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The table you have provided shows the "Required Annualized After-Corporate-Tax—but Before Shareholder-Level Tax—Return on Shares" (\( r_c^* \)) for different shareholder tax rates (\( t_p = t_{\text{div}} \), \( t_{\text{cg}} \)) and holding periods (\( n \)).

### Understanding the Terms:

- \( t_p \) (or \( t_{\text{div}} \)): Shareholder tax rate on dividends.
- \( t_{\text{cg}} \): Shareholder tax rate on capital gains.
- \( R_p \): Partnership before-tax return, set to 10%.
- \( r_c^* \): After corporate tax but before shareholder-level tax rates.
- \( n \): Holding period (1, 5, 10, 20, 50 years).

The formula used to calculate the values \( r_c^* \) in the table likely relates to compounding effects over different holding periods and tax rates. Without the exact equation, let's try a general setup:

\[
r_c^* = \text{Function} (R_p, t_p, t_{\text{cg}}, n)
\]

The table seems to give the return based on \( t_p \) and \( t_{\text{cg}} \) for different holding periods.

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Let me know if you would like to focus on a particular set of calculations or if you need a step-by-step breakdown for a specific scenario (e.g., \( t_p = 50\%, t_{\text{cg}} = 20\% \), and \( n = 5 \))!

Would you like more details on this or the exact formulas? Here are 5 related questions that can help expand your understanding:

1. How is the relationship between holding periods (\( n \)) and returns (\( r_c^* \)) derived?
2. How do the different tax rates impact the final return?
3. Why does the after-tax return decrease for longer holding periods under higher tax rates?
4. What role does the dividend tax rate (\( t_{\text{div}} \)) play compared to the capital gains tax rate (\( t_{\text{cg}} \)) in this calculation?
5. How can the partnership before-tax return (\( R_p \)) affect the overall return calculation?

**Tip**: Understanding tax effects on investments can help optimize portfolio decisions based on different holding periods and tax obligations.

Explore how to calculate the required annualized after-corporate-tax returns on shares before shareholder-level taxes, considering different tax rates and holding periods. This detailed breakdown includes core formulas and highlights the impact of dividends, capital gains tax rates, and the compounding effect over time.

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