Consider
a mutual fund with $203 million in assets at the start of the year and
with 10 million shares outstanding. The fund invests in a portfolio of
stocks that provides dividend income at the end of the year of $5
million. The stocks included in the fund's portfolio increase in price
by 7%, but no securities are sold, and there are no capital gains
distributions. The fund charges 12b-1 fees of 0.75%, 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? (Use rounded "Net Asset Value". Round your answer to 2 decimal places.)
|
Explanation:
a.
| Start of year NAV = |
Market value of assets − Market value of liabilities
|
| Shares outstanding |
| = |
$203,000,000
| = $20.300 |
| 10,000,000 |
| End of year NAV is based on the 7% price gain, less the 0.75% 12b-1 fee: |
| End of year NAV = $20.300 × 1.07 × (1 − 0.0075) = $21.558 |
b.
| Given the dividends per share is $0.50, we can calculate the rate of return using the following equation: |
| Rate of return = |
Δ(NAV) + Distributions
|
| Start of year NAV |
| = |
($21.558 − $20.300) + $0.50
| = 0.0866 = 8.66% |
| $20.300 |
