Question

Suppose that at the start of the year, a no-load mutual fund has a net asset value of $27.25 per share. During the year, it pays its shareholders a capital gain and dividend distribution of $1.50 per share and finishes the year with an NAV of $30.46.

a. What is the return to an investor who holds 258.176 shares of this fund in his (nontaxable) retirement account? Do not round intermediate calculations. Round your answer to two decimal places.
b. What is the after-tax return for the same investor if these shares were held in an ordinary savings account? Assume that the investor is in the 30% tax bracket. Do not round intermediate calculations. Round your answer to two decimal places.
c. If the investment company allowed the investor to automatically reinvest his cash distribution in additional fund shares, how many additional shares could the investor acquire? Assume
that the distribution occurred at year end and that the proceeds from the distribution can be reinvested at the year-end NAV. Do not round intermediate calculations. Round your answers to three decimal places.
Nontaxable distribution: shares
Taxable distribution: shares

Answer 1

An investor in a nontaxable account would have a return of approximately 17.28%, while in a taxable account, the after-tax return would be approximately 15.63%. If allowed to reinvest, they would acquire 12.711 additional shares in a nontaxable account and 8.898 shares in a taxable account.

Step-by-step explanation:

Return to an investor in a nontaxable account:

To calculate the return, we need to account for the increase in NAV and the distributions paid. The overall value at the end of the year is 258.176 shares * $30.46 NAV = $7,866.07. The value at the beginning of the year was 258.176 shares * $27.25 NAV = $7,037.30. The distribution adds 258.176 shares * $1.50 = $387.26. So, the total return is ($7,866.07 + $387.26) - $7,037.30 = $1,216.03. The return as a percentage is $1,216.03 / $7,037.30 = approximately 17.28%.

After-tax return for the same investor in an ordinary savings account:

Taxable income from distribution is $387.26. Tax owed on this at 30% is $116.18. The after-tax income is $387.26 - $116.18 = $271.08. The after-tax return is the total return minus taxes: $1,216.03 - $116.18 = $1,099.85. The after-tax return as a percentage is $1,099.85 / $7,037.30 = approximately 15.63%.

Additional shares from reinvestment:

The investor could acquire additional shares equal to the distribution divided by the ending NAV: $387.26 / $30.46 = 12.711 additional shares. For a taxable account, after paying tax, the investor could purchase $271.08 / $30.46 = 8.898 shares.