Question

The Hastings Sugar Corporation has the following pattern of net income each year and associated capital expenditure projects. The firm can earn a higher return on the projects than the stockholders could earn if the funds were paid out in the form of dividends.

Year	Net income	Profitable capital expenditure
1	\(14 million	\)7 million
2	\(16 million	\)11 million
3	\(12 million	\)6 million
4	\(16 million	\)8 million
5	\(16 million	\)9 million

The Hastings Corporation has 3 million shares outstanding. (The following questions are separate from each other.)

a. If the marginal principle of retained earnings is applied, how much in total cash dividends will be paid over the five years?

b. If the firm simply uses a payout ratio of 30 percent of net income, how much in total cash dividends will be paid?

c. If the firm pays a 10 percent stock dividend in years 2 through 5, and also pays a cash dividend of $3.40 per share for each of the five years, how much in total dividends will be paid?

d. Assume the payout ratio in each year is to be 20 percent of the net income and the firm will pay a 10 percent stock dividend in years 2 through 5, how much will dividends per share for each year be? (Assume the cash dividend is paid after the stock dividend.)

Short answer

1. The total cash dividend to be paid is $ 33 million.
2. The total cash dividend to be paid when pay-out ratio is 30% is $22.2 million.
3. The total cash dividend to be paid is $75,888,000 when the stock dividend is issued and the dividend per share is $3.40.
4. The dividend per share will be $ 0.93 in the first year, $0.97 in second year, $0.60 in third year, $0.80 in fourth year, and $0.73 in fifth year.

Step-by-step solution

Calculation of cash dividends to be paid

The total cash dividend to be paid is $ 33 million.

Year	Net income	Profitable capital expenditure	Cash dividends
1	$14 million	$7 million	$7 million
2	$16 million	$11 million	$5 million
3	$12 million	$6 million	$6 million
4	$16 million	$8 million	$8 million
5	$16 million	$9 million	$7 million
Total cash dividends to be paid			$33 million

The formula used is:

$\mathbf{\text{Cash dividends}}\mathbf{=}\mathbf{\text{Net income}}\mathbf{-}\mathbf{\text{Profitable capital expenditures}}$

Calculation of cash dividends to be paid when pay-out ratio is 30%

The total cash dividend to be paid is $ 22.2 million.

Year	Net income	Pay-out ratio	Cash dividends
1	$14 million	30%	$4.2 million
2	$16 million	30%	$4.8 million
3	$12 million	30%	$3.6 million
4	$16 million	30%	$4.8 million
5	$16 million	30%	$4.8 million
Total cash dividends to be paid			$22.2 million

The formula used is:

$\mathbf{\text{Cash dividends}}\mathbf{=}\mathbf{\text{Net income}}\mathbf{\times }\mathbf{\text{Pay - out ratio}}$

Calculation of cash dividends to be paid when stock dividend is issued and the dividend per share is $3.40

The total cash dividend to be paid is $75,888,000 when the stock dividend is issued and the dividend per share is $3.40.

Year	Shares outstanding	Dividend per share	Cash dividends
1	3 million	$3.40	$10,200,000
2	3.6 million	$3.40	$12,240,000
3	4.32 million	$3.40	$14,688,000
4	5.18 million	$3.40	$17,612,000
5	6.22 million	$3.40	$21,148,000
Total cash dividends to be paid			$75,888,000

The formula used is:

$\mathbf{\text{Cash dividends}}\mathbf{=}\mathbf{\text{Shares outstanding}}\mathbf{\times }\mathbf{\text{Dividend per share}}$

Calculation of dividend per share when pay-out ratio is 20% and the stock dividend is 10%

The dividend per sharewill be $ 0.93 in first year, $0.97 in second year, $0.60 in third year, $0.80 in fourth year, and $0.73 in fifth year.

Year	Net income	Pay-out ratio	Dividend payable	Shares outstanding	Dividend per share
1	$14 million	20%	$2.8 million	3 million	$0.93
2	$16 million	20%	$3.2 million	3.3 million	$0.97
3	$12 million	20%	$2.4 million	3.63 million	$0.60
4	$16 million	20%	$3.2 million	3.99 million	$0.80
5	$16 million	20%	$3.2 million	4.39 million	$0.73

The formula used is:

$\mathbf{\text{Dividend per share}}\mathbf{=}\frac{\mathbf{\text{Dividend payable}}}{\mathbf{\text{Shares outstanding}}}$