversification minimizes risk without sacrificing expected returns.
- Systematic risk (market risk) cannot be diversified away.
Types of Risk:
- Unique Risk: Affects a specific company or industry (e.g., labor strikes).
- Market Risk: Affects the entire market (e.g., changes in GDP, inflation).
Chapter 12: Capital Asset Pricing Model (CAPM) and Beta
Market Portfolio and Beta
Market Portfolio: A theoretical portfolio containing all assets in the economy. In practice, a broad market index like the S&P 500 is used.
Beta (β): Measures a stock’s sensitivity to market movements. A beta of 1 indicates the stock moves in line with the market. A beta greater than 1 implies higher volatility, while a beta less than 1 suggests lower volatility.
Calculating Portfolio Beta:
Portfolio Beta = Σ [Weight(s) * Beta(s)]
CAPM and Expected Return
CAPM Equation: E(ri) = rf + βi * (E(rM) – rf)
Where:
- E(ri) = Expected return on asset i
- rf = Risk-free rate
- βi = Beta of asset i
- E(rM) = Expected return on the market portfolio
Example:
If the risk-free rate is 3%, the market risk premium is 7%, and Dell’s beta is 1.27, then:
Expected Return on Dell = 3% + 1.27 * (7%) = 11.9%
Total Risk vs. Systematic Risk
Total Risk: Measured by standard deviation (σ), includes both market risk and firm-specific risk.
Systematic Risk: Measured by beta (β), represents the risk inherent to the overall market.
Project Evaluation and Cost of Capital
The cost of capital for a project depends on its risk, not the company’s overall risk. Projects with higher risk require a higher discount rate.
Chapter 13: Weighted Average Cost of Capital (WACC)
WACC and its Components
WACC: The average rate of return a company expects to pay on its capital structure.
WACC Formula: WACC = (E/V * Re) + (D/V * Rd * (1 – Tc)) + (P/V * Rp)
Where:
- E = Market value of equity
- D = Market value of debt
- V = Total market value of the firm (E + D + P)
- Re = Cost of equity
- Rd = Cost of debt
- Tc = Corporate tax rate
- P = Market value of preferred stock
- Rp = Cost of preferred stock
Measuring Capital Structure
Use market values, not book values, when calculating WACC.
Calculating Required Rates of Return
Cost of Debt (Rd): Typically estimated using the yield to maturity (YTM) on the company’s existing debt.
Cost of Equity (Re):
- CAPM: Re = rf + β * (rm – rf)
- Dividend Discount Model (DDM): Re = (D1 / P0) + g
Cost of Preferred Stock (Rp): Rp = Dividend / P0
Example:
Assume a company has the following information:
- Equity: 50 million shares, $80 per share, beta = 1.15
- Debt: $1 billion outstanding, current quote = 110% of face value, coupon rate = 9%, 15 years to maturity
- Market risk premium = 9%
- Risk-free rate = 5%
- Tax rate = 40%
Calculating WACC:
- E = 50 million * $80 = $4 billion
- D = $1 billion * 110% = $1.1 billion
- V = $4 billion + $1.1 billion = $5.1 billion
- Re = 5% + 1.15 * 9% = 15.35%
- Rd = 7.85% (calculated using YTM)
- WACC = (0.78 * 15.35%) + (0.22 * 7.85% * (1 – 0.40)) = 13.01%