Skyline Innovations has net income of $300, total equity of $2,500, a debt-equity ratio of 0.8, and a plowback ratio of 50%. What is the internal growth rate?
Question:
Skyline Innovations has net income of $300, total equity of $2,500, a debt-equity ratio of 0.8, and a plowback ratio of 50%. What is the internal growth rate?
This is AI generated Response.
Asked by: Test User 100083
Created at: 2025-05-01 10:19:45
Asked by: Test User 100083
Created at: 2025-05-01 10:19:45
Final Answer:
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Let's break down the problem step-by-step.
**Given Data:**
- Net income (NI) = \$300
- Total equity (TE) = \$2,500
- Debt-equity ratio (D/E) = 0.8
- Plowback ratio (b) = 50% = 0.5
---
### Step 1: Find the Return on Equity (ROE)
ROE = Net Income / Total Equity
\[
ROE = \frac{300}{2500} = 0.12 \text{ or } 12\%
\]
---
### Step 2: Find the **Retained Earnings** to use in growth calculation
Since the plowback ratio is 50%, retained earnings are:
\[
\text{Retained Earnings} = \text{Net Income} \times b = 300 \times 0.5 = 150
\]
---
### Step 3: Find the **Total Assets**
From the debt-equity ratio:
\[
D/E = 0.8
\]
Total assets (A) relate to equity and debt:
\[
A = E + D
\]
But:
\[
D = D/E \times E = 0.8 \times 2500 = 2000
\]
Therefore:
\[
A = E + D = 2500 + 2000 = 4500
\]
---
### Step 4: Find the **Total Asset Turnover (TAT)** or **Return on Assets (ROA)**
To find the internal growth rate, we need the firm's **ROA**:
\[
ROA = \frac{\text{Net Income}}{\text{Total Assets}} = \frac{300}{4500} = 0.0667 \text{ or } 6.67\%
\]
### Step 5: Calculate the **Internal Growth Rate (IGR)**
The formula for IGR is:
\[
IGR = \frac{ROA \times b}{1 - ROA \times b}
\]
where:
- \(ROA\) is the return on assets
- \(b\) is the plowback ratio
Plugging in the numbers:
\[
IGR = \frac{0.0667 \times 0.5}{1 - 0.0667 \times 0.5} = \frac{0.03335}{1 - 0.03335} = \frac{0.03335}{0.96665} \approx 0.0345
\]
Expressed as a percentage:
\[
IGR \approx 3.45\%
\]
---
## **Final Answer:**
**The internal growth rate of Skyline Innovations is approximately \(\boxed{3.45\%}\).**
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