One way to compare the accumulation of income by alternative business entity forms is to use mathematical

Question:

One way to compare the accumulation of income by alternative business entity forms is to use mathematical models. The following models express the investment after-tax accumulation calculation for a particular entity form:
Flow-through entities and sole proprietorships: Contribution Ã— [1 + R(1 ˆ’ tp)]n
C corporation: Contribution Ã— {[1 + R(1 ˆ’ tc)]n(1 ˆ’ tg) + tg}
Where:

In the C corporation model, the corporation operates for n years, paying taxes currently and distributing no dividends. At the end of its existence, the corporation liquidates, causing the shareholder to recognize a capital gain. In the flow-through model, the entity or sole proprietorship distributes just enough cash for the owner or owners to pay individual taxes, and the entity reinvests the remaining after-tax earnings in the business.
Now consider the following facts. Twelve years ago, your client formed a C corporation with a $100,000 investment (contribution). The corporation€™s before-tax rate of return (R) has been and will continue to be 10%. The corporate tax rate (tc) has been and will continue to be 35%. The corporation pays no dividends and reinvests all after-tax earnings in its business. Thus, the corporation€™s value grows at its after-tax rate of return. Your client€™s marginal ordinary tax rate (tp) has been 33%, and her capital gains rate (tg) has been 15%. Your client expects her ordinary tax rate to drop to 25% at the beginning of this year and stay at that level indefinitely. Her capital gains tax rate will remain at 15%. Assume the corporate stock does not qualify for the Sec. 1202 exclusion.
Your client wants you to consider two alternatives:
(1) Continue the business in C corporation form for the next 20 years and liquidate at that time (32 years in total).
(2) Liquidate the C corporation at the end of the 12-year period, invest the after-tax proceeds in a sole proprietorship, and operate as a sole proprietorship for the next 20 years.
The sole proprietorship€™s before-tax rate of return (R) also will be 10% for the next 20 years. Earnings from the sole proprietorship will be taxed currently at your client€™s ordinary tax rate, and your client will withdraw just enough earnings from the business to pay her taxes on the business€™s income. The remaining after-tax earnings will remain in the business until the end of the investment horizon (20 years from now).
Required:
Show the results of each alternative along with supporting models and calculations. Ignore self employment taxes and the accumulated earnings tax. Which alternative should your client adopt?