Question

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 $820,000 next year and $1,280,000 in two years, including the proceeds from the liquidation. There are 36,000 shares of stock outstanding and shareholders require a return of 14 percent.

a. What is the current price per share of the stock? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Share price            $

b. The Board of Directors is dissatisfied with the current dividend policy and proposes that a dividend of $920,000 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Shares sold            

What is the new price per share of the existing shares of stock? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

New share price            $

Answer 1

a. The price of a share of stock is the present value of the dividends.

The dividend per share each year will be:

Year 1 dividend per share = $820,000 / 36,000 = $29.29

Year 2 dividend per share = $1,280,000 / 36,000 = $35.56

The required return is 14 percent, so the stock price today is:

P₀= $29.29 / 1.14 + $35.56 / 1.14² = $53.06

b. The dividend increase for existing shareholders for Year 1 will be the new dividend amount minus by the old dividend amount, which is:

Dividend increase = $920,000 – 820,000 = $100,000

In order to pay this increase in dividends, the firm must sell new shares. The number of new shares that must be sold is the dividend increase divided by the stock price, or:

New shares to sell = $100,000 / $53.06 = 1884.66

The new shareholders invested a total of $100,000 in the company at Year 1. At Year 2, the total dividends that must be paid to these new shareholders is the investment amount of $100,000 times one plus the required return of 14 percent, or:

Dividends to new shareholders at Year 2 = $100,000(1.14) = $114,000

Since this amount must be paid to the new shareholders at Year 2, it will reduce the amount available to current shareholders. The amount available to current shareholders at Year 2 will be:

Total dividends to current shareholders at Year 2 = $1,280,000 – 114,400 = $1,166,000

So, the dividend per share to the current shareholders will now be:

Year 1 dividend per share = $920,000 / 36,000 = $25.56

Year 2 dividend per share = $1,166,000 / 36,000 = $32.39

The new stock price today is: P₀= $25.56 / 1.14 + $32.39 / 1.14² = $47.34

This is the same price as we found with the original dividend policy