2. value: 10.00 points Consider a mutual fund with $206 million in assets at the
ID: 1170599 • Letter: 2
Question
2.
value:
10.00 points
Consider a mutual fund with $206 million in assets at the start of the year and with 20 million shares outstanding. The fund invests in a portfolio of stocks that provides dividend income at the end of the year of $2 million. The stocks included in the fund's portfolio increase in price by 6%, but no securities are sold, and there are no capital gains distributions. The fund charges 12b-1 fees of 0.50%, which are deducted from portfolio assets at year-end.
a. What is net asset value at the start and end of the year? (Enter your answers in dollars rounded to 3 decimal places.)
b. What is the rate of return for an investor in the fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Rate of return %
Net Asset Value Start of the year $ End of the yearExplanation / Answer
Solution: a. Net Asset Value $ Start of the year $10.300 End of the year $10.863 Working Notes: Net Asset Value at start of the year (NAV0) =(Market value of assets at start - Current liabilities at start) /Shares outstanding = ($206,000,000 - $0)/20,000,000 =206,000,000/20,000,000 =$10.30 per shares =$10.30 per shares Net Asset Value at end of the year (NAV1) =NAV0 x 1.06 x (1-(12b-1fee)) =$10.30 x 1.06 x (1-0.50%) =$10.30 x 1.06 x (1-0.005) =$10.30 x 1.06 x 0.995 =$10.86341 =$10.863 b. Rate of return = 6.44 % Working Notes: Rate of return = (Net Asset Value at end of the year - Net Asset Value at start of the year + Dividend per share)/Net Asset Value at start of the year Rate of return = (NAV1 - NAV0 + D)/NAV0 Dividend per share (D)= Total dividend income/Shares outstanding =$2,000,000/20,000,000 =$0.10 per share Rate of return = (NAV1 - NAV0 + D)/NAV0 =($10.86341 - $10.30 + $0.10)/$10.30 =0.0644087 =6.44 % Please feel free to ask if anything about above solution in comment section of the question.
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