Profit margin=0.088
Capital intensity ratio=0.49
Debt-equity ratio=0.64
Net income=$99,000
Dividends=$46,000
Based on the above information, calculate the sustainable growth rate.

The **Sustainable Growth Rate (SGR)** is calculated using the following formula:

\[
SGR = \dfrac{ROE \times Retention \ Ratio}{1 - (ROE \times Retention \ Ratio)}
\]

Where:
- **ROE (Return on Equity)** is the return the company generates on its equity. It is calculated as:
\[
ROE = \dfrac{Net \ Income}{Equity}
\]
- **Retention Ratio** is the proportion of net income retained in the business, calculated as:
\[
Retention \ Ratio = 1 - Payout \ Ratio = 1 - \dfrac{Dividends}{Net \ Income}
\]

### Step-by-Step Solution:

1. **Retention Ratio:**
\[
Retention \ Ratio = 1 - \dfrac{Dividends}{Net \ Income} = 1 - \dfrac{46,000}{99,000} = 1 - 0.4646 = 0.5354
\]

2. **ROE (Return on Equity):**
To calculate ROE, we first need to find the equity. The **debt-equity ratio** is given as 0.64, which implies:
\[
Debt \ to \ Equity \ Ratio = \dfrac{Debt}{Equity} = 0.64
\]
Therefore, for every \$1 of equity, there is \$0.64 of debt. This gives us:
\[
Equity = \dfrac{Net \ Income}{Profit \ Margin} = \dfrac{99,000}{0.088} = 1,125,000
\]

Now, using the debt-equity ratio:
\[
Debt = 0.64 \times Equity = 0.64 \times 1,125,000 = 720,000
\]

Thus, total assets are:
\[
Assets = Equity + Debt = 1,125,000 + 720,000 = 1,845,000
\]

Finally, using ROE:
\[
ROE = \dfrac{Net \ Income}{Equity} = \dfrac{99,000}{1,125,000} = 0.088
\]

3. **Sustainable Growth Rate (SGR):**
\[
SGR = \dfrac{ROE \times Retention \ Ratio}{1 - (ROE \times Retention \ Ratio)}
\]

Substituting values:
\[
SGR = \dfrac{0.088 \times 0.5354}{1 - (0.088 \times 0.5354)} = \dfrac{0.0471}{1 - 0.0471} = \dfrac{0.0471}{0.9529} = 0.0494 \approx 4.94\%
\]

Thus, the **sustainable growth rate (SGR)** is approximately **4.94%**.

---

Would you like more details or have any questions?

Here are 5 related questions to further expand on this topic:

1. How does the debt-equity ratio influence the sustainable growth rate?
2. What is the impact of increasing the retention ratio on the sustainable growth rate?
3. How does the capital intensity ratio affect a company's growth prospects?
4. Can a company grow faster than its sustainable growth rate? What are the implications?
5. How do changes in profit margin affect the sustainable growth rate?

**Tip:** Always remember that SGR assumes that the company is growing without any additional external financing—it's the growth the company can sustain internally.

Learn how to calculate the sustainable growth rate using given financial metrics including profit margin, capital intensity ratio, debt-equity ratio, net income, and dividends. This problem involves key financial concepts like ROE and retention ratio, making it suitable for undergraduate finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation