Problem: Brigit Hall has decided to establish a university endowment fund at T.T. Penguin’s former university, using an $8 million donation from Penguin. The fund will be used to construct a new building in five years, which is expected to cost $10 million at that time. In the interim, Penguin would like to generate end-of-year scholarship payments from the fund. Assume that the invested funds will earn an effective annual return of 6%.
1) How much can be paid in scholarships in each of the next five years, still leaving $10 million in the fund after five years?
2) The endowment fund will be set up so that $3 million is invested in 20-year semi-annually paying bonds with a coupon rate of 5% that are currently selling at 89.3843% of par value. What is the yield to maturity on these bonds? What is their expected effective annual return?
3) The other $5 million will be invested in an equity fund that is expected to pay dividends of $4 per $100 of net asset value at the end of this year. The dividends are expected to grow at an annual rate of 4% thereafter. What is the expected return on this equity fund?
4) Assume that the expected standard deviation of the bond is 8%, the expected equity fund standard deviation is 20%, and the correlation of their returns is 0.55. Estimate the portfolio standard deviation.
5) Estimate the beta of this portfolio and determine the required return according to the security market line (SML), given the following information:
• Expected return on the market is 11%.
• Standard deviation of the market is 18%.
• Risk-free rate is 5%.
• Correlation coefficient between the fund’s bond returns and the market returns is 0.40.
• Correlation coefficient between the equity fund and the market returns is 0.85.
6) Ignore your answer for part (b) and assume instead that the expected effective annual return equals 6.5%. Similarly, ignore your answer for part (c) and assume instead that the expected return in that part equals 11%. Also assume a capital structure of 37.5% of debt and 62.50% of equity. Does the portfolio lie above or below the SML?
7) Independent of parts (a) to (f) above, Hall is considering investing in a relatively new company whose profitability has been growing at a compound rate of 20% per year. Using the constant growth DDM (dividend discount model), Hall calculates that the share price should be $60; this is substantially more than the actual market price of the shares [$40]. What is the most likely reason for the wide disparity between the observed price and that which Hall estimates?