Abacus Co. wishes to maintain a growth rate of 13.2 percent a year, a debt–equity ratio of 1.6, and a

Abacus Co. wishes to maintain a growth rate of 13.2 percent a year, a debt–equity ratio of 1.6, and a dividend payout ratio of 25 percent. The ratio of total assets to sales is constant at 0.96.

What profit margin must the firm achieve? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Profit margin

%

Explanation:

We have all the variables to calculate ROE using the DuPont identity except the profit margin. If we find ROE, we can solve the DuPont identity for profit margin. We can calculate ROE from the sustainable growth rate equation. For this equation we need the retention ratio, so:

b	=	1 – 0.25
b	=	0.75

Using the sustainable growth rate equation and solving for ROE, we get:

Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]

0.132 = [ROE(0.75)] / [1 – ROE(0.75)]

ROE = 0.1555, or 15.55%

Now we can use the DuPont identity to find the profit margin as:

ROE	=	PM(TAT)(EM)
0.1555	=	PM(1 / 0.96)(1 + 1.60)
PM	=	(0.1555) / [(1 / 0.96)(2.6)]
PM	=	0.0574, or 5.74%