You are endowed with $5,000 of after-tax cash and 20-year investment horizon. Yo

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?

      R

Factor

      6%

3.207

      8%

4.661

      10%

6.728

      12%

9.646

      14%

13.744

Explanation / Answer

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

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