15. Consider a no-load mutual fund with $400 million in assets, 50 million in debt, and 15 million shares at the start of the year; and $500 million in assets, 40 million in debt, and 18 million shares at the end of the year. During the year investors have received income distributions of $0.50 per share, and capital gains distributions of $0.30 per share. Assuming that the fund carries no debt, and that the total expense ratio is 0.75%, what is the rate of return on the fund

Answer:

12.09%.

Explanation:

Calculation to determine the rate of return on the fund

First step is to calculate the beginning year NAV

Beginning year NAV = ($400 million assets - 50 million debt) / 15 million shares

Beginning year NAV = 23.33

Second step is to calculate the ending year NAV

Ending year NAV = ($500 million assets - (500*0.75% expense) - 40 million debt] / 18 million shares

Ending year NAV =[456.25/18 million shares]

Ending year NAV =25.35

Now let calculate the return using this formula

Return = (Ending NAV -beginning NAV + Capital gain + income) / Beginning NAV)

Let plug in the formula

Return = (25.35-23.33+0.30+0.50)/23.33

Return = 12.09%

Therefore the rate of return on the fund is 12.09%