A firm wants a sustainable growth rate of 2.55 percent while maintaining a dividend payout ratio of 35 percent and a profit margin of 4 percent. The firm has a capital intensity ratio of 2. What is the debt–equity ratio that is required to achieve the firm's desired rate of growth?

In order to determine the required debt to equity ratio, we must first determine the equity multiplier. And to be able to determine the equity multiplier, we first need the return on equity (ROE).

Debt to equity ratio = total liabilities / equity
Equity multiplier (EM) = 1 + Debt to equity ratio

First we must determine the return on equity (ROE)

0.0255 = {ROE x (1-.35)} / {1-[ROE x (1-.35)]}

0.0255 = 0.65ROE / (1 - 0.65ROE)

0.0255(1 - 0.65ROE) = 0.65 ROE

0.0255 - 0.016575ROE = 0.65ROE

0.0255 = 0.666575ROE

ROE = 0.0255/0.666575

ROE = 0.0383

0.0383 = 0.04 x (1 / 2) x EM

0.0383 = 0.02EM

EM = 0.0383 / 0.02 = 1.92

1.92 = 1 + Debt to Equity ratio

Debt to equity ratio = 1.92 - 1 = 0.92