1) The council of your town considers the renovation of an old sports center which does not generate any form of income. In its current state, the center requires € every year for maintenance. The renovation plan has an estimated cost of € If renovated, the maintenance cost of the center is estimated at €3.000 per year for the first 3 years and € per year for the next 5 years. At the end of the 8 year period the renovated center will be rented to a private company which will pay the council € per year forever. If the cost of capital for the council is 6% annually, evaluate the renovation plan.

Answer Without the renovation, the present value of the annual maintenance cost is / 6% = € If renovated, the present value of the annual maintenance cost for the next 8 years is: a) (3.000/1,06) + (3.000/1,06 2 ) + (3.000/1,06 3 ) = €8.019 = x 2,673 (using the annuity table).

b) (10.000/1,06 4 ) + (10.000/1,06 5 ) + (10.000/1,06 6 ) + (10.000/1,06 7 ) + (10.000/1,06 8 ) = € = x 4,212 x 0,8396 (using the discount factors from the tables). The value of the rent in 8 years from now is: / 0,06 = , and its present value is / 1,06 8 = € = x 0,6274 (using the tables)

Ιf renovated, the present value of the costs, including the cost of renovation is: = € , and the present value of the future income is: € These figures give a total present value of cost of = € If the center is not renovated, the present value of the future cost is € This figure is higher than € so the renovation is the best choice for the council.

2) You have the following information for a company: current stock price €12, P/E 20 (based on the last reported profits), last dividend (already paid) €0,24, number of shares issued 2 million. You believe that the required return for this stock is 6% and that the dividend and profits will grow at 4% forever.

a. Would you buy that stock? b. What percentage of the stock’s current value is due to the present value of growth opportunities? Explain what that figure means. c. If the average P/E ratio of the sector the company operates in is 12, what does that say about the company? d. The company has just made an investment of €10,5 mln which is expected to generate net income for the shareholders of €1,5 mln each year for the next 12 years. How should the investment affect the value of the share?

Answer a. P = DIV 1 / (k-g) = (0,24 x 1,04) / (0,06 – 0,04) = €12,48> €12 I would buy it because it is undervalued. b. EPS 0 = 12/20 = €0,60 PVGO = P 0 - = 12 – [(0,60 x 1,04) / 0,06] = €1,60 = 13,3% of stock price

c. That the company has better growth prospects than other companies in the sector or that for some reason it is overpriced. It could also mean that last reported profits were unusually low or that the company has much lower risk than other companies in the sector. d. Net Present Value = (1,5 x 8,384) – 10,5 = €2,076 million / = €1,038 rise in the price of the share.

3) A government bond pays annual coupon of 5%, matures in 3 years, has nominal value of €1.000 and yield to maturity of 4%. You believe that interest rates will be cut by 1% very soon. a. Calculate the change in the bond’s price if interest rates drop by 1%, using modified duration, and calculate the real change in the bond’s price. b. The last coupon payment was on the 17/6/XX. The financial press reported on the 20/8/XX that the price of the bond is 96,40. How much money would an investor have to pay on the 20/8/XX to buy the bond?

Answer a. Modified Duration = 2,861 / 1,04 = 2,751 TCPV 15048,080, ,230,0450, ,450,9082, ,76 2,861

Actual new bond price: (50/1,03) + (50/1,03 2 ) + (1050/1,03 3 ) = €1.056,57 Real percentage change: (1.056,57 – 1.027,76) / 1.027,56 = 2,8% Change based on duration: 2,751% b. Years since last coupon payment: ( ) / 365 = 0,175 years Accrued interest: 50 x 0,175 = €8,75 Dirty bond price: 8, = €972,75

4) A fund manager suggests an investment that has an expected return of 9% and standard deviation of returns of 13%. The market index has an expected return of 8% and standard deviation of 10%. If you can borrow and lend at the risk free rate which is 4%, would you make the investment the fund manager suggests? Justify your answer. Answer E(r) = 4% + [(8%-4%)/10%]x13% = 9,2% No because for that level of risk you could have return of 9,2%.

5) Stock portfolios A and B have standard deviation of returns σ Α =15% and σ Β =12% respectively. You estimate that their return will be r A =10% and r B =8%. The risk free rate is 3%, the correlation coefficient between portfolio A and the market portfolio is 0,8, the correlation coefficient between portfolio B and the market portfolio is 0,6 and the correlation coefficient between portfolio A and portfolio B is 0,85. The expected return of the market portfolio is 9% and standard deviation of returns 13%. You want to invest €

a) If you invest €4.000 in portfolio A and €6.000 in the risk free rate, is your investment efficient? Show all your calculations. b) If you invest €2.000 in portfolio A, €3.000 in portfolio B and €5.000 in the risk free rate, what is the beta of your investment and what is your expected return according to the CAPM?

Answer a)r p = (0,4 x 0,1) + (0,6 x 0,03) = 5,8% σ p = 0,4 x 0,15 = 6% r p = 0,03 + [(0,09 – 0,03)x (0,06 / 0,13)] = 5,77% < 5,8% so it’s efficient b)β Α = (0,15 x 0,8) / 0,13 = 0,923 β Β = (0,12 x 0,6) / 0,13 = 0,5538 β p =(0,2 x 0,923) + (0,3 x 0,5538) + (0,5 x 0) = 0,35 r p = 0,03 + [0,35 (0,09 – 0,03)] = 5,1%

6) You sell a futures contract on the stock of Allianz at €70. The contract refers to 100 shares. At the end of the same day the settlement price is €68. The next day the settlement price is €69 and the following day you close your position when the price of the contract is at €72. The required margin is 10%. Show all the relevant cash flows and your profit or loss from your position.

Answer You have a total loss of €200. DaySettleme nt price P/L (€) Margi n (€) Require d Margin (€) Flow in Margin (€) Total -200

7) You have a portfolio of stocks worth € The beta of your portfolio against the market index is 1,2. The futures contract on the market index is at points and has a multiplier of 5. How can you hedge the risk of your portfolio? Suppose a fund manager with a similar position tells you that he has sold 40 futures contracts. What are his expectations about the market?

Answer N f = = = -36 You sell 36 futures to hedge your risk. If a fund manager sold more than 36 futures (i.e. 40 futures) he expects that the market index will drop.