Question

You are endowed with $5,000 of after-tax cash and 20-year investment horizon. You have a marginal tax rate of 40% and you expect to face the same rate over the next 20 years. You expect that investing passively in an index fund will generate a 10% return each year, pretax, for the next 20 years

The future value of a $1 investment for 20 periods is as follows:

R		Factor
6%		3.207
8%		4.661
10%		6.728
12%		9.646
14%		13.744

You choose to learn tax planning and invest passively. You invest in a 401(k) account (or similar tax-deferred vehicle) such that the after-tax cash cost of the investment is $5,000. What is the after-tax future value of your investment?

Answer 1

In 401k account pre tax contributions are made but withdrawals are taxed from the account. Therefore, we should first find the pre tax amount of contribution. We are endowed with $5000 of after tax cash. So, the pre tax cash amount will be = $5000/ 0.6 (Since tax rate is 40%)

=$8333.33

Let's now find the future value of the amount invested -

FV = PV (1+i)ⁿ

Rate Factor Future Value    After tax Future Value

6% 3.207 $8333.33 X 3.207 = $26,725   $26,725 X 0.6 = $16,035

8% 4.661   $8333.33 X 4.661 = $38,842 $38,842 X 0.6 = $23,305.2

10% 6.728   $8333.33 X 6.728 = $56,067 $56,067 X 0.6 = $33,640.2

12% 9.646   $8333.33 X 9.646 = $80,383 $80,383 X 0.6 = $48,230

14% 13.744 $8333.33 X 13.744 = $114,533 $114,533 X 0.6 = $68,720