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.

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.