Comprehensive Study Guide on the Cost of Capital and WACC

Determinants of Intrinsic Value and the Role of WACC

• Intrinsic Value Calculation: The value of a firm is determined by the present value of its future free cash flows, discounted at the Weighted Average Cost of Capital (WACC). The formula for value is:     $\text{Value} = \frac{FCF_1}{(1 + WACC)^1} + \frac{FCF_2}{(1 + WACC)^2} + \dots + \frac{FCF_{\infty}}{(1 + WACC)^{\infty}}$
• Free Cash Flow (FCF): This is defined as the net operating profit after taxes minus the required investments in operating capital.
• Determinants of WACC:
  • Market interest rates: Influence the cost of debt.
  • Firm’s business risk: Affects the required returns of investors.
  • Market risk aversion: Influences the risk premium expected by investors.
  • Firm’s debt/equity mix: The proportion of funding from different capital sources.
  • Cost of debt and Cost of equity: Individual component costs that aggregate into the WACC via their respective weights.

Capital Structure and Financial Policy

• Capital Components: These are specific sources of funding provided by investors. Key components include:
  • Long-term debt.
  • Permanent short-term debt (used by some firms).
  • Preferred stock.
  • Common equity.
• Notes on Short-term Debt: Temporary short-term debt used for seasonal fluctuations in inventory is typically not considered part of the permanent capital structure.
• Cost of Capital vs. Required Rate of Return: These are not identical due to taxes and transaction costs. For example, while a firm may pay an interest rate of $8\%$ on debt, the net cost to the firm is lower because interest expense is tax-deductible.
• Opportunity Cost: The firm's cost of capital is also referred to as the firm's opportunity cost of capital. This is the return stockholders could earn on alternative investments of equal risk.
• Financial Policy: This dictates the desired sources of financing and the specific mix (ratios) in which they will be utilized.

The Component Cost of Debt

• Before-tax vs. After-tax Costs: Tax effects of financing can be incorporated in capital budgeting cash flows or the cost of capital. Most firms incorporate these effects in the cost of capital, focusing specifically on after-tax costs. Note that only the cost of debt is directly affected by tax deductibility.
• Bondholder's Required Rate of Return ($r_b$): This is calculated by setting the market price of the bond equal to the present value of all future interest payments and the principal repayment:     $\text{Bond market price} = \frac{\text{interest}_1}{(1 + r_b)^1} + \frac{\text{interest}_2}{(1 + r_b)^2} + \dots + \frac{\text{interest}_n + \text{principal}}{(1 + r_b)^n}$
• After-tax Cost of Debt ($k_{bAT}$): Because interest is tax-deductible, the effective cost to the firm is calculated using the nominal rate ($k_{bBT}$) and the tax rate ($T$):     $k_{bAT} = k_{bBT}(1 - T)$
• Example: Jana Industries Debt Analysis:
  • Bond details: $15$-year maturity, $12\%$ coupon rate, semiannual payments, noncallable.
  • Parameters: $1,000$ face value; current price is $1,153.72$.
  • Tax rate: $40\%$.
  • Condition: New bonds would be privately placed with no flotation costs.
• Impact of Flotation Costs on Debt: If flotation costs are present, they are subtracted from the bond proceeds.
  • Formula for Net Proceeds per Bond:         $\text{Net proceeds} = \frac{\text{interest}_1}{(1 + k_b)^1} + \dots + \frac{\text{interest}_n + \text{principal}}{(1 + k_b)^n}$
  • Case Study: $30$-year par value bond ($1,000$), $10\%$ annual coupon, $40\%$ tax rate, and flotation costs of $20$. The cost of debt must be adjusted for the reduced proceeds of $980$.

The Component Cost of Preferred Stock

• Characteristics: Preferred dividends are not tax-deductible, so no tax adjustment is made. The nominal rate ($r_{ps}$) is used as the component cost ($k_{ps}$).
• Flotation Costs: Flotation costs for preferred stock are typically significant and are reflected by using the net price in the calculation.
• Formula:     $k_{ps} = \frac{D_{ps}}{P_{ps} - F}$
  • Where $D_{ps}$ is the preferred dividend, $P_{ps}$ is the price, and $F$ is the flotation cost.
• Example: Jana Industries Preferred Stock:
  • Current price: $116.95$.
  • Dividend: $10\%$ coupon on $100$ par value (quarterly dividend).
  • Flotation cost: $5.85$ per share.
• Risk Profile: Preferred stock is more risky to investors than debt because companies are not legally required to pay preferred dividends. However, firms strive to pay them because:
  1. They cannot pay common dividends if preferred dividends are skipped.
  2. It becomes difficult to raise additional capital.
  3. Preferred stockholders may gain control of the firm in some circumstances.

