Question

Imagine a corporation with $1,000,000 of assets and a debt ratio of 40%. ROE (return on equity) is expected to be 20% for the foreseeable future. Assuming the firm maintains the same amount of debt indefinitely (as opposed to keeping the same debt ratio), respond to the following questions.                                          

a. If the firm doesn’t pay out any dividends or re-purchase any shares, what do you expect the firm’s earnings to be for the next three years?

Complete the table to show your calculations.

Year	Beginning balance, equity	Net income	Return on equity = net income /opening equity	Dividends and/or repurchases	Ending balance, equity
1	600,000	120,000	20%	0	720,000
2	720,000	144,000	20%	0	864,000
3	864,000	172,800	20%	0	1,036,800

b. If the firm doesn’t pay any dividends or re-purchase any shares, at what rate would the firm grow from year to year?

Complete the table.

Year	Beginning balance, equity	Net income	Return on equity = net income /opening equity	Dividends and/or repurchases	Ending balance, equity	Growth rate
1	600,000	120000	20%	0	720,000	%
2	720,000	144000	20%	0	864,000	%
3	864,000	172800	20%	0	1036800	%

c. If the firm pays 50% of its earnings as dividends, at what rate would the firm grow from year to year?

Complete the table.

Year	Beginning balance, equity	Net income	Return on equity = net income /opening equity	Dividends	Ending balance, equity	Growth rate
1			%			%
2			%			%
3			%			%

d. If the firm uses 80% of its earnings to re-purchase shares from its shareholders, at what rate would the firm grow from year to year?

Complete the table.

Year	Beginning balance, equity	Net income	Return on equity = net income /opening equity	Repurchases	Ending balance, equity	Growth rate
1			%			%
2			%			%
3			%			%

e. If the firm pays 50% of its earnings as dividends and uses an additional 20% of its earnings to repurchase shares from its shareholders, at what rate would the firm grow from year to year?

Complete the table.

Year	Beginning balance, equity	Net income	Return on equity = net income /opening equity	Dividends	Repur-chases	Ending balance, equity	Growth rate
1			%				%
2			%				%
3			%				%

f. If you have done the calculations correctly in the tables above, you should have the same growth rate every year. How long could the company grow at this constant rate if all the given factors remained the same?

Need some help filling out the blanks. Thanks so much!

Answer 1

a]

Total assets = $1,000,000.

Debt ratio = 40%

Debt = $1,000,000 * 40% = 400,000.

Equity = $1,000,000 - $400,000 = $600,000.

Ending equity each year = beginning equity + net income - dividends.

Year	Beginning balance, equity	Net income	Return on equity = net income /opening equity	Dividends and/or repurchases	Ending balance, equity
1	600,000	120,000	20%	0	720,000
2	720,000	144,000	20%	0	864,000
3	864,000	172,800	20%	0	1,036,800
1	600,000	120,000	20%	0	720,000
2	720,000	144,000	20%	0	864,000
3	864,000	172,800	20%	0	1,036,800
1	600,000	120,000	20%	0	720,000
2	720,000	144,000	20%	0	864,000
3	864,000	172,800	20%	0	1,036,800

b)The retention ratio is 100%, since dividends are zero.

Growth rate = ROE * retention ratio.

Growth rate = 20% * 100% = 20%.

c]

Growth rate = ROE * retention ratio.

The retention ratio is 50%, since dividend payout ratio is 50%.

Growth rate = 20% * 50% = 10%.

d]

Growth rate = ROE * retention ratio.

The retention ratio is 20%, since repurchases are 80%.

Growth rate = 20% * 20% = 4%.

a. 120000$

b. 1st year = 600000+(600000*20%) = 600000+120000 = 720000

2nd year = 720000+(720000+20%) = 720000+144000 = 864000

3rd year = 864000+(864000+20% = 864000+172800 = 1036800 (every year 20% grow rate)

c. 1st year = 600000+(600000*10%) = 600000+60000 = 660000

2nd year = 660000+(660000+10%) = 660000+66000 = 726000

3rd year = 726000+(726000+10% = 726000+72600 = 798600 (every year 10% grow rate)

d. 1st year = 600000+((600000*20%)*80%) = 600000+(120000*80%) = 600000+96000 = 696000

2nd year = 696000+((696000+20%)*80%) = 696000+(139200*80%) = 696000+111360 = 807360

3rd year = 807360+((807360+20%*80%) = 807360+(161472*80%) = 807360+129178 = 936538 (every year 16% grow rate)