Mid-term Exam March 27, 2012, 9:3o - 11:00
1. True or False Comment on the correctness of the following statements with maximum 5 lines each. (20%) a) The IRR is larger than the discount rate if the NPV>0 False, there are projects with more than one IRR where the statement is not true and there are projects that have the inflow now and the outflows in future years where this relation is inversed. b) Yield to maturity is not a valid measure of expected return for a zero coupon bond since it does not take into account future reinvestment opportunities. False, it is a valid measure because there are no reinvestments for the duration of the bond. c) The dividend discount model ignores capital gains. False, the DDM can be decomposed into the capital gain and the dividend yield d) As long as the correlation is below 1, the standard deviation of a portfolio is less than the weighted average standard deviation of the individual securities. True, can be shown through standard deviation formula
2. Bonds (10%) You have just bought a 3-year 5% annual coupon bond with a face value of €1000. The current discount rate is 10%. The first coupon will be paid one year from now. a) At how much of par value is the bond trading? P=5%*1000/0. 1*(1-1/(1+0.1)^3)+1000/(1+0.1)^3=€875.66. So the bond is selling at 87.57% of par value. b) What is the current yield? CY=50/876.66=5.71%
3. Equity (10%) Noogle is expected to start distributing dividends 5 years from now. During the following 5 years, it is expected to distribute a constant dividend of €10 per share per year. After that, dividends will grow at 1%.The number of shares outstanding is 2.000.000. a) What is the price of the stock if the required rate of return is 10%? Price=(10/0.1*(1-1/(1+0.1)^5))*1/(1+0.1)^4 + 10*(1+0.01)/(0.1-0.01)*1/(1+0.1)^9=€73.5 Noogle is also contemplating investing in a new search algorithm. The expected investment costs €1 million but would allow the company to make €0,5...