Question

Lawton Lawns, Inc. wishes to reduce their leverage. They currently have 40 shares of

common stock outstanding, selling today at $212.42 per share. Over a relevant time period, the
correlation of the returns of the stock with the returns of the market has been 0.62. The standard
deviation of the stock’s returns is 44.30% and the standard deviation of the market’s returns is
28.91%. They have 10 bonds outstanding, each selling at $1,062.10. The bonds pay coupons of
7% and have eight years until maturity. The yield to maturity is either 5.5% or 6%. To reduce
their leverage, they will issue another 20 shares of common stock, and use the proceeds to buy
back bonds at today’s price. You may assume that the prices of both the common stock and the
bonds do not change in this transaction. The corporate tax rate is 28%. The ten-year T-bond is
yielding 3.5%, and the return on the market portfolio is expected to be 13.5%. What will the
WACC of Lawton Lawns be after they reduce their leverage?

Answer 1

To calculate the WACC of Lawton Lawns after reducing their leverage, we need to consider the costs of equity and debt. By using the given market values, costs, and tax rate, we can calculate the WACC using the formula (E/V) * Re + (D/V) * Rd * (1 - Tax Rate), where E is the market value of equity, V is the total market value of equity and debt, Re is the cost of equity, D is the market value of debt, Rd is the cost of debt, and Tax Rate is the corporate tax rate.

Step-by-step explanation:

To calculate the Weighted Average Cost of Capital (WACC) after Lawton Lawns reduces their leverage, we need to consider the costs of both equity and debt. The formula for WACC is:

WACC = (E/V) * Re + (D/V) * Rd * (1 - Tax Rate)

Where:

• E is the market value of equity
• V is the total market value of equity and debt
• Re is the cost of equity
• D is the market value of debt
• Rd is the cost of debt
• Tax Rate is the corporate tax rate

Given the information provided:

• The market value of equity after issuing 20 more shares is: 40 + 20 = 60 shares
• The market value of equity = Total shares * Share price = 60 * $212.42
• The market value of debt after buying back bonds = Total bonds * Bond price = 10 * $1,062.10
• The total market value of equity and debt = Market value of equity + Market value of debt
• The cost of equity can be calculated using the Capital Asset Pricing Model (CAPM): Re = Risk-free rate + Beta * Market risk premium
• The risk-free rate is the yield on the 10-year T-bond, which is given as 3.5%
• The market risk premium is the expected return on the market portfolio minus the risk-free rate, which is given as 13.5% - 3.5%
• The beta can be estimated using the correlation of the stock's returns with the market returns and the standard deviation of the stock's returns and the market's returns
• The cost of debt is the yield to maturity of the bonds

By plugging in the values into the WACC formula, we can calculate the WACC of Lawton Lawns after they reduce their leverage.