Question

1b) Consider a no-load mutual fund with $200 million in assets and 10 million shares at the start of the year and with $250 million in assets and 11 million shares at the end of the year. During the year investors have received income distributions of $2 per share and capital gain distributions of $.25 per share. Assuming that the fund carries no debt, and that the total expense ratio is 1%, what is the rate of return on the fund? (6 points)

Answer 1

Solution :

Calculation of NAV at the start of the year :

As per the information given in the question we have

Total value of assets at the start of the year = $ 200 million

No. of shares outstanding at the start of the year = 10 million

Thus the NAV per share at the start of the year = Total value of assets at the start of the year / No. of shares outstanding at the start of the year

Applying the available information in the formula we have

= $ 200 / 10 = $ 20

The NAV per share at the start of the year = $ 20

Calculation of NAV at the end of the year :

As per the information given in the question we have

Total value of assets at the end of the year = $ 250 million

No. of shares outstanding at the end of the year = 11 million

Total expense ratio = 1 % = 0.01

Thus the NAV per share at the end of the year = ( Total value of assets at the end of the year * ( 1 – Expense Ratio ) ) / No. of shares outstanding at the end of the year

Applying the available information in the formula we have

= [ $ 250 * ( 1 – 0.01 ) ] / 11 = $ 20

= ( $ 250 * 0.99 ) / 11

= $ 247.50 / 11

= $ 22.50

The NAV per share at the end of the year = $ 22.50

Calculation of Rate of return on the fund :

As per the information given in the question we have

NAV per share at the start of the year = $ 20

NAV per share at the end of the year = $ 22.50

Income distribution per share = $ 2

Capital gain Distribution per share = $ 0.25

Thus the formula for calculating the Rate of return on the fund is

= [NAV per share at the end of the year - NAV per share at the start of the year + Income distribution per share + Capital gain Distribution per share ] / NAV per share at the start of the year

Applying the available information in the formula we have

= ( $ 22.50 - $ 20 + $ 2 + $ 0.25 ) / $ 20

= $ 4.75   / $ 20

= 0.2375

= 23.75 %

Thus the rate of return on the fund = 23.75 %