Question

1. Suppose an open end mutual fund has $10000 worth of assets. There are 1000 shares outstanding.
   1. (10 points) If the fund value rises by 8% and there is a 25 basis point management fee that is subtracted from the asset value at the end of the year, what is the return on a share of the fund?

2. (10 points) Suppose that at the beginning of the year a new investor comes in and invests another $1000. If the same return and fees happen as in (a) above, what will be the return for the new investor?

3. (10 points) Suppose instead of what happened in (b) the new investor puts money in the fund at the end of the year, after the asset value has changed and after the fees have been charged. How many shares will the new investor have?

Answer 1

a. per share value of fund in the beginning = beginning value of assets/no. of shares outstanding = $10,000/1,000 = $10

fund value at the end of year = [beginning fund value*(1 + % rise in fund value)*(1-management fee) = [$10,000*(1+0.08)]*(1-0.0025‬) = ($10,000*1.08)*0.9975‬ = $10,800‬*0.9975 = $10,773

per share value of fund in the end = $10,773/1,000 = $10.773‬

return on a share of fund = (per share value of fund in the end/per share value of fund in the beginning) - 1 = ($10.773/$10) - 1 = 1.0773‬ - 1 = 0.0773‬ or 7.73‬%

b. no. of shares new investor will get = investment amount/per share fund value = $1,000/$10 = 100

no. of shares outstanding = existing shares + shares of new investor = 1,000 + 100 = 1,100

fund value at the end of year = [($10,000 + $1,000)*(1+0.08)]*(1-0.0025‬) = ($11,000*1.08)*0.9975‬ = $11,880‬*0.9975 = $11,850.3‬

per share value of fund in the end = $11,850.3‬/1,100 = $10.773

return for the new investor = (per share value of fund in the end/per share value of fund in the beginning) - 1 = ($10.773/$10) - 1 = 1.0773‬ - 1 = 0.0773‬ or 7.73‬%

c. no. of shares new investor will have = investment amount/per share value of fund in the end = $1,000/$10.773 = 92.8 rounded off to 93 shares