Question

Komiko Tanaka invests $13,000 in LymaBean, Inc. LymaBean does not pay any dividends. Komiko projects that her investment will generate a 11 percent before-tax rate of return. She plans to invest for the long term. If she holds the investment for 6 years and then she sells it when the long-term capital gains rate is 15 percent, what is her after-tax rate of return?

Answer 1

Amount invested = 13000

Rate of return = 11%

Term = 6 years

Amount received after 6 years = amt invested* (1+rate)^{no of yr}

= 13000 * (1.11)⁶

= 24315

Capital gain = amount received - investment

= 24315-13000 = 11315

Tax on capital gain = 11315*15% = 1697

Net gain after capital gain tax = 11315 - 1697= 9618

Amount received net of tax = 24315-1697 = 22618

After tax rate of return

={ (amt received net of tax/amount invested)^{1/no of year} }-1

= (22618/13000)^1/6 - 1

= Approximately 9.65 or 9.7%