Question

Last year, you invested $90,000 into Jones mutual fund. The fund had a NAV of $45 when you opened your account. Jones fund charges a 3% front end load and a 2% back end load. During the course of the year, the fund paid $5/share in distributions, which you fully reinvested in the fund by purchasing new shares at a price of $44/share. The fund currently has a NAV of $48.

How many shares did you buy when you opened your position? Round intermediate steps to four decimals and your final answer to the nearest whole share. How many additional shares did you purchase with your distributions? Round to the nearest whole share. And Lastly calculate your HPR.

Answer 1

Initial investment amount = $90,000

There are 3% front end load of $90,000 = $2,700

Therefore Net fund invested = $90,000 - $2,700 =$87,300

The fund had a NAV of $45

Shares did you buy when you opened your position = Net fund invested /fund’s NAV

=$87,300 /$45

= 1,940 shares

During the course of the year, the fund paid $5/share in distributions

The distribution amount = fund paid per share in distributions * Initial number of shares

= $5 *1,940 shares

=$9,700

The distribution amount is fully reinvested in the fund by purchasing new shares at a price of $44/share (assume that there is no front end load on reinvestment of distribution income)

Additional shares did you purchase with your distributions

=$9,700 / $44

=220.4545 shares or 220 shares (rounding to nearest whole number)

Now Total number of shares = Shares did you buy when you opened your position + Additional shares did you purchase with your distributions

= 1,940 shares +220 shares

= 2,160 shares

The fund currently has a NAV of $48/ shares

Therefore,

Current value of investment = 2,160 shares * $48/ shares

= $103,701.816

If it is sold, there is 2% back end load

Net Current value of investment = $103,701.816 *(1-2%)

= $101,627.7797

Therefore,

Holding period return = (Current value of investment – initial investment) / initial investment

= ($101,627.7797 - $90,000)/ $90,000

= $11,627.7797 / $90,000

=0.1292 or 12.92%