Question

A firm wants a sustainable growth rate of 2.55% while maintaining a 35.00% dividend payout ratio and a profit margin of 4.00%. The firm has a capital intensity ratio of 2. What is the debt-equity ratio that is required to achieve the firm's desired ratio of growth?

A) 0.09

B) 0.23

C) 0.96

D) 0.91

Answer 1

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 = 1.91

1.91 = 1 + Debt to Equity ratio

Debt to equity ratio = 1.91-1=0.91

so, the answer is option D