Question

A common stock currently has a beta of 1.7, the risk-free rate is 5 percent annually, and the market return is 12 percent annually. The stock is expected to generate a constant dividend of $5.70 per share. A pending lawsuit has just been dismissed and the beta of the stock drops to 1.2. The new equilibrium price of the stock will be

Answer 1

After the stock's beta drops from 1.7 to 1.2, the new equilibrium price of the stock, calculated using the Gordon Growth Model and CAPM, is $42.54. This assumes constant dividends and no other changes to the stock's characteristics.

Step-by-step explanation:

The question pertains to the valuation of common stock and its change in equilibrium price following a reduction in the stock's beta after a lawsuit was dismissed. Using the Capital Asset Pricing Model (CAPM), we can ascertain that the expected return on the stock would change after the beta is adjusted. The expected return is calculated using the formula Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate).

Before the lawsuit was dismissed, the expected return would be 5% + 1.7 * (12% - 5%) = 16.9%. However, after the beta drops to 1.2, the new expected return would be 5% + 1.2 * (12% - 5%) = 13.4%. Assuming that the stock's dividends are expected to remain constant at $5.70 per share, we can use the Gordon Growth Model, where the price of a stock is equal to the dividend per share divided by the required rate of return minus the growth rate (which is zero in this case because dividends are constant).

To find the new equilibrium price, we take the dividend of $5.70 and divide it by the new expected return of 13.4%. This gives us an equilibrium price of $5.70 / 0.134 = $42.54. Hence, the new equilibrium price of the stock would be $42.54, assuming all other factors remain constant.

Answer 2

The new equilibrium price of the stock, after the beta decreases from 1.7 to 1.2, is calculated using the CAPM and Gordon Growth Model formulas. The new required rate of return is 13.4%, and the resulting stock price is $42.54 per share given the $5.70 constant dividend and assuming a zero growth rate.

Step-by-step explanation:

To determine the new equilibrium price of a stock after its beta decreases, we can use the Capital Asset Pricing Model (CAPM) formula:

Re = Rf + β * (Rm - Rf)

Where:

• Re is the required rate of return on the equity
• Rf is the risk-free rate
• β (beta) is the measure of the stock's volatility in relation to the market
• Rm is the expected return of the market

Original beta:

1. Calculate required return on equity with β = 1.7: Re = 5% + 1.7 * (12% - 5%) = 16.9%

New beta:

1. Calculate required return on equity with β = 1.2: Re = 5% + 1.2 * (12% - 5%) = 13.4%
2. Using the Gordon Growth Model (which assumes a constant dividend), the stock price is calculated by P = D / (Re - g), where D is the constant dividend and g is the growth rate (which is implied to be zero since the dividend is constant).
3. So, the new equilibrium price of the stock is P = $5.70 / (0.134 - 0) = $42.54

The dismissal of the pending lawsuit and the resulting decrease in beta leads to a lower required rate of return and thus a higher stock price.