One way to compare the accumulation of income by alterative 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 (S corporations, partnerships, and LLCs): ATA = [1 + R(1 − tp)]n
C corporation: ATA = [1 + R(1 − tc)]n (1 − tg) + tg
Where:
• After-tax accumulation in n years  ATA = 
• Before-tax rate of return; R =
• tp owner’s marginal tax rate on ordinary income =
• tc corporation’s marginal tax rate =
• tg owner’s tax rate on capital gains =
• Number of periods n =
For each alternative business form, the owner makes an initial investment of $1. The following operating assumptions apply:
• Before-tax rate of return (R) = 0.18
• Marginal tax rate for owner (tp) = 0.396
• Corporate tax rate (tc) = 0.35
• Capital gains rate (tg) = 0.238 for regular capital gains, including the 3.8% tax on net investment income (assume the Sec. 1202 50% exclusion for small business corporations does not apply)
• Investment horizon (n) = 2, 4, 20, 50, or 101 years
A flow-through entity distributes only enough cash each year for the owners to pay their taxes. The corporation pays no dividends. The shareholders sell their stock at the end of the investment horizon, and their gains are taxed at capital gains rates. (See Chapter I:18 of the Individuals volume for a detailed explanation of these models.)
Required: 
What is the after-tax accumulation if each business form is operated for the investment horizon and then sold for the amount of the accumulation? Which entity form is best for each investment horizon? How would your calculations and conclusions change if the C corporation’s tax rate is 25%?