Question

23 . A closed-end fund starts the year with a net asset value of $21. By year-end, NAV equals $20.5. At the beginning of the year, the fund is selling at a 3% premium to NAV. By the end of the year, the fund is selling at a 4% discount to NAV. The fund paid year-end distributions of income and capital gains of $2.50. What is the rate of return to an investor in the fund during the year?

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Answer 1

Solution :

The formula for calculating the rate of return of the mutual fund is

= ( Selling price of the Fund + Income and capital gain distribution – Purchase price of the Fund ) / Purchase price of the fund

As per the information given in the question we have:

Income and Capital gains distribution = $ 2.50 ;

Year end NAV = $ 20.50   ;

By the end of the year, the fund is selling at a 4% discount to NAV.

Thus Selling price of the fund = Year end NAV * ( 1 – 0.04 ) = $ 20.50 * ( 1 – 0.04 ) = $ 20.50 * 0.96 = $ 19.68

NAV at the beginning of the year = $ 21   ;

At the beginning of the year, the fund is selling at a 3% premium to NAV.

Thus Purchase price of the fund = NAV at the beginning of the year * ( 1 + 0.03 )

= $ 21 * ( 1 + 0.03 ) = $ 21 * 1.03 = $ 21.63

Applying the above values in the formula for rate of return of the fund to the investor we have

= ( $ 19.68 + $ 2.50 – $ 21.63 ) / $ 21.63

= $ 0.55 / $ 21.63

= 0.025428

= 2.5428 %

= 2.54 % ( when rounded off to two decimal places )

The​ rate of return to an investor in the fund during the year is = 2.54 %