Management Engineering - Finance Lab + Corporate FInance

Full exam

Exercise 1 Mr. Goglio , a rising top banker, is selecting bonds traded on the exchange for its clients. The following bonds are considered : • UK234 : rated A, coupon 1% paid annually, maturity 30 months • AZ382 : rated BBB, annual coupon 2% compounded every 6 months (i.e. 1% every se mester), maturity 15 months • EY298 : rated BB, zero coupon bond, maturity 12 months The principal is paid back at maturity in all cases. The interest rate term structure is rather flat (the annual risk -free interest rate is equal to -0.1% for maturities up to 20 months and +0.1% for maturities from 21 months to 30 months). Currently, this is the spread that the market is requesting for different rating notches: Rating AA A BBB BB B CCC Annual spread +0.3% +0.6% +1.1% +1.8% +2.5% +4% Compute: 1. The equilibrium dirty price and eventually the clean price for the bonds 2. The yield to maturity (YTM) 3. The duration and volatility Explain if, in the cases that the three bonds were putable, we expect larger or lower prices, YTM, duration and volatility, other p arameters unchanged. Exercise 2 Gallo’s is a company financed with equity capital and debt. The number of equity shares outstanding is equal to 9 million and the value of the shares on the market is € 6 each. The value of the debt outstanding is equal to € 16 million (annual interest rate 5%). On average, each year the operating margin of the company is equal to € 7 million. Assuming that there is no taxation on corporate income and that the net profit i s distributed as a dividend each year, compute: 1. The market value of the assets and of the equity capital and the earning per share EPS 2. The expected profitability of the assets ( kA) and of the equity capital (k E) 3. Show that Proposition II by M&M predicts the value of k E Pollo’s is a company very similar to Gallo’s: same assets, same operating margin, same employees, same cost and revenue functions. The only difference is that it is not financed with debt (but with equity capital only). 4. Find how investors on the market can ‘replicate’ a portfolio of Gallo’s shares investing into Pollo’s shares and investing into debt (or borrowing) Just after paying a dividend, Pollo’s announces to the market that starting from the following year a part of the profits each year (40%) will be ploughed back and reinvested. Assuming that the capital reinvested in the company will deliver the same percentage profitability as the other existing assets, each year, compute: 5. The new expected value of the company earnings for the next 3 years and the growth rate in the long run 6. The value of the equity capital after the announcement to the market 7. The expected value of the equity capital 12 months after the announcement (according to the information available today) Exercise 3 In the derivative market, futures on meat are traded. Today the price of the meat is equal to $ 20 / kilo. The annual risk free interest rate is equal to 2% in the US and 1% in the Euro area, the volatility of the price of the meat is equal to 30% and if you store the meat the cost of carry is equal to $ 0.25 per kilo, to be paid at the end of each quarter. Find out: 1) The forward p rice of meat at the maturity of 3, 6, 9 months 2) The value of a forward contract (maturity 9 months, delivery price $ 20 / kilo) 3) How we can build up an arbitrage portfolio if the price of the contract mentioned at the previous question is equal to zero (be c areful!) 4) The value of a European call option and a European put option on the meat (strike price $ 18 / kilo, time to maturity 1 year, in this case only neglect the costs of carry ) 5) Which type of companies could be interested in call options on the meat Finally, explain (and demonstrate) why it is never efficient in this case to strike an American call option on the meat and buy the meat before its maturity. Academic year 20 20 -20 21 The test must be completed in 120 minutes . Write immediately surname and name on papers provided by the staff. During the test you cannot read personal notes or books. If – to your opinion – the text is not clear, or is ambiguous, you can introduce proper assumptions. Corporate Finance (Prof. G. Giudici) Written test – Ju ly 5 th 20 21