Boehm Incorporated Is Expected To Pay A $1.50 Per Share

We use the Gordon Growth Model (also known as the Dividend Discount Model for a perpetuity growing at a constant rate) to find the value per share of Boehm Incorporated’s stock. The formula for this model is:

$P_0=\frac{D_1}{r_s-g}P\_0\; =\; \backslash frac\{D\_1\}\{r\_s\; –\; g\}$​​

where:

• $P_{0}P\_0$ is the current stock price.
• $D_{1}D\_1$​ is the dividend at the end of the first year.
• $r_{s}r\_s$​ is the required rate of return.
• $gg$ is the growth rate of the dividend.

Given:

• D_1 = $1.50
• $r_s=15\mathrm{\%}=0.15r\_s\; =\; 15\backslash \%\; =\; 0.15$
  
• $g=7\mathrm{\%}=0.07g\; =\; 7\backslash \%\; =\; 0.07$
  

Plugging these values into the formula:

$P_0=\frac{1.50}{0.15-0.07}P\_0\; =\; \backslash frac\{1.50\}\{0.15\; –\; 0.07\}$​

$P_0=\frac{1.50}{0.08}P\_0\; =\; \backslash frac\{1.50\}\{0.08\}$​

$P_0=18.75P\_0\; =\; 18.75$

So, the value per share of Boehm’s stock is $\mathrm{\$}18.75\backslash \$18.75$.