A firm has a return on equity of 20% and a dividend payout ratio of 30%.The firm's anticipated growth rate is _________.
A)6%
B)10%
C)14%
D)20%
E)none of the above

Question

Quizplus · Accepted Answer

The firm's retention ratio (1 - dividend payout ratio) is 70%. Using the DuPont identity, return on equity (ROE) can be calculated as: 
ROE = Net Profit Margin x Total Asset Turnover x Equity Multiplier
Equity Multiplier = Total Assets / Equity
Assuming a constant total asset turnover, we can calculate the Equity Multiplier as:
Equity Multiplier = ROE / (Net Profit Margin x Total Asset Turnover)
Equity Multiplier = 0.20 / (1 - 0.30) = 0.29
Using the formula for sustainable growth rate, we get:
Sustainable Growth Rate = ROE x Retention Ratio = 0.20 x 0.70 = 0.14 or 14%. Therefore, the answer is C.

A Firm Has a Return on Equity of 20% and a Dividend