Question

# A firm wants a sustainable growth rate of 3.73 percent while maintaining a dividend payout ratio...

A firm wants a sustainable growth rate of 3.73 percent while maintaining a dividend payout ratio of 39 percent and a profit margin of 8 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?

Retention ratio=1-payout ratio

=(1-0.39)=0.61

Sustainable growth rate=(ROE*Retention ratio)/[1-(ROE*Retention ratio)]

0.0373=(ROE*0.61)/[1-(ROE*0.61)]

0.0373[1-(ROE*0.61)]=(ROE*0.61)

0.0373-0.022753ROE=0.61ROE

ROE=0.0373/(0.022753+0.61)

=0.058948752

Capital intensity ratio=Total assets/Sale

Hence Total assets=2Sales

Total asset turnover=Sales/Total assets

=Sales/2Sales

=0.5

ROE=Profit margin*Total asset turnover*Equity multiplier

0.058948752=0.08*0.5*Equity multiplier

Equity multiplier=0.058948752/(0.08*0.5)

=1.4737188

Equity multiplier=Total assets/Equity

Total assets =1.4737188equity

Total assets=debt+equity

Hence debt==1.4737188equity-equity

=0.4737188equity

Hence debt-equity ratio=debt/equity

=0.4737188equity/equity

=0.4737(Approx).

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