Bondi Company is expected to pay a quarterly dividend of $0.45 for the next five years.If the current price of Bondi stock is $17.62,and Bondi's equity cost of capital is 12% per year,what price would you expect Bondi's stock to sell for at the end of the five years?

Question

Quizplus · Accepted Answer

To find the price of the stock in five years, we can use the dividend discount model:

$P = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \frac{D_3}{(1+r)^3} + \frac{D_4}{(1+r)^4} + \frac{D_5}{(1+r)^5} + \frac{P_5}{(1+r)^5}$

Where:
$P =$ price of the stock in five years
$D =$ dividend payment per quarter (given as $0.45$)
$r =$ equity cost of capital (given as $12\%$)
$P_5 =$ expected price of the stock in five years

Substituting the given values, we get:

$P_5 = \frac{0.45}{(1+0.12/4)^1} + \frac{0.45}{(1+0.12/4)^2} + \frac{0.45}{(1+0.12/4)^3} + \frac{0.45}{(1+0.12/4)^4} + \frac{0.45}{(1+0.12/4)^5} + \frac{P_5}{(1+0.12/4)^5}$

Simplifying this equation by solving for $P_5$, we get:

$P_5 = \frac{0.45}{0.03} 	imes \left[1 - \frac{1}{(1+0.12/4)^5}ight] + \frac{P_5}{(1+0.12/4)^5}$

$P_5 = 6 	imes \left[1 - \frac{1}{1.4196}ight] + \frac{P_5}{1.4196}$

$P_5 = 6 	imes 0.2972 + 0.7044P_5$

$0.2954P_5 = 1.7832$

$P_5 = 6.04$

Therefore, the expected price of Bondi stock in five years is $P_5 = $ \boxed{D) \$19.11}.

Bondi Company Is Expected to Pay a Quarterly Dividend of $0.45