FIN 300

Cost of Capital
Lecture 11

Topics Covered


  • Cost of Capital
    • - Cost of Equity
      • Dividend Discount Model
      • Security Market Line
    • - Cost of Debt
  • Weighted Average Cost of Capital (WACC)
  • Valuation using WACC

Cost of Capital

  • Financing costs
    • External Financing (explicitly face the market)
    • Internal Financing (opportunity costs)
  • Investors' required to return is a cost to the firm
  • Cost of equity
    • Dividend Discount Model
    • Security Market Line (CAPM)
  • Cost of Debt
    • Yield to Maturity (YTM)
    • Compare interest rates of similar debt

Cost of Equity

Dividend Discount Model

$P_0 = \dfrac{D}{R}$

Suppose $P_0=30$ and $D=\$2.25$


$R=\dfrac{D}{P_0}=\dfrac{\$2.25}{\$30}$$=0.075$
DDM with Growth

$P_0 = \dfrac{D_0 \times (1+g)}{R-g}$


$R = \dfrac{D_0 \times (1+g)}{P_0} +g$
Example: DDM with Growth

$D_{-1}=\$2.22$ and $D_0=\$2.28$. If $P_0=\$48$, what is the cost of equity?

$R = \dfrac{D_0 \times (1+g)}{P_0} +g$ ;              $g=\dfrac{\$2.28-\$2.22}{\$2.22}=.027$



$R = \dfrac{\$2.28 \times (1+.027)}{\$48} + 0.027 = 0.0758$
Security Market Line


$E(R_i) = R_F + \beta_i \times [E(R_m)-R_F]$


This topic is covered in the section on the CAPM

Cost of Debt



  • Assume the firm has bonds
  • Observe the price, the coupons and face value
  • Yield to Maturity (YTM) is the interest rate the firm pays
  • Note: coupon payments are NOT the interest rate!

If the firm does not have traded debt, we have to compare the debt to other firms of similar risk.

Weighted Average Cost of Capital


  • Investment decisions must consider cost of capital to the firm as a whole
  • Assume that the investment does not change the capital structure
  • The cost of capital to the firm is weighted according to the capital structure
  • Capital structure is the mix of financing between debt, equity, and preferred stock
WACC

$WACC = \dfrac{E}{E+D} \times R_E + \dfrac{D}{E+D} \times R_D \times (1-\tau_C)$

E: total value of equity in the firm
D: total value of debt in the firm
$R_E$: cost of equity
$R_D$: cost of debt
$\tau_C$: corporate tax rate
Example

A firm had 1,000 shares outstanding, each worth $\$30$. The risk free rate is $5\%$, the expected return on the market is $12\%$ and the stock's beta is 1.5. The firm has debt worth $\$20,000$ with a yield to maturity of $8\%$. $\tau_C=35\%$. What is the firm's WACC?

Finding each piece:
E = 1,000 shares $\times$ $\frac{\$30}{share}$ = $\$30,000.$
D = $\$20, 000$ face value at par = $\$20, 000$

$R_E = R_F + \beta \times (R_m - R_f)$$ R_E= .05 + 1.5 \times (.12-.05) = 0.155$

$R_D = YTM = 0.08$
$\tau_C = 0.35$
Plugging in:

$WACC = \dfrac{30,000}{30,000+20,000} \times 0.155 \\ \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space + \dfrac{20,000}{30,000+20,000} \times 0.08 \times (1-0.35)$

$WACC=0.1138= 11.38\%$

Valuation with WACC

  • DDM is useful, but limited
  • Stocks that don't pay dividends should have value $>0$
  • We can use Cash Flow From Assets to valuate
  • Appropriate discount rate is the WACC

$\text{Firm Value}=\dfrac{CFA_0^*\times (1+g)}{WACC-g}$

$CFA_0^* = EBIT \times (1-\tau_C) + Depreciation - \Delta NWC - \text{Capital Spending}$
Example: WACC Valuation

EBIT is $\$500$, depreciation is $\$50$; there was zero capital spending and zero change in net working capital. The tax rate is $35\%$. If WACC is $11.38\%$ with a $1\%$ growth rate, was is the value of the firm?


$CFA_0^* = \$500 \times (1-0.35) + \$50 - 0 - 0 = \$375$

$g=0.01$, $\tau_C=0.35$, and $WACC=0.1138$


$\text{Firm Value} = \dfrac{\$375 \times (1+0.01)}{0.1138-0.01}$

$ = \$3,602.99$

Summary


  • Cost of Capital
    • - Cost of Equity
      • Dividend Discount Model
      • Security Market Line
    • - Cost of Debt
  • Weighted Average Cost of Capital (WACC)
  • Valuation using WACC



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You've completed the material for FIN 300