Intro to Finance: Cost of Capital - Cost of Common, Equity CAPM DDM Bond Yield Plus Risk Premium

What This Is

The cost of common equity is a crucial concept in finance that represents the minimum return required by investors to compensate for the risk of investing in a company's common stock. It's essential for calculating the Weighted Average Cost of Capital (WACC) and making investment decisions. For example, if Apple's cost of common equity is 10%, it means investors expect a 10% return on their investment in Apple's common stock.

Key Formulas & Symbols

• CAPM = Rf + ?(Rm - Rf) where CAPM = Capital Asset Pricing Model, Rf = risk-free rate,-= beta, Rm = market return.
• Rf: the risk-free rate, typically the yield on a long-term government bond (e.g., 10-year Treasury bond).
• ?: a measure of a stock's systematic risk (e.g., Apple's beta is 1.1).

• Rm: the market return, typically the return on the S&P 500 index.

• DDM = P0 / (r - g) where DDM = Dividend Discount Model, P0 = current stock price, r = cost of equity, g = growth rate.

• P0: the current stock price (e.g., Apple's current stock price is $150).
• r: the cost of equity (e.g., 10%).

• g: the growth rate of dividends (e.g., 5%).

• Bond Yield Plus Risk Premium = (1 + r) where r = bond yield + risk premium.

• r: the bond yield plus risk premium (e.g., 8% bond yield + 2% risk premium = 10%).

• WACC = (E/V) * Re + (D/V) * Rd * (1 - T) where WACC = Weighted Average Cost of Capital, E = market value of equity, V = total market value, Re = cost of equity, D = market value of debt, Rd = cost of debt, T = tax rate.

• E: the market value of equity (e.g., Apple's market value of equity is $1 trillion).
• V: the total market value (e.g., Apple's total market value is $2 trillion).
• Re: the cost of equity (e.g., 10%).
• D: the market value of debt (e.g., Apple's market value of debt is $500 billion).
• Rd: the cost of debt (e.g., 5%).
• T: the tax rate (e.g., 20%).

Step-by-Step Calculation

1. Calculate the CAPM using historical data:
2. Rf = 2% (10-year Treasury bond yield)
3. ? = 1.1 (Apple's beta)
4. Rm = 8% (S&P 500 return)

5. CAPM = 2% + 1.1(8% - 2%) = 9.8%

6. Calculate the cost of equity using the DDM:

7. P0 = $150 (Apple's current stock price)
8. r = 10% (cost of equity)
9. g = 5% (growth rate of dividends)

10. DDM = $150 / (10% - 5%) = $3,000

11. Calculate the WACC:

12. E = $1 trillion (Apple's market value of equity)
13. V = $2 trillion (Apple's total market value)
14. Re = 10% (cost of equity)
15. D = $500 billion (Apple's market value of debt)
16. Rd = 5% (cost of debt)
17. T = 20% (tax rate)
18. WACC = (1/2) * 10% + (1/2) * 5% * (1 - 20%) = 7.5%

Common Mistakes

• Mistake: Using book value instead of market value for WACC.

• Correction: Use market value to reflect the current market price of the company's equity and debt.

• Mistake: Confusing IRR and NPV ranking.

• Correction: IRR is the rate of return on an investment, while NPV is the present value of future cash flows. Use IRR to rank projects, and NPV to determine whether a project is worthwhile.

• Mistake: Not considering the tax effect on debt.

• Correction: Include the tax effect on debt when calculating WACC, as it can significantly impact the company's cost of capital.

Exam / CFA Tips

• Tip: Be aware of the difference between YTM and current yield.

• YTM (Yield to Maturity) is the total return on a bond, while current yield is the annual return on the bond's current price.

• Tip: Use geometric mean when calculating the average return on a portfolio.

• Geometric mean is more accurate than arithmetic mean when calculating the average return on a portfolio with multiple components.

Quick Practice Problem

Problem: Calculate the bond's yield to maturity. Scenario: A 5-year bond with a face value of $1,000, a 5% coupon rate, and a current price of $900. Answer: 6.2% Explanation: Use the formula for yield to maturity: YTM = (C + (F - P) / N) / P, where C = coupon payment, F = face value, P = current price, and N = number of periods.

Last-Minute Cram Sheet

1. CAPM = Rf + ?(Rm - Rf): use historical data to calculate CAPM.
2. DDM = P0 / (r - g): use current stock price and growth rate to calculate DDM.
3. Bond Yield Plus Risk Premium = (1 + r): add risk premium to bond yield to calculate cost of equity.
4. WACC = (E/V) * Re + (D/V) * Rd * (1 - T): use market values and costs to calculate WACC.
5. The dividend discount model (DDM) requires g < r – otherwise the model explodes: ensure growth rate is less than cost of equity.
6. The weighted average cost of capital (WACC) is sensitive to the tax rate: consider tax effect on debt when calculating WACC.
7. IRR is the rate of return on an investment: use IRR to rank projects.
8. NPV is the present value of future cash flows: use NPV to determine whether a project is worthwhile.
9. YTM is the total return on a bond: use YTM to calculate the bond's yield to maturity.
10. Geometric mean is more accurate than arithmetic mean: use geometric mean when calculating the average return on a portfolio.