The Component Cost of Common Equity

• Methods of Raising Common Equity:
  1. Directly: Issuing new shares of common stock.
  2. Indirectly: Reinvesting earnings that are not paid out as dividends (Retained Earnings).
• Cost of Reinvested Earnings ($k_s$): There is an opportunity cost to retaining earnings. Investors could have received dividends to buy other securities or the company could have repurchased stock. Therefore, the cost of common equity from retained earnings is the return stockholders could earn on alternative investments of equal risk.
• Calculating the Cost of Equity ($r_s$):
  1. CAPM (Capital Asset Pricing Model):         $k_{cs} = r_F + (r_M - r_F)b = r_F + (RPM)b$
     • Where $r_F$ is the risk-free rate, $r_M$ is the market return, $RPM$ is the market risk premium, and $b$ is the beta.
  2. DGM (Dividend Growth Model):         $k_{cs} = \frac{D_1}{P_0} + g$
• Case: Jana Industries Estimations:
  • Current Stock Price ($P_0$): $50$.
  • Last Dividend ($D_0$): $3.12$.
  • Constant Growth Rate ($g$): $5.8\%$.
  • Beta ($b$): $1.2$.
  • Yield on T-bonds ($r_F$): $5.6\%$.
  • Market Risk Premium ($RPM$): $6\%$.
• Implementation Issues with CAPM:
  • The risk-free rate ($r_{RF}$) is usually estimated using long-term ($10$ to $20$ years) government bonds.
  • The Market Risk Premium ($RPM$) is typically estimated between $3.5\%$ and $6\%$.
  • Beta estimates are often "noisy" and have wide confidence intervals.
• Cost of New Common Stock ($k_{ncs}$):
  • When issuing new shares, flotation costs must be incorporated into the Dividend Growth approach.
  • Formula: $k_{ncs} = \frac{D_1}{NP_{ncs}} + g$
  • Where $NP_{ncs}$ is the net proceeds per share ($\text{Price} - \text{Flotation cost}$).
  • Example for Jana: $50$ price, $7.50$ flotation cost, $3.12$ last dividend, $5.8\%$ growth.

Weighted Average Cost of Capital (WACC)

• Definition: The WACC reflects the aggregate cost of all capital components according to their weight in the capital structure.
• Formula:     $WACC = w_b k_b(1 - T) + w_{ps} k_{ps} + w_{cs} k_{cs}$
  • $w_b, w_{ps}, w_{cs}$: Weights of debt, preferred stock, and common equity respectively.
  • $k_b, k_{ps}, k_{cs}$: Component costs of debt, preferred stock, and common equity.
• Example Calculation:
  • Market variables: Stock price = $50$; Shares outstanding = $3$ million.
  • Total Preferred Stock = $25$ million.
  • Total Debt = $75$ million.
  • Component Costs: Before-tax Debt ($k_b$) = $10\%$, Preferred ($k_{ps}$) = $9\%$, Common Equity ($k_{cs}$) = $12.8\%$.

Strategic Considerations and Divisional WACC

• Investment Evaluation: WACC serves as the discount rate for new investments ONLY if the projects offer the same risk as the firm as a whole.
• Divisional Cost of Capital: If a project's risk differs from the firm average, a specific cost of capital should be calculated for that division. Using a company-wide WACC for a multi-divisional firm with varying risk levels leads to:
  • Systematic overinvestment in high-risk projects.
  • Systematic underinvestment in low-risk projects.
• Factors Influencing WACC:
  • Uncontrollable Factors: Market conditions (interest rates), market risk premium, and tax rates.
  • Controllable Factors: Capital structure policy, dividend policy, and investment policy (firms with riskier projects generally have a higher cost of equity).