Chapter 14, Problem 13QP

Dividend Policy. The Quick Buck Company is an all-equity firm that has been in existence for the past three years. Company management expects that the company will last for two more years and then be dissolved. The firm will generate cash flows of $550,000 next year and $840,000 in two years, including the proceeds from the liquidation. There are 20,000 shares of stock outstanding and shareholders require a return of 12 percent.

 a.    What is the current price per share of the stock?

b.    The board of directors is dissatisfied with the current dividend policy and proposes that a dividend of $650,000 be paid next year. To raise the cash necessary for the increased dividend, the company will sell new shares of stock. How many shares of stock must be sold? What is the new price per share of the existing shares of stock?

Summary Introduction

To determine: The current price per share of the stock.

Introduction:

Dividend policy:

Dividend policy is the framework which helps the company to take decisions on the distribution of earnings to their shareholders.

Answer to Problem 13QP

The current price per share of the stock is $58.04.

Explanation of Solution

Given information:

QB Company expects they will have $550,000 cash for the next year and $840,000 in two years. There are 20,000 shares of stock outstanding. The required rate of return by the shareholders is 12%.

Formulae:

The formula to calculate the dividend per share:

$\text{Dividend per share}=\frac{\text{Expected cash}}{\text{Number of share outstanding}}$

The formula to calculate the stock price:

$\text{Stock price}=\left(\frac{\text{1st year dividend}}{{\left(1+\text{Rate of returns}\right)}^1}\right)+\left(\frac{\text{Two years divdind}}{{\left(1+\text{Rate of returns}\right)}^2}\right)$

Compute the dividend per share:

For one year:

$\begin{array}{c}\text{Dividend per share}=\frac{\text{Expected cash}}{\text{Number of share outstanding}}\\ =\frac{\$550,000}{20,000}\\ =\$27.50\end{array}$

Hence, the dividend per share is $27.50.

For the next two years:

$\begin{array}{c}\text{Dividend per share}=\frac{\text{Expected cash}}{\text{Number of share outstanding}}\\ =\frac{\$840,000}{20,000}\\ =\$42\end{array}$

Hence, the dividend per share for two years is $42.

Compute the stock price:

$\begin{array}{c}\text{Stock price}=\left(\frac{\text{1st year dividend}}{{\left(1+\text{Rate of returns}\right)}^1}\right)+\left(\frac{\text{Two years divdind}}{{\left(1+\text{Rate of returns}\right)}^2}\right)\\ =\left(\frac{\$27.50}{{\left(1+0.12\right)}^1}\right)+\left(\frac{\$42}{{\left(1+0.12\right)}^2}\right)\\ =\$24.55+\$33.49\\ =\$58.04\end{array}$

Hence, the current price per share of the stock is $58.04.

Summary Introduction

To determine: The number of shares to sell.

Answer to Problem 13QP

The number of shares to sell is 1,723.08.

Explanation of Solution

Given information:

The proposed dividend is $650,000.

Formulae:

The formula to calculate the increased dividend:

$\text{Increase dividend}=\text{Proposed dividend}-\text{Existing dividend}$

The formula to calculate the new number of shares to sell:

$\text{New number of shares to sell}=\frac{\text{Increase in dividend}}{\text{Stock price}}$

Compute the dividend increase:

$\begin{array}{c}\text{Increase in dividend}=\text{Proposed dividend}-\text{Existing dividend}\\ =\$650,000-\$550,000\\ =\$100,000\end{array}$

Hence, increase in dividend is $100,000.

Compute the new number of shares to sell:

$\begin{array}{c}\text{New number of shares to sell}=\frac{\text{Increase in dividend}}{\text{Stock price}}\\ =\frac{\$100,000}{\$58.04}\\ =1,723.08\end{array}$

Hence, the new number of shares to sell is 1,723.08.

Summary Introduction

To determine: The new price per share of the existing shares of stocks.

Answer to Problem 13QP

The new price per share of the existing shares of stocks is $58.04.

Explanation of Solution

Compute the new price per share of the existing shares of stocks:

Note: The investment in the first year is $100,000 and investment in the next two years will be at the rate 12%.

The formula to calculate the dividend to new shareholders:

$\text{Dividend to new shareholders}=\text{First year dividend}\left(1+\text{Rate of return}\right)$

Compute the dividend to new shareholders:

$\begin{array}{c}\text{Dividend to new shareholders}=\text{First year dividend}\left(1+\text{Rate of return}\right)\\ =\left[\$100,000\left(1+0.12\right)\right]\\ =\$112,000\end{array}$

Hence, the dividends to new shareholders are $112,000.

This is because the dividends are paid to new shareholders; this will reduce the amount available to the current shareholders.

Compute the amount available to the current shareholders:

$\begin{array}{c}\text{Dividend}=\text{Cash}-\text{Dividend to new shareholders}\\ =\$840,000-\$112,000\\ =\$728,000\end{array}$

Hence, the dividends available to the current shareholders are $728,000.

Compute the new price per share of the existing shares of stock:

For one year:

$\begin{array}{c}\text{Dividend per share}=\frac{\text{Expected cash}}{\text{Number of share outstanding}}\\ =\frac{\$650,000}{20,000}\\ =\$32.50\end{array}$

Hence, the dividend per share is $32.50.

For the next two years:

$\begin{array}{c}\text{Dividend per share}=\frac{\text{Expected cash}}{\text{Number of share outstanding}}\\ =\frac{\$728,000}{20,000}\\ =\$36.40\end{array}$

Hence, the dividend per share for two years is $36.40.

Compute the new stock price:

The formula to calculate the new stock price:

$\begin{array}{c}\text{New stock price}=\left(\frac{\text{1st year dividend}}{{\left(1+\text{Rate of returns}\right)}^1}\right)+\left(\frac{\text{Two years divdind}}{{\left(1+\text{Rate of returns}\right)}^2}\right)\\ =\left(\frac{\$32.50}{{\left(1+0.12\right)}^1}\right)+\left(\frac{\$36.40}{{\left(1+0.12\right)}^2}\right)\\ =\$29.017+\$29.017\\ =\$58.04\end{array}$

Hence, the current price per share of the stock is $58.04.

Thus, the original dividend policy’s price is the same as the above.