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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.