Chapter 9, Problem 31QP

Nonconstant Growth Storico Co. just paid a dividend of $3.40 per share. The company will increase its dividend by 20 percent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on Storico stock is 13 percent, what will a share of stock sell for today?

Summary Introduction

To determine: The current share price of a stock.

Non Constant Growth:

Non constant growth is a type of stock valuation. In this growth of dividend is not constant, as sometime it increases and sometime it decreases. More fluctuation is seen in the amount of dividend and in the amount of share price.

Answer to Problem 31QP

Solution: The current share price of a stock is $57.81.

Explanation of Solution

Given,

Dividend is $3.40 per share.

Growth rate is 20%.

For next the dividend growth rate is reduce by 5% until it reaches to the industry average of 5%.

Required rate of return is13%.

Calculated values

Share price in year 3 is $67.74.

Formula to calculate the current share price of stock,

$\text{Share price}=\left[\begin{array}{l}\left(\frac{{\text{D}}_{\text{0}}\left(\text{1}+{\text{G}}_{\text{1}}\right)}{{\left(\text{1}+\text{R}\right)}^{\text{n}}}\right)+\left(\frac{{\text{D}}_{\text{0}}\left(\text{1}+{\text{G}}_{\text{1}}\right)\left(\text{1}+{\text{G}}_{\text{2}}\right)}{{\left(\text{1+R}\right)}^{\text{n+1}}}\right)+\\ \left(\frac{{\text{D}}_{\text{0}}\left(\text{1}+{\text{G}}_{\text{1}}\right)\left(\text{1}+{\text{G}}_{\text{2}}\right)\left(\left(\text{1}+{\text{G}}_{\text{3}}\right)\right)}{{\left(\text{1}+\text{R}\right)}^{\text{n+2}}}\right)+\left(\frac{{\text{P}}_{\text{3}}}{{\left(\text{1}+\text{R}\right)}^{\text{n}+\text{2}}}\right)\end{array}\right]$

Where,

• ${\text{D}}_{\text{0}}$ is dividend.
• ${\text{G}}_{\text{1}}$ is growth rate in year 1.
• ${\text{G}}_{\text{2}}$ is growth rate in year 2.
• ${\text{G}}_{\text{3}}$ is growth rate in year 3.
• $\text{R}$ is required rate of return.
• ${\text{P}}_{\text{3}}$ is share price in year 3.

Substitute $3.40 for dividend, 20% for $G_1$, 15% for $G_2$, 10% for $G_3$, 13% for required rate of return and $67.74 for share price in year 7 in the above formula.

$\begin{array}{c}\text{Share price}=\left[\begin{array}{l}\left(\frac{\$3.40\left(1+0.20\right)}{\left(1+0.13\right)}\right)+\left(\frac{\$3.40\left(1+0.20\right)\left(1+0.15\right)}{{\left(1+0.13\right)}^2}\right)+\\ \left(\frac{\$3.40\left(1+0.20\right)\left(1+0.15\right)\left(1+0.10\right)}{{\left(1+0.13\right)}^3}\right)+\left(\frac{\$67.74}{{\left(1+0.13\right)}^3}\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(\frac{\$3.40\left(1.20\right)}{\left(1.13\right)}\right)+\left(\frac{\$3.40\left(1.20\right)\left(1.15\right)}{{\left(1.13\right)}^2}\right)\\ +\left(\frac{\$3.40\left(1.20\right)\left(1.15\right)\left(1.10\right)}{{\left(1.13\right)}^3}\right)+\left(\frac{\$67.74}{{\left(1.13\right)}^3}\right)\end{array}\right]\\ =\$3.61+\$3.67+\$3.58+\$46.95\\ =\$57.81\end{array}$

Working note:

Calculate the share price of stock in year 3,

$\begin{array}{c}\text{Share price}=\frac{\text{Dividend}\times \left(1+{\text{G}}_1\right)\times \left(1+{\text{G}}_2\right)\times \left(1+{\text{G}}_3\right)\times \left(1+{\text{G}}_4\right)}{\left(\mathrm{R}-\text{G}\right)}\\ =\frac{\$3.40\times \left(1+0.20\right)\times \left(1+0.15\right)\times \left(1+0.10\right)\times \left(1+0.05\right)}{\left(0.13-0.05\right)}\\ =\frac{\$3.40\times 1.20\times 1.15\times 1.10\times 1.05}{0.08}\\ =\$67.74\end{array}$

Conclusion

Thus, the current share price of a stock is $57.81.