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# Investments for Tax Purposes

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Following is a problem and the answer. Can anyone explain the steps that were used and why? Is there an easier way to perform the calculations?

A Taxpayer is considering three alternative investments of \$10,000. Assume the taxpayer is in the 28% marginal tax bracket for ordinary income and 15% for qualifying capital gains in all tax years. The selected investment will be liquidated at the end of 5 years. The alternatives are:

A taxable corporate bond yielding 5% before tax and the interest can be reinvested at 5% before tax

A Series E bond that will have a maturity value of \$12,000 (a 4% before-tax rate of return

Land that will increase in value

The gain on the land will be classified and taxed as a long-term capital gain. The income from the bonds is taxed at ordinary income. How much must the land increase in value to yield a greater after-tax return than either of the bonds?

Given: Compound amount of \$1 and compound value of annuity payments at the end of five years:

Interest rate \$1 Compounded for 5 yrs \$1 Annuity compounded for 5 yrs
5% \$1.28 \$5.53
4% \$1.22 \$5.42
3.6% \$1.19 \$5.37

The taxable bond and reinvested earnings will accumulate at an after-tax rate
of 3.6% [(1-.28) × .05] to equal \$11,900 at the end of 5 years [(\$10,000 × 1.19) = \$11,900].
The income from the Series EE bond will not be taxed until maturity in five years,
and the after-tax value will be \$11,584 [\$12,200 - .28(\$12,200 - \$10,000)].

Thus, the after-tax proceeds from the land must exceed \$11,900.
Because the gain on the land will be taxed as a long-term capital gain, the sales
proceeds less 15% of the appreciation must exceed \$11,900.
\$10,000 + (1 - .15)(X - \$10,000) = \$11,900
\$10,000 + .85X - \$8,500 = \$11,900
.85X = \$10,400
X = \$12,235
Thus, the land must increase in value by at least \$2,235 to yield a greater after-tax return than the investment in either of the bonds.

#### Solution Preview

There isn't really an easier way to do this. You have three investments and you need to know which one has the highest return. The only way to compare them is to calculate the returns.

I.
The corporate bond is a very simple calculation with one little twist, every year you must pay taxes on your interest, fortunately the tax rate is given as 28%. Thus you will net the remaining 72% which you can reinvest. So the after tax return (money left to reinvest for the next year) is 72% x 5% = 3.6%, so you will be earning 3.6% each year. After year one you'll have 10,000 principle+ 10,000 *3.6% interest = 10,000*(1.036). The interest will compound after each year so after year 2 you will have 10,000 * (1.036)*(1.036). The formula for 5 years is ...

#### Solution Summary

Analyzing various investments for tax purposes.

\$2.19