On January 1, a mutual fund owns 500 shares of Stock A, 700 shares of Stock B, a
ID: 2754337 • Letter: O
Question
On January 1, a mutual fund owns 500 shares of Stock A, 700 shares of Stock B, and 900 shares of Stock C. The fund has 5,000 shares outstanding. On July 1, the fund sells 450 shares of Stock C. Also on this day, a shareholder purchases 600 new shares of the fund. All money from the purchase of fund shares and the sale of Stock C is used to purchase as many shares of Stock D as possible, rounded to the nearest even hundred shares, i.e. 100, 200, 300, etc). Any money left over from this purchase is invested in cash which has no return. On December 31, the fund sells 200 shares of Stock A.
1) What is NAV of the fund on January 1, July 1, and Dec 31?
2) Assuming the fund distributes all realized capital gains, what is the capital gain distribution per share?
3) What is the annual return for a shareholder who was invested on January 1?
4) What was the fund turnover for the year?
Jan 1 - (Stock A - $34); (B-$63); (C-$52); (D-$48)
July 1 - (Stock A - $38); (B-$65); (C-$61); (D-$46)
Dec. 31 (Stock A - $40); (B-$68); (C-$65); (D-$54)
Please show how the answers were derived. I'm not sure how to get the numbers for July 1st (of course if this isn't correct the entire problem is wrong). Please show formulas for calculating the capital gains distribution per share and the annual return.
Explanation / Answer
1)
NAV on January 1 =( Value of Stock A + Value of Stock B + + Value of Stock C)/(No of share outstanding of Fund)
NAV on January 1 = (500*34 +700*63 +900*52)/5000
NAV on January 1 = $ 21.58
NAV on July 1 = ( Value of Stock A + Value of Stock B + + Value of Stock C )/(No of share outstanding of Fund)
NAV on July 1 = (500*38 +700*65 +900*61)/5000
NAV on July 1 = $ 23.88
Total Fund after sale of stock c & cash raised through issue = 500*38 +700*65 +900*61 + 600*23.88
Total Fund after sale of stock c & cash raised through issue = 133,728
Cash available before purchase of stock D = 450*61 + 600*23.88
Cash available before purchase of stock D = 41,778
No of share of stock D purchased = 41778/46
No of share of stock D purchased = 908.22
No of share of stock D purchased = 900 share
Cash remain in hand after purchase of stock d = 41778 - 900*46
Cash remain in hand after purchase of stock d = 378
NAV on Dec 31 = ( Value of Stock A + Value of Stock B + Value of Stock C + Value of Stock D + cash )/(No of share outstanding of Fund)
NAV on Dec 31 = (500*40 +700*68 +450*65 + 900*54 + 378)/(5000+600)
NAV on Dec 31 = $ 26.04
2)
Capital gain distribution per share = (450*(61-52))/5000 + (200*(40-34))/5600
Capital gain distribution per share = $ 1.02
3)
Annual return for a shareholder = (NAV on Dec 31 - NAV on Jan 1)/NAV on Jan 1
Annual return for a shareholder = (26.04-21.58)/21.58
Annual return for a shareholder = 20.67%
4)
Fund turnover for the year = (450*61+200*40)/ (500*40 +700*68 +450*65 + 900*54 + 378)
Fund turnover for the year = 24.31%