Question

Company XYZ is trying to decide whether to cut its expected dividends for next year from $10 per share to $4 per share in order to have more money to invest in new projects. If it does not cut the dividend, the firm's expected rate of growth in dividends is 3 percent per year and the price of their common stock will be $200 per share. However, if it cuts its dividend, the dividend growth rate is expected to rise to 5 percent in the future. Assuming that the investor's required rate of return for the stock does not change, what would you expect to happen to the price of its common stock if it cuts the dividend to $4? Should the company XYZ cut its dividend? a) $133.33 ; Should not cut its dividend. b) $166.67 ; Should not cut its dividend. c) $122.41 : Should cut its dividend. d) $145.32 ; Should cut its dividend. e) $114.75; Should not cut its dividend.

Answer 1

Note: As per answering guidelines, only the first question out of above has been answered.

Solution:

Calculation of cost of equity if the dividend remains unchanged at $10 per share.

We know that using dividend discount model, the following equation holds true:

Cost of equity (Ke)= [{Current dividend * (1+growth rate)} / Price of share] + growth rate

Therefore, if the company doesn't cut it's dividend than its cost of equity at the time of declaration of dividend will be as follows:

Ke= [$10*(1+3%)/$200] + 3%= 5.15% + 3% = 8.15%

Now, the cost of equity is to be remain unchanged as given in the question. Further, if the company cuts it's dividend to $4 per share resulting in rise in expected growth rate to 5%, then using the same equation of dividend discount model as described above, we get as follows:

Ke= [{Current dividend*(1+growth rate)}/price of share] + growth rate

8.15%= [{$4*(1+5%)}/Price per share] + 5%

3.15%= $4.2/price per share

Price per share= $133.33.

Therefore, the correct option is a and the company should not cut it's dividend as it will lead to fall in share price.