What Is the After-tax Rate of Return on a Tax-deferred Investment?

Wednesday, February 25, 2015 11:15
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What Is the After-tax Rate of Return on a Tax-deferred Investment?

Suppose you have a deferred annuity with a pre-tax value of $100 and a cost basis of $60. And suppose the pre-tax rate of return is 10%, and your tax rate is 30%. What is the one-year after-tax rate of return?

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If you measure this as the one-year growth rate in the after-tax values, the answer is 7.95% (rounded). The after-tax value is $88 at the beginning of the year and $95 at the end of the year, and 95/88 minus 1 is 0.0795.

You can divide the tax-deferred investment into two pieces: a fully taxable piece and a tax-free piece. The fully taxable piece has an after-tax return that you calculate in the usual way: multiply the pre-tax return by 1 minus the tax rate. The tax-free piece has an after-tax return that is equal to the pre-tax return.

If the tax rate is constant, the after-tax return of the tax-deferred investment is the weighted sum of the after-tax returns of the two pieces. The weight of the fully taxable piece is the cost basis divided by the initial after-tax value, and the weight of the tax-free piece is the remainder.

In the example above, the fully taxable piece has an after-tax return of 7% and a weight of 60/88, and the tax-free piece has an after-tax return of 10% and a weight of 28/88. And (.07)(60/88) + (.10)(28/88) = 0.0795 (allowing for rounding).

Suppose you buy a tax-deferred investment and drop it after one year. The fully taxable piece has a weight of 100%, because the cost basis equals the initial investment, so the tax-deferred investment looks like a fully taxable investment.

On the other hand, if you buy and hold the tax-deferred investment for a thousand years, the cost basis will be just a miniscule fraction of the after-tax value, so the weight of the tax-free piece will be almost 100%, and the one-year after-tax rate of return will be almost the same as the pre-tax rate of return.

So what?

A few weeks ago I reviewed several large life insurance policies for a family office, and they wanted to explore their alternatives. Would it make sense to drop the policies, pay income tax on the gains and invest the money somewhere else? The cost basis was equal to about 77% of the cash surrender values, and maybe about 85% of the after-tax values. It might be possible to justify paying income tax now to have more investment flexibility and capital-gains tax rates in the future.

But if you pulled out the cash value up to the cost basis, the weighting of the tax-free piece would go from 15% to 100%, and it would be very difficult to make a case for removing more money from the tax-deferred environment in this situation.

Of course, you could arrive at the same conclusion without any arithmetic, but the arithmetic reinforces common sense.

 

 

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