Allen, inc., has a total debt ratio of .34. what is its debt-equity ratio

Total debt ratio is the ratio of total debt to total assets 
i.e 
Total debt ratio = Total debt / Total assets  
But Total assets is nothing but total equity plus total debt  
Now let us consider, 
TD = Total debt  
TE = Total equity 
TA= Total assets   
Therefore, 
Total debt ratio = TD/TA 
But as mentioned above 
TA = TD + TE  
total debt ratio = Total debt/(total debt+total equity) 
total debt ratio = .34(given) 
.34 = TD / (TD + TE)  
Solving this equation yields:  
0.34 = 1/(1+ TE/TD) 
0.34(1+TE/TD) = 1 
0.34 + 0.34TE/TD =1 
.34(TE/TD) = 1 - 0.34 
0.34 (TE/TD) = 0.66 
0.34TE = 0.66TD  
Now, Debt equity ratio is the ratio of Total debt to total equity  
Debt-equity ratio = TD / TE 
Debt-equity ratio = 0.34 / 0.66 
Debt-equity ratio = 0.51515152

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