Question

For the most recent fiscal year, the Hammock Company’s total assets were $850 and net income was equal to $97. Of the $97 net income, $44 was retained. What is the internal growth rate for the Hammock Company?

Answer 1

To calculate the internal growth rate (IGR) for Hammock Company, we can use the following formula:

\[
\text{Internal Growth Rate (IGR)} = \frac{\text{Return on Equity (ROE)} \times \text{Retention Ratio}}{1 - (\text{Return on Equity (ROE)} \times \text{Retention Ratio})}
\]

First, we'll need to calculate the Return on Equity (ROE):

\[
\text{ROE} = \frac{\text{Net Income}}{\text{Total Equity}}
\]

1. **Calculate Total Equity**: Since we know total assets and that all net income is either retained or distributed, we can calculate total equity or implied equity. Here, we need to determine it from the net income and the retained earnings.

\[
\text{Total Equity} = \text{Net Income} + \text{Dividends Paid} \quad \text{(Dividends Paid can be calculated as Net Income - Retained Earnings)}
\]

From the provided data:
- Net Income = $97
- Retained Earnings = $44

Therefore, Dividends Paid = \(97 - 44 = 53\)

Using the given information, since we only need total assets to determine total equity, assuming there are no other liabilities,
we can consider that:
\[
\text{Total Equity} = \text{Total Assets} = 850
\]

2. **Calculate ROE**:

\[
\text{ROE} = \frac{97}{850} \approx 0.1141 \quad \text{(or } 11.41\%\text{)}
\]

3. **Calculate Retention Ratio**:

The retention ratio is calculated as follows:
\[
\text{Retention Ratio} = \frac{\text{Retained Earnings}}{\text{Net Income}} = \frac{44}{97} \approx 0.4536 \quad \text{(or } 45.36\%\text{)}
\]

4. **Calculate IGR**:

Now substitute the values into the IGR formula:
\[
\text{IGR} = \frac{ROE \times \text{Retention Ratio}}{1 - (ROE \times \text{Retention Ratio})}
\]

So,
\[
\text{IGR} = \frac{0.1141 \times 0.4536}{1 - (0.1141 \times 0.4536)} = \frac{0.05173}{1 - 0.05173} = \frac{0.05173}{0.94827} \approx 0.0546 \quad \text{(or } 5.46\%\text{)}
\]

Therefore, the internal growth rate for Hammock Company is approximately **5.46%**.