In: Finance
A closed-end fund starts the year with a net asset value of $30. By year-end, NAV equals $31.90. At the beginning of the year, the fund is selling at a 2% premium to NAV. By the end of the year, the fund is selling at a 7% discount to NAV. The fund paid year-end distributions of income and capital gains of $3.30. a. What is the rate of return to an investor in the fund during the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Rate of return % b. What would have been the rate of return to an investor who held the same securities as the fund manager during the year? (Round your answer to 2 decimal places.) Rate of return %
a). Fund NAV at the beginning of the year = $30
It is selling at a 2% premium, so selling price is 20*(1+2%) = $30.60
Year-end distribution = $3.30
Fund NAV at the end of the year = $31.90
It is selling at a 7% discount, so exit price is 31.90*(1-7%) = $29.67
Total return = (exit price - price at which fund was bought) + distribution = (29.67-30.60) + 3.3 = $2.97
Total return % = total return/price at which fund was bought = 2.97/30.60 = 9.70%
b). If an investor had invested in the same securities as the fund:
Buying price = $30
exit price = $31.90
Distribution = $3.30
Total return = (exit price - buying price) + distribution = (31.90-30) + 3.30 = $5.20
Total return % = total return/buying price = 5.20/30 = 17.33%
Note: It is not specified whether the distribution amount of $3.30 consists only of dividends or other capital gains, as well. So, it has been assumed to be the same for the investor who directly invests in the same set of securities.