The ROA of your firm is 5%. The firm also has a debt-asset ratio of 70%. If your firm reinvests 100% of its earnings, at what rate can your assets grow without having to change your capital structure? Further, at what rate can your assets grow without having to raise capital externally?   I know the formula for sustainable growth is ROE x b / 1 - ROE x b   Internal growth ROA x 1 - b / 1 - (ROA x 1- b)   But I do not know how to get the information with what is provided.  I think I'm missing a formula to go from ROA (which is the 5% provided) to ROE.   Can you show me how to solve this problem? Thank you in advance for your help.

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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The ROA of your firm is 5%. The firm also has a debt-asset ratio of 70%. If your firm reinvests 100% of its earnings, at what rate can your assets grow without having to change your capital structure?
Further, at what rate can your assets grow without having to raise capital externally?
 
I know the formula for sustainable growth is
ROE x b / 1 - ROE x b
 
Internal growth
ROA x 1 - b / 1 - (ROA x 1- b)
 
But I do not know how to get the information with what is provided.  I think I'm missing a formula to go from ROA (which is the 5% provided) to ROE.
 
Can you show me how to solve this problem?
Thank you in advance for your help.
 
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