Homework for Class 5
1. An investor is evaluating the historical performance of
Homework for Class 5
1. An investor is evaluating the historical performance of an investment fund. The following annual values are provided to the investor: (There was no income, so the returns only depend on value changes.)
a. Calculate the investment returns for each year.
b. Compute the arithmetic mean return.
c. Calculate the geometric mean return. (Remember to use return relatives.)
d. Which mean return makes the most sense to you.
Year
Fund Value
0
100
1
115
2
150
3
130
4
105
5
100
2. A commercial real estate investment fund must report its quarterly investment performance to investors. A summary of its (1) beginning and end-of-quarter assets and equity and (2) cash inflows and outflows during the quarter are as follows:
Other investments will earn 4% interest (1% per quarter) and fund debt will be at a 6% rate (1.5% per quarter).
The properties were appraised at the end of the quarter for $655 million.
a. What would be the beginning equity value?
b. What would be the ending equity value?
c. If all cash flows from operations, equity contributions, acquisitions, and distributions occurred at the end of the quarter, what would be the quarterly fund return (IRR)?
d. Assume that all cash distributions to investors occurred equally in 30-day intervals during the quarter. (Investor contributions still occur at the end of the quarter.) Approximate the fund IRR using the Modified Dietz approach. Hint: Recall what I told you about how the formula simplifies when distributions are monthly.
e. Assuming the same cash flows in (d) what would the return be before fees?
f. Assuming this same cash flows in (d) what would be return at the property level?
3. An open-end fund has the following values over the past 10 years. There were no distributions to investors during the 10 years.
a.What was the time weighted return (TWR) for the fund over the 10 years?
b.Suppose an investor put $10 million in the fund at the beginning of the first year and then liquidated her holdings in the fund at the end of the 10th year. What IRR would the investor have earned?
c.Suppose another investor invested $10 million into the fund at the beginning of year 5 (end of year 4). He liquidated his interest in the fund (sold his shares) at the end of year 9. What IRR did he earn?
d.Suppose a third investor puts her money into the fund at the end of year 6 and liquidates at the end of year 10. What is her IRR?
e.Why did the performance of these three investors differ? What is the best indication of the performance of the fund manager over the 10 years?
4. An investment has the following cash flows and IRR. What are the values implied by the IRR at the end of years 1 through 4? (The value at the beginning of year 1 would be $500,000 and the value at the end of year 5 atter sale would be zero.)
Year
End of Year Cash Flows
0
($500,000)
1
$25,000
2
$35,000
3
$52,300
4
$60,000
5
$660,000
IRR =
12.00%