Question

Compute the price of a share of stock that pays a $\backslash (5$per year dividend and that you expect to be able to sell in one year for $\backslash )40$, assuming you require a $5\%$return.

Short answer

Hence, $\$18.2609$is the price of share.

Step-by-step solution

Share : 

A share is an undivided unit of a firm's capital that defines a shareholder's ownership of that company.

Explanation : 

Given,

The dividend on the share is $\$1$.

The sale price of share is $\$20$.

The required rate of return is $15\%$.

Formula :

$P_0=\frac{D_1}{\left(1+k_e\right)}+\frac{P_1}{\left(1+k_e\right)}$

where,

$P_0$= stock price at present.

$D_1$= dividend for the first year.

$P_1$= stock price after a year.

$k_e$= required rate of return.

Substitute $\$1$for $D_1$, $\$20$for $P_1$and $0.15$for $k_e$.

$$\begin{gathered} P_0=\frac{\$1}{\left(1+0.15\right)}+\frac{\$20}{\left(1+0.15\right)} \\ =\$0.8696+\$17.3913 \\ =\$18.2609 \end{gathered}$$

Hence, $\$18.2609$is the price of share.