Problem: Suppose that the investor in the above question at first was cautious, buying only one unit at the end of 2004. Then a year later, he felt that the market would rebound in 2006 after its poor performance in 2005. So he made an additional capital contribution to buy one more unit at that time. Then, with the great performance of the fund in 2006, he decided to cash out one of his units at the end of 2006 (assume the fund would purchase the unit back for its appraisalbased value as of the end of 2006).

a. Calculate the investor's IRR.

b. Why is this IRR higher than that calculated in the previous question, and also higher than the mean period-by-period return to the fund over the 2005-2007 period?

c. Why is the time-weighted HPR a better measure for judging the performance of the fund, and the IRR a better measure for judging the performance of the investor in this case?

d. Under what conditions would the IRR not be a fair measure of the investment decision maker's ex post performance?

Question: A common type of real estate investment vehicle used by institutional investors is known as a ‘‘unit fund'' or ‘‘open-end'' commingled fund (CREF). Investors can put capital into, and withdraw capital out of, such funds on the basis of the appraised value of the assets in the fund, which are regularly and frequently reappraised. Thus, if the assets are appraised at $10 million, and you invest $100,000, you have a 1% share, entitling you to 1% of the net cash flow and proceeds from sales within the fund. Now consider a ‘‘passive'' buy-and-hold strategy over a three-year period in such a fund. Suppose you invest $200,000 in the fund at the end of 2004, to obtain two ‘‘units'' (i.e., shares). During 2005, the fund pays $5,000 per unit from net rental income, and at the end of 2005 is reappraised to a net asset value of $98,000 per unit. During 2006, the fund pays $10,000 per unit in net rental income, and the appraised value at the end of 2006 surges to $112,000 per unit. Finally, during 2007, the fund pays out $7,000 in net income and at the end of 2007 the assets of the fund are sold in the real estate market and liquidated for net cash proceeds of $118,000 per unit. Use your calculator or a computer spreadsheet (the latter will be faster and more reliable) to answer the following questions, reporting your answers to the nearest basis point.

a. Assuming that appraised value accurately reflects market value (opportunity cost) of the assets at intermediate points in time, what are the period-by-period total returns for each of the three years the investment was held (2005, 2006, and 2007)?

b. Based on these period-by-period returns, what is the geometric average annual total return during the three-year holding period of the investment (2005-2007)?

c. What is the internal rate of return (IRR, per annum) of the investment over its three-year holding period?

d. Which of these two average returns over the three-year life of the investment tells exactly what the profit would have been per original dollar invested if the investor had taken the cash paid out plus proceeds from liquidating his units at the end of each year and used all (and only) this cash to immediately purchase units (and fractions thereof) in the fund again for the following year (i.e., so that there was no cash flow into or out of the investment except at the beginning and end of the three-year period)?