Question

I need help with this 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.                                           (12 marks)

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			%	0
2			%	0
3			%	0

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			%	0		%
2			%	0		%
3			%	0		%

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?

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.

А Year в C Beginning Net balance, income equity 1 600,000 120,000 2 720,000 144,000 3 864,000 172,800 D Return on equity 20% 20% 20% Dividends Ending balance, equity 720,000 864,000 1,036,800

C А Year Net income Return on Dividends equity Ending balance, equity Beginning balance, equity 600000 =F2 =F3 =B2*D2 =B3*D3 =B4*D4 10.2 0.2 =B2+C2-E2 =B3+C3-E3 =B4+C4-E4 0.2

b]

Growth rate = ROE * retention ratio.

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

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%.