To find the cost of common equity and the Weighted Average Cost of Capital (WACC) for Palencia Paints Corporation, we'll follow structured steps:
### Step 1: Calculate the Cost of Common Equity
We'll use the Dividend Discount Model (DDM) to determine the cost of common equity, where the cost of common equity ([tex]\( r_s \)[/tex]) is given by:
[tex]\[ r_s = \frac{D_1}{P_0} + g \][/tex]
where:
- [tex]\( D_1 \)[/tex] is the expected dividend next year.
- [tex]\( P_0 \)[/tex] is the current stock price.
- [tex]\( g \)[/tex] is the constant growth rate of dividends.
1. Current Dividend: [tex]\( D_0 = \$2.25 \)[/tex]
2. Growth Rate: [tex]\( g = 5\% \)[/tex] or [tex]\( 0.05 \)[/tex]
3. Next Year's Dividend ( [tex]\( D_1 \)[/tex]):
[tex]\[ D_1 = D_0 \times (1 + g) \][/tex]
[tex]\[ D_1 = 2.25 \times (1 + 0.05) \][/tex]
[tex]\[ D_1 = 2.3625 \][/tex]
4. Current Stock Price: [tex]\( P_0 = \$22 \)[/tex]
Using the DDM formula, we get:
[tex]\[ r_s = \frac{2.3625}{22} + 0.05 \][/tex]
[tex]\[ r_s = 0.107386 + 0.05 \][/tex]
[tex]\[ r_s = 0.157386 \text{ or } 15.74\% \][/tex]
### Step 2: Calculate the After-Tax Cost of Debt
1. Before-Tax Cost of Debt: [tex]\( r_d = 8\% \)[/tex] or [tex]\( 0.08 \)[/tex]
2. Tax Rate: [tex]\( T = 25\% \)[/tex] or [tex]\( 0.25 \)[/tex]
3. After-Tax Cost of Debt ([tex]\( r_d(1 - T) \)[/tex]):
[tex]\[ r_d(1 - T) = 0.08 \times (1 - 0.25) \][/tex]
[tex]\[ r_d(1 - T) = 0.08 \times 0.75 \][/tex]
[tex]\[ r_d(1 - T) = 0.06 \text{ or } 6\% \][/tex]
### Step 3: Calculate the Weighted Average Cost of Capital (WACC)
Given:
- Debt ratio: [tex]\( wd = 35\% \)[/tex] or [tex]\( 0.35 \)[/tex]
- Equity ratio: [tex]\( we = 65\% \)[/tex] or [tex]\( 0.65 \)[/tex]
- After-Tax Cost of Debt: [tex]\( r_d(1 - T) = 6\% \)[/tex] or [tex]\( 0.06 \)[/tex]
- Cost of Common Equity: [tex]\( r_s = 15.74\% \)[/tex] or [tex]\( 0.157386 \)[/tex]
The WACC is calculated using the formula:
[tex]\[ WACC = (wd \times r_d(1 - T)) + (we \times r_s) \][/tex]
Substituting the values:
[tex]\[ WACC = (0.35 \times 0.06) + (0.65 \times 0.157386) \][/tex]
[tex]\[ WACC = 0.021 + 0.102301136 \][/tex]
[tex]\[ WACC = 0.123301136 \text{ or } 12.33\% \][/tex]
### Summary
1. Cost of Common Equity ([tex]\( r_s \)[/tex]): [tex]\( 15.74\% \)[/tex]
2. Weighted Average Cost of Capital (WACC): [tex]\( 12.33\% \)[/tex]
Thus, the cost of common equity for Palencia Paints Corporation is 15.74%, and the WACC is 12.33%.
