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 isROE x b / 1 - ROE x b Internal growthROA 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.

Question
Asked Apr 6, 2019
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.
 
check_circleExpert Solution
Step 1

Calculating the value of internal growth rate. We have,

Internal Growth Rate = ROA X RR / (1 – ROA X RR)

Here,

ROA = Return on Asset = 5 %

RR = Retention Ratio = 100%

(It is because firm reinvest 100% of its earnings)

By substituting these value in the above formula. We get;

Internal Growth Rate = (5% x 100%) / (1 – 5% x 100%)

Internal Growth Rate = 0.05 / (1 – 0.05)

Internal Growth Rate = 0.05 / 0.95

Internal Growth Rate = 0.0526*100

Internal Growth Rate = 5.26 %

Step 2

Since, the internal growth rate is the growth rate a firm can sustain if it uses only internal financing like retained earning...

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