Management Engineering - Finance Lab + Corporate FInance

Full exam

Exercise 1 Itsasin Inc. is a company financed with equity capital only. The number of shares outstanding is equal to 40 million and the share price on the market is equal to € 3. The annual operating margin on average is equal to € 20 million and every year all the p rofits are paid as dividends to shareholders . Assume that there is no taxation on corporate income. Compute: 1) The market value of the company assets 2) The earning -per -share (EPS) 3) The expected profitability for shareholders Gowest Ltd is a company absolutely s imilar to Itsasin (same assets, same products, same technology , same dividend policy ) but is financed also with debt (the amount of the debt is € 30 million, the annual interest rate on debt is 5%). Compute: 4) The market value of the company assets (introducing explicitly the needed assumptions) 5) The market value of the equity capital 6) The expected profitability for shareholders (check that Proposition II by Modigliani and Mille r is right) Now imagine that just after paying a dividend the managers of Itsasin announce that starting from the end of the next 12 months the company will reinvest every year 40% of the annual profits to finance interesting business opportunities. Assuming that the profitability of the assets will not change, compute: 7) The chan ge in the value of the equity capital at the announcement 8) The earning -per.share and the dividends in the next 3 years 9) The growth rate of the dividends in the future Exercise 2 On the stock exchange sovereign bonds issued by two governments (A and B) are traded. Bonds issued by country A are considered risk -free, while bonds issued by country B are considered risky, because of the significant stock of public debt. In particular , consider the following bonds, that have the same par value: • Zero -coupon bond issued by A, maturity 9 months, price on the market 99.500 • Bond issued by A, maturity 9 months, annual coupon 2% paid each semester, clean price 100.994 • Bond issued by B, maturity 9 months, annual coupon 4% paid each semester, clean price 100.991 Dete rmine: 1) Some points of the risk -free interest rate term structure 2) Accrued interest and dirty price of the bonds 3) The average spread that the market charges to the bond issued by B (i.e. the average return premium compared to risk -free rates on the term structure) 4) Duration and price volatility of the three bonds 5) If it is possible to create an arbitrage portfolio, taking advantage of the larger yield to maturity offered by one of the bonds listed above (and how) 6) Which (and how many) of the b onds ahead should we buy in order to create a portfolio characterised by an expected annual return equal to 1.5% Exercise 3 The Suburbia Stock Exchange (SSE) is introducing derivatives on sunflower seeds. On the market today the price of sunflower seeds is equal to $ 20 / cwt (*). The annual risk free interest rate is equal to 2%, the volatility of the price of the seeds is equal to 30% and if you store the seeds the cost of carry is equal to $ 0.25 per cwt , to be paid at the end of each quarter. Can you support the SSE analysts to find out: 1) The forward price of sunflower seeds at the maturity of 3, 6, 9 months 2) The value of a forward contract (maturity 9 months, delivery price $ 20 / cwt) 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 careful!) 4) The value of a European call option and a European put option on the seeds (strike price $ 18 / cwt, 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 sunflower seeds The SSE analysts are trying to fill the graph on the right, which describes the value today of a forward contract long f L on sunflower seeds, delivery price $ 20 / cwt , as a function of the maturity T, other things described above being equal. Can you help them? (*) = 1 cwt (hundredweight) is equal to 100 pounds, i.e. approximately 50 kg 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 – February 3rd 20 21 fL T 0