First, we need to calculate the cost of each component of the capital structure:
Common stock:
Cost of equity = risk-free rate + beta * (market return - risk-free rate) + tax rate * (inflation rate - risk-free rate)
Beta is not given, so we cannot calculate the cost of equity using the CAPM model. Instead, we will use the dividend discount model (DDM):
Cost of equity = (expected dividend per share / current stock price) + expected growth rate
The expected dividend per share can be calculated as the product of the current dividend per share and the expected payout ratio:
Expected dividend per share = (current dividend per share * expected payout ratio)
Expected payout ratio = 1 - retention ratio
Retention ratio = 1 - (net income - preferred dividends) / net income
Net income is not given, so we cannot calculate the retention ratio. Instead, we will assume a retention ratio of 30%, which means that Semper Fun Sports will retain 70% of its earnings to reinvest in the business.
Current dividend per share is not given, so we cannot calculate the expected dividend per share. Instead, we will assume a current dividend per share of $2.00, which is reasonable for a company with a high expected return on equity.
Expected growth rate can be calculated as the product of the retention ratio and the return on equity:
Expected growth rate = retention ratio * expected return on equity
Expected return on equity can be calculated as the sum of the risk-free rate and the product of the beta and the equity risk premium:
Expected return on equity = risk-free rate + beta * (market return - risk-free rate)
Assuming a beta of 1.2, the expected return on equity is:
Expected return on equity = 4.53% + 1.2 * (12.75% - 4.53%) = 14.98%
Assuming a retention ratio of 30%, the expected growth rate is:
Expected growth rate = 30% * 14.98% = 4.49%
Assuming a current dividend per share of $2.00, the expected dividend per share is:
Expected dividend per share = $2.00 * (1 - 30%) = $1.40
Using the DDM formula, the cost of equity is:
Cost of equity = ($1.40 / $41.40) + 4.49% = 7.82%
Preferred stock:
Cost of preferred stock = preferred dividend / current price
Assuming a preferred dividend of $2.06 (13.41% of $15.39) and a current price of $15.39, the cost of preferred stock is:
Cost of preferred stock = $2.06 / $15.39 = 13.39%
Bonds:
Cost of debt = yield-to-maturity * (1 - tax rate)
Assuming a tax rate of 18.00%, the cost of debt is:
Cost of debt = 4.32% * (1 - 18.00%) = 3.54%
Next, we need to calculate the weight of each component in the capital structure:
Weight of common stock = (number of shares * price per share) / total market value
Total market value = (number of common shares * price per share) + (number of preferred shares * price per share) + (number of bonds * face value)
Total market value = (300,000 * $41.40) + (400,000 * $15.39) + (10,000 * $1,000) = $31,170,000
Weight of common stock = (300,000 * $41.40) / $31,170,000 = 39.22%
Weight of preferred stock = (number of shares * price per share) / total market value
Weight of preferred stock = (400,000 * $15.39) / $31,170,000 = 19.77%
Weight of debt = (number of bonds * face value) / total market value
Weight of debt = (10,000 * $1,000) / $31,170,000 = 3.22%
Finally, we can calculate the weighted average cost of capital (WACC):
WACC = weight of common stock * cost of common stock + weight of preferred stock * cost of preferred stock + weight of debt * cost of debt
WACC = 39.22% * 7.82% + 19.77% * 13.39% + 3.22% * 3.54% = 8.85%
Therefore, the weighted average cost of capital for Semper Fun Sports is 8.85%.