Shares in growth products inc. are priced at $100. investors expect the total pr

Question

Shares in growth products inc. are priced at $100. investors expect the total pretax rate of return to be 10%. the tax rate on both capital gains and dividends is 15%.
a. If the entire return on the shares is in the form of dividends, what is the investor's annualized after-tax rate of return for a holding period of 1 year? 5 years? 10 years? 20 years?
b. what is the investors annualized after-tax rate of return for each holding period if all of the pretax return is in the form of capital gains?
c. explain why capital gains may be prefered to dividends even if the tax rate on the two are equal.

Explanation / Answer

(a) Entire return is in the form of dividends and it is 10% So annual dividend = 100*10% = 10 Tax on dividend is 15% = 10*15% = 1.5 After tax return = (10-1.5) = 8.5 After tax rate of return = 8.5/100 = 8.5% We get an annual after tax return of 8.5% irrespective of holding period in this case. (b) Entire return is in the form of capital gain and is 10% 1 year holding period: So increase in share price after one year = 100*10% = 10 Share price after 1 year = 100 + 10 =110 Tax on capital gain = 10*15% = 1.5 after tax rate of return = (10-1.5)/100 = 8.5% 5 year holding period: So share price after 5 years = 100*(1+10%)^5 = 161.051 After tax return = 161.051-100 = 61.051 Tax on capital gain = (161.051-100)*15% = 9.15765 annualized after tax rate of return = [(161.051-9.15765)/100]^(1/5) -1 = 8.71957% 10 year holding period: So share price after 10 years = 100*(1+10%)^10 = 259.374 After tax return = 259.374-100 = 159.374 Tax on capital gain = (259.374-100)*15% = 23.906 annualized after tax rate of return = [(259.374-23.906)/100]^(1/10) -1 = 8.94145% 20 year holding period: So share price after 20 years = 100*(1+10%)^20 = 672.749 After tax return = 672.749-100 = 572.749 Tax on capital gain = (672.749-100)*15% = 85.912 annualized after tax rate of return = [(672.749-85.912)/100]^(1/20) -1 = 9.2511% (c) For a growth stock, capital gains are preferred to dividends as they yield higher holding period returns. Since the profits from the previous period are reinvested to gain higher returns unlike cashed out like dividends, capital gains give higher returns than dividends though they have the same tax rate. Please rate my answer! thanks in advance :)

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