Question

The earnings per share of ZZL Ltd is expected to be $2.50 next year and the company is expected to retain 40% of these earnings forever. The earnings are expected to grow at a constant annual rate of 6% forever and the stock is currently trading at $10 per share. The standard deviation of the stock’s returns is 30% and its covariance with the market portfolio is 0.135. The expected return and standard deviation of the market portfolio is 15% and 50%, respectively, and the T-bill rate is 5%.

Based on this information, indicate whether the shares are underpriced or overpriced and explain why. Show your calculations.

Calculate the equilibrium share price. Show your calculations.

Answer 1

payout rate=1-retention rate=1-40%=60.0000%

Beta=Covariance of stock with market/(standard deviation of market returns^2)=0.135/(50%*50%)=0.54

required return=risk free rate+beta*(market return-risk free rate)=5%+0.54*(15%-5%)=10.4000%

Intrinsic Value=Expected EPS*payout rate/(required return-growth rate)=2.50*60.0000%/(10.4000%-6%)=34.09090909

As market price is more than intrinsic value, the stock is overpriced

Equilibrium share price=Intrinsic Value=34.09090909