RobertA

Demonstrate the use of the DuPont analysis of return on equity in conjunction with the sustainable growth rate expression. The following statistics are selected from Kyle Star Partners (Kyle) financial statements:

Sales	$100 million
Net Income	$15 million
Dividends	$5 million
Total Assets	$150 million
Total Equity	$50 million

What is Kyle’s sustainable growth rate?

A) 24.5%.

B) 33.3%.

C) 20.0%.

---

SGR	= ROE × [(net income − dividends) / net income]
	= (15 million / 50 million) × (15 million − 5 million) / 15 million
	= 20.0%

RobertA

Which of the following is NOT a component of the sustainable growth rate formula using the DuPont model?

A) EBIT/interest expense.

B) Net income/sales.

C) Earnings retention ratio.

---

SGR = b × ROE
where:
b = earnings retention rate = (1 − dividend payout rate)
ROE = return on equity
The SGR is important because it tells us how quickly a firm can grow with internally generated funds. A firm’s rate of growth is a function of both its earnings retention and its return on equity. ROE can be estimated with the DuPont formula, which presents the relationship between margin, sales, and leverage as determinants of ROE. In the 3-part version of the DuPont model: ROE = (NI/sales)(sales/assets)(assets/equity)

RobertA

If a firm has a return on equity of 15%, a current dividend of $1.00, and a sustainable growth rate of 9%, what are the firm’s current earnings?

A) $2.50.

B) $1.50.

C) $1.75.

---

The earnings can be determined by solving for earnings in the sustainable growth formula:
9% = [1 − ($1 / $Earnings)] × 0.15 or $1 / 0.4 = $Earnings = $2.50

RobertA

Heather Callaway, CFA, is concerned about the accuracy of her valuation of Crimson Gate, a fast-growing telecommunications-equipment company that her firm rates as a top buy. Crimson currently trades at $134 per share, and Callaway has put together the following information about the stock:

Most recent dividend per share	$0.55
Growth rate, next 2 years	30%
Growth rate, after 2 years	12%
Trailing P/E	25.6
Financial leverage	3.4
Sales	$11.98 per share
Asset turnover	11.2
Estimated market rate of return	13.2%

Callaway’s employer, Bates Investments, likes to use a company’s sustainable growth rate as a key input to obtaining the required rate of return for the company’s stock.
Crimson’s sustainable growth rate is closest to:

A) 14.8%.

B) 13.2%.

C) 16.6%.

---

Sustainable growth rate = ROE × retention rate
Earnings per share = price / (P/E) = $134 / 25.6 = $5.23
The retention rate represents the portion of earnings not paid out in dividends. = (5.23 − 0.55) / 5.23 = 0.89 or 89%
ROE = profit margin × asset turnover × financial leverage
ROE = 5.23 / 11.98 × 11.2 × 3.4 = 16.6%
Sustainable growth rate = 89% × 16.6% = 14.8%

RobertA

Supergro has current dividends of $1, current earnings of $3, and a return on equity of 16%, what is its sustainable growth rate?

A) 12.2%.

B) 8.9%.

C) 10.7%.

---

g = (1 – 1/3)(0.16) = 0.107

RobertA

Dynamite, Inc., has current earnings of $26, current dividend of $2, and a returned on equity of 18%. What is its sustainable growth?

A) 16.62%.

B) 14.99%.

C) 13.37%.

---

g = [1 − ($2 / $26)]0.18 = 16.62%

RobertA

In computing the sustainable growth rate of a firm, the earnings retention rate is equal to:

A) Dividends / required rate of return.

B) 1 − (dividends / assets).

C) 1 − (dividends / earnings).

---

Earnings retention rate = 1 − (dividends / earnings).

RobertA

The sustainable growth rate, g, equals:

A) pretax margin divided by working capital.

B) dividend payout rate times the return on assets.

C) earnings retention rate times the return on equity.

---

The formula for sustainable growth is: g = b × ROE, where g = sustainable growth, b = the earnings retention rate, and ROE equals return on equity.

RobertA

Sustainable growth is the rate that earnings can grow:

A) without additional purchase of equipment.

B) indefinitely without altering the firm's capital structure.

C) with the current assets.

---

Sustainable growth is the rate of earnings growth that can be maintained indefinitely without the addition of new equity capital.

RobertA

GreenGrow, Inc., has current dividends of $2.00, current earnings of $4.00 and a return on equity of 16%. What is GreenGrow’s sustainable growth rate?

A) 9%.

B) 6%.

C) 8%.

---

GreenGrow’s sustainable growth rate is 8%.

g = [1 – ($2/$4)](0.16) = 8%