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.

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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