Firm’s Weighted Average Cost of Capital with Debt & Equity

Question:

A firm has 80 bonds outstanding that are selling at their par value of Rs. 1,000 each. Bonds with similar characteristics are yielding a pretax 8.6 percent. The firm also has 4,000 shares of equity stock outstanding. The stock has a beta of 1.1 and sells for Rs. 40 a share. The RBI 10-year T-bill is yielding 4 percent, the market risk premium is 8 percent, and the firm’s tax rate is 21 percent.

What is the firm’s weighted average cost of capital, assuming its earnings are sufficient to classify all interest as a tax-deductible expense?

Steps to Calculate WACC:

1. Calculate the Cost of Debt (Kd):
   • Formula: Kd=Pretax Yield×(1−Tax Rate)K_d = \text{Pretax Yield} \times (1 – \text{Tax Rate})Kd​=Pretax Yield×(1−Tax Rate)
   • Given: Pretax Yield = 8.6%, Tax Rate = 21%
   • Calculation: Kd=8.6%×(1−0.21)=8.6%×0.79=6.8%K_d = 8.6\% \times (1 – 0.21) = 8.6\% \times 0.79 = 6.8\%Kd​=8.6%×(1−0.21)=8.6%×0.79=6.8%
2. Calculate the Cost of Equity (Ke):
   • Formula: Ke=Rf+β×Market Risk PremiumK_e = R_f + \beta \times \text{Market Risk Premium}Ke​=Rf​+β×Market Risk Premium
   • Given: Risk-Free Rate (R_f) = 4%, Beta (β) = 1.1, Market Risk Premium = 8%
   • Calculation: Ke=4%+1.1×8%=4%+8.8%=12.8%K_e = 4\% + 1.1 \times 8\% = 4\% + 8.8\% = 12.8\%Ke​=4%+1.1×8%=4%+8.8%=12.8%
3. Calculate the Market Value of Debt and Equity:
   • Debt Market Value: $$\text{Debt}=80\text{ bonds}\times Rs.1,000=Rs.80,000$$
   • Equity Market Value: $$\text{Equity}=4,000\text{ shares}\times Rs.40=Rs.160,000$$
4. Calculate the Total Market Value:
   • Total Market Value: $$\text{Total Value}=\text{Debt}+\text{Equity}=Rs.80,000+Rs.160,000=Rs.240,000$$
5. Calculate the Weights for Debt and Equity:
   • Weight of Debt (W_d): Wd=DebtTotal Value=Rs.80,000Rs.240,000=13≈0.333W_d = \frac{\text{Debt}}{\text{Total Value}} = \frac{Rs. 80,000}{Rs. 240,000} = \frac{1}{3} \approx 0.333Wd​=Total ValueDebt​=Rs.240,000Rs.80,000​=31​≈0.333
   • Weight of Equity (W_e): We=EquityTotal Value=Rs.160,000Rs.240,000=23≈0.667W_e = \frac{\text{Equity}}{\text{Total Value}} = \frac{Rs. 160,000}{Rs. 240,000} = \frac{2}{3} \approx 0.667We​=Total ValueEquity​=Rs.240,000Rs.160,000​=32​≈0.667
6. Calculate the Weighted Average Cost of Capital (WACC):
   • Formula: WACC=(Wd×Kd)+(We×Ke)\text{WACC} = (W_d \times K_d) + (W_e \times K_e)WACC=(Wd​×Kd​)+(We​×Ke​)
   • Calculation: $$\text{WACC}=(0.333\times 6.8\%)+(0.667\times 12.8\%)$$ $$\text{WACC}=2.27\%+8.54\%=10.81\%$$

Answer:

The firm’s Weighted Average Cost of Capital (WACC) is 10.81%.

Description:

To calculate a firm’s WACC, consider the cost of debt and equity, market values, and relevant tax rates. For this firm, the WACC is 10.81%, reflecting the weighted average costs of both debt and equity financing.