To calculate the net new financing needed for next year, we can break the problem down into several steps:

Step 1: Calculate Retained Earnings

First, we need to calculate how much of the net income will be retained by the firm after the dividend payout. This can be done using the firm's payout ratio.

The formula for retained earnings is:

$\text{Retained Earnings} = \text{Net Income} \times (1 - \text{Payout Ratio})$

Given:

• Net Income = $49,600
• Payout Ratio = 10.1% = 0.101

$\text{Retained Earnings} = 49,600 \times (1 - 0.101) = 49,600 \times 0.899 = 44,550.4$

Retained Earnings ≈ $44,550.

Step 2: Calculate Change in Stockholders' Equity

The retained earnings will increase the stockholders' equity. So, the change in stockholders' equity is equal to the retained earnings:

$\Delta \text{Equity} = \text{Retained Earnings} = 44,550$

Step 3: Calculate Total New Financing Required

Now, we calculate the total assets needed, subtract the increase in liabilities (non-debt liabilities such as accounts payable), and account for the increase in equity to find the financing gap.

The formula is:

$\text{Net New Financing} = \text{Ending Assets} - (\text{Beginning Liabilities} + \text{Increase in Non-Debt Liabilities}) - (\text{Beginning Equity} + \Delta \text{Equity})$

Where:

• Ending Assets = $506,000
• Beginning Liabilities = $120,500
• Increase in Non-Debt Liabilities = $9,900
• Beginning Equity = $295,000
• Change in Equity = $44,550 (from retained earnings)

Substitute the values:

$\text{Net New Financing} = 506,000 - (120,500 + 9,900) - (295,000 + 44,550)$ $\text{Net New Financing} = 506,000 - 130,400 - 339,550$ $\text{Net New Financing} = 506,000 - 469,950 = 36,050$

Final Answer:

The net new financing needed for next year is approximately $36,050.

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Would you like more details on any step or have further questions? Here are some related topics to explore:

1. How does the payout ratio affect retained earnings?
2. What are non-debt liabilities and how do they affect financing needs?
3. How do changes in stockholders' equity influence financing?
4. What is the difference between net income and retained earnings?
5. How is the ending balance of assets estimated?

Tip: Always ensure you understand the role of liabilities when calculating new financing to avoid underestimating or overestimating your capital needs.