Question 18.3: Your firm has $70 million in equity and $30 million in debt ...

PLAN
We can use Eqs. 18.4 and 18.5 to compute your firm’s internal and sustainable growth rates under the old and new policy. To do so, we’ll need to compute its ROA, ROE, and retention rate (plowback ratio). The company has $100 million (= $70 million in equity + $30 million in debt) in total assets

\text{Internal Growth Rate} = \left(\frac{\text{Net Income}}{\text{Beginning Assets}}\right) \times (1-\text{Payout Ratio}) = ROA\times \text{Retention Rate}           (18.4)

\text{Sustainable Growth Rate} = \left(\frac{\text{Net Income}}{\text{Beginning Equity}}\right) \times (1-\text{Payout Ratio}) = ROE\times \text{Retention Rate}          (18.5)

ROA = \frac{\text{Net Income}}{\text{Beginning Assets}}=\frac{14}{100}= 14\%        ROE = \frac{\text{Net Income}}{\text{Beginning Equity}}=\frac{14}{70}= 20\%

Old Retention Rate = (1 – Payout Ratio ) = (1 – 0.20 ) = 0.80
New Retention Rate = (1 – 0.30 ) = 0.70

EXECUTE
Using Eq. 18.4 to compute the internal growth rate before and after the change, we have:   Old Internal Growth Rate = ROA × Retention Rate = 14% × 0.80 = 11.2%
New Internal Growth Rate = 14% × 0.70 = 9.8%
Similarly, we can use Eq. 18.5 to compute the sustainable growth rate before and after:  Old Sustainable Growth Rate = ROE × Retention Rate = 20% × 0.80 = 16%
New Sustainable Growth Rate = 20% × 0.70 = 14%

EVALUATE
By reducing the amount of retained earnings available to fund growth, an increase in the payout ratio necessarily reduces your firm’s internal and sustainable growth rates.