Question

Suppose the risk-free rate is 3.46% and an analyst assumes a market risk premium of 6.46%. Firm A just paid a dividend of $1.29 per share. The analyst estimates the β of Firm A to be 1.25 and estimates the dividend growth rate to be 4.64% forever. Firm A has 288.00 million shares outstanding. Firm B just paid a dividend of $1.89 per share. The analyst estimates the β of Firm B to be 0.78 and believes that dividends will grow at 2.38% forever. Firm B has 182.00 million shares outstanding. What is the value of Firm B?

Answer 1

Risk free rate = 3.46%

market risk premium = 6.46%

Beta of firm B = 0.78

thus, required return(k) of Firm B would be

$k_B\textup{= risk free rate + beta*market risk premium}$

$k_B\textup{= 0.0346 + 0.78*0.0646}$

$\large k_B\textup{= 0.084988}$

Last dividend of Firm B (D0) = $1.89

Constant growth rate of firm B (g) = 2.38%

Current Price of Firm B share would be:

$P_B = \frac{D0*(1+g)}{k_B-g}$

$P_B = \frac{1.89*(1+0.0238)}{0.084988-0.0238}$

$P_B = \frac{1.934982}{0.061188}$

$P_B = 31.6235536379682$

Outstanding share of Firm B = 182,000,000

Thus,

Value of Firm B would be:

$V_B = \textup{Outstanding Shares} * \textup{Per share price} (P_B)$

$V_B = 182,000,000*31.6235536379682$

$\bg_green \large V_B = \$5,755,486,762.11$

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.