Questions: A corporation's capital structure is comprised of debt, preferred stock, and common stock. The risk-free rate of interest is 4.5 percent, the common stock beta is 0.65, and the market risk premium is 8.5 percent. If the percentage of common equity in the corporation's capital structure is 20 percent and the percentages of preferred stock in the corporation's capital structure is equal to the percentage of the corporation's capital structure in debt, the percentage of preferred stock in the corporation's capital structure is percent.

A corporation's capital structure is comprised of debt, preferred stock, and common stock. The risk-free rate of interest is 4.5 percent, the common stock beta is 0.65, and the market risk premium is 8.5 percent. If the percentage of common equity in the corporation's capital structure is 20 percent and the percentages of preferred stock in the corporation's capital structure is equal to the percentage of the corporation's capital structure in debt, the percentage of preferred stock in the corporation's capital structure is percent.

Transcript text: A corporation's capital structure is comprised of debt, preferred stock, and common stock. The risk-free rate of interest is 4.5 percent, the common stock beta is 0.65 , and the market risk premium is 8.5 percent. If the percentage of common equity in the corporation's capital structure is 20 percent and the percentages of preferred stock in the corporation's capital structure is equal to the percentage of the corporation's capital structure in debt, the percentage of preferred stock in the corporation's capital structure is $\square$ percent. $\square$

Solution

Solution Steps

To solve this problem, we need to determine the percentage of preferred stock in the corporation's capital structure. Given that the percentage of common equity is 20%, and the percentages of preferred stock and debt are equal, we can set up an equation to solve for the percentage of preferred stock.

Let $ P $ be the percentage of preferred stock.
Let $ D $ be the percentage of debt.
Given that $ P = D $ and the total capital structure must sum to 100%, we can write the equation: $ 20\% + P + D = 100\% $.
Substitute $ D $ with $ P $ in the equation: $ 20\% + P + P = 100\% $.
Solve for $ P $.

Step 1: Define Variables and Given Data

We are given the following information:

The percentage of common equity in the corporation's capital structure is $ 20\% $.
The percentages of preferred stock and debt are equal.

Step 2: Set Up the Equation

Let $ P $ be the percentage of preferred stock and $ D $ be the percentage of debt. Since $ P = D $, we can write the equation for the total capital structure as: \[ 20\% + P + D = 100\% \] Substituting $ D $ with $ P $: \[ 20\% + P + P = 100\% \] \[ 20\% + 2P = 100\% \]

Step 3: Solve for $ P $

Rearrange the equation to solve for $ P $: \[ 2P = 100\% - 20\% \] \[ 2P = 80\% \] \[ P = \frac{80\%}{2} \] \[ P = 40\% \]