Question

Suppose you invest $100,000 in a mutual fund for 10 years. The fund earns 6% pretax per year, makes no annual distributions (and thus there is no income to be taxed each year) and you sell the fund at the end of the 10 years. You pay a 20% tax on capital gains and a 40% tax on ordinary income. What is the pre-tax total dollar accumulation at the end of 10 years? What is the after-tax total dollar accumulation at the end of 10 years? Suppose instead you invest the $100,000 in preferred stock paying 6% per annum with the dividend taxed at 20% per year (as dividends receive their own tax preferred rate). Assume the after-tax dividends are reinvested in the preferred stock. What is the after-tax total dollar accumulation at the end of 10 years? What do you conclude from comparing the above alternatives?

Answer 1

a) Fund pre-tax Amount $ 179,084.77

b) Funds after-tax $ 163,267.82

c) Dividends after-tax amount : $ 159,813.27

Step-by-step explanation:

We calcuale the future value of the fund at 6% annual rate over a 10-years period:

`Principal \: (1+ r)^(time) = Amount`

Principal 100,000.00

time 10.00

rate 0.06000

`100000 \: (1+ 0.06)^(10) = Amount`

Amount 179,084.77

after taxes, as this were held for a longer period will be considered long term gain and taxes at 20%:

179,084.77 - 100,000 = 79,084.77 capital long-term gain subject to taxation

79,084.77 * (1-0.20) = 63,267.82

Now we add the 100,000: 163,267.82

Alternative scenario:

6% less 20% dividends tax after-tax return on dividends:

0.06 x (1 - 0.2) = 0.048

We calcualte the future value using this rate:

`Principal \: (1+ r)^(time) = Amount`

Principal 100,000.00

time 10.00

rate 0.04800

`100000 \: (1+ 0.048)^(10) = Amount`

Amount 159,813.27