Let's methodically address each part of the problem using the provided data:
### a) The current total value of the firm
#### Value of Debt (V_D):
- Par value of debt: RM3,000,000
- Current market price per RM1,000 par value bond: RM1,150
- Current market value of debt:
\[ V_D = \frac{\text{Market price per bond}}{\text{Par value per bond}} \times \text{Par value of total debt} \]
\[ V_D = \frac{1,150}{1,000} \times 3,000,000 \]
\[ V_D = 1.15 \times 3,000,000 \]
\[ V_D = RM3,450,000 \]
#### Value of Equity (V_E):
- Number of shares: 46,000
- Current price per share: RM50
- Current market value of equity:
\[ V_E = \text{Number of shares} \times \text{Price per share} \]
\[ V_E = 46,000 \times 50 \]
\[ V_E = RM2,300,000 \]
#### Total value of the firm (V_T):
\[ V_T = V_D + V_E \]
\[ V_T = 3,450,000 + 2,300,000 \]
\[ V_T = RM5,750,000 \]
### b) The proportion of debt in this firm's capital structure
\[ \text{Proportion of Debt} = \frac{V_D}{V_T} \]
\[ \text{Proportion of Debt} = \frac{3,450,000}{5,750,000} \]
\[ \text{Proportion of Debt} = 0.60 \]
\[ \text{Proportion of Debt} = 60\% \]
### c) The proportion of equity in this firm's capital structure
\[ \text{Proportion of Equity} = \frac{V_E}{V_T} \]
\[ \text{Proportion of Equity} = \frac{2,300,000}{5,750,000} \]
\[ \text{Proportion of Equity} = 0.40 \]
\[ \text{Proportion of Equity} = 40\% \]
### d) The after-tax cost of debt (r_d)
#### Before-tax cost of debt:
- Yield to maturity (YTM) on new debt: 7.67%
#### After-tax cost of debt:
\[ r_d = \text{YTM} \times (1 - \text{Tax Rate}) \]
\[ r_d = 7.67\% \times (1 - 0.40) \]
\[ r_d = 7.67\% \times 0.60 \]
\[ r_d = 4.602\% \]
### e) The cost of common stock (r_e)
The cost of common stock given by the Dividend Discount Model (DDM):
\[ r_e = \frac{D_1}{P_0} + g \]
\[ D_1 = \text{Expected dividend next year} = RM5.50 \]
\[ P_0 = \text{Current stock price} = RM50 \]
\[ g = \text{Dividend growth rate} = 3.67\% \]
\[ r_e = \frac{5.50}{50} + 0.0367 \]
\[ r_e = 0.11 + 0.0367 \]
\[ r_e = 0.1467 \]
\[ r_e = 14.67\% \]
### f) The firm's weighted average cost of capital (WACC)
\[ WACC = (w_d \times r_d) + (w_e \times r_e) \]
Where:
- \( w_d \) is the proportion of debt
- \( r_d \) is the after-tax cost of debt
- \( w_e \) is the proportion of equity
- \( r_e \) is the cost of equity
\[ WACC = (0.60 \times 4.602\%) + (0.40 \times 14.67\%) \]
\[ WACC = (0.60 \times 0.04602) + (0.40 \times 0.1467) \]
\[ WACC = 0.027612 + 0.05868 \]
\[ WACC = 0.086292 \]
\[ WACC = 8.63\% \]
### Summary:
a) The current total value of the firm: RM5,750,000
b) The proportion of debt in this firm's capital structure: 60%
c) The proportion of equity in this firm's capital structure: 40%
d) The after-tax cost of debt: 4.602%
e) The cost of common stock: 14.67%
f) The firm's weighted average cost of capital: 8.63%
A firm currently has the following capital structure which it views as optimal.
Debt: RM3,000,000 par value of 9% bonds outstanding with an annual before-tax yield to maturity of 7.67% on a new issue. The bonds stareding sell for RM1,150 per RM1,000 par value.
Common stock: 46,000 shares outstanding currently selling for RM50 per share. The firm expects to pay a RM5.50 dividend per share one year from now and is experiencing a 3.67% growth rate in dividends, which it expects to continue indefinitely.
The firm's marginal tax rate is 40%, and it expects to be able to finance all new projects with debt and internal common equity.
Determine:
a) The current total value of the firm
b) The proportion of debt in this firm's capital structure
c) The proportion of equity in this firm's capital structure
d) The after-tax cost of debt
e) The cost of common stock
f) The firm's weighted average cost of capital
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