Management Engineering - Finance Lab + Corporate FInance

Full exam

Exercise 1 On the market for corporate bond s we find the following securities: • IT98 : rated A, zero coupon bond, maturity 10 months , price on the market today 100. 083 • IT53 : rated BBB, annual coupon 1.1 %, maturity 14 months , clean price on the market today 100.348 • IT09 : rated BB, annual coupon 2.5%, maturity 14 months, clean price on the market today 101.498 The principal is paid back at maturity in all cases. Currently, this is the spread that the market is requesting for different rating notches , compared to AAA risk free bonds : Rating AA A BBB BB B CCC Annual spread +0. 1% +0. 3% +0.8 % +1. 2% +2. 0% +3.2 % Find: 1. Some points of the interest rate term structure 2. The duration of the three bonds 3. The yield -to-maturity (YTM) of the three bonds 4. The estimated volatility of the three bonds 5. If it is possible to build an arbitrage portfolio in the situation that the clean price of the IT09 bond is equal to 101.500 (and eventually how) 6. Which bonds would you select today to build a portfolio with a duration equal to 1 year (and the relative weight in the portfolio of each bond, approximately) 7. The annual tax saving that the issuers of the three bonds can enjoy (assuming that the corporate tax rate is equal to 28% and the par value of each emission is equal to € 80 million) Exercise 2 SGNAM is a utility company with stable cash flows and the market consensus on the profitability of the company for the future is as follows: Year 1 Year 2 Year 3 Year 4 and thereafter Return on equity (ROE) ROE 1=18% ROE 2=20% ROE 3=18% ROE LT=16% Payout ratio (PR) PR 1=70% PR 2=80% PR 3=80% PR LT=90% The return on equity is the ratio between the net profit during the year and the book value of the equity capital at the beginning of the year. The company is not levered and for sake of simplicity there are no taxes on corporate income. The equity capital is made up by 250 million shares and the book value per shares is today 0.9 €. The annual cost of equity capital k E is equal to 7% while the risk free rate on the market is equal to 0.5%. The earnings of the past 12 months are equal to € 50 million and have been distributed yesterday as dividends. Compute: 1. The expected dividends in the short run (and the growth rate in the long run) 2. The theoretical market value of the shares 3. The present value of growth opportunity (PVGO) 4. The equilibrium P/E (price -to-earnings) ratio today 5. The equilibrium M/B (market -to-book) ratio today 6. The increase in the value of the assets of SGNAM if the company, under the assumptions described above, will buy back 10 million shares, cancel them and issue debt for the same amount of money spent in the buyback Exercise 3 Melissa is a financial analyst specialized in commodities. She thinks that the price of crude oil on the market is very volat ile. Today the price is equal to $ 70 per barrel, but in 12 months it can go up to $ 80 per barrel or can go down to $ 40 per barre l. The risk free annual interest rate is equal to 1%. Help Melissa in computing: 1. The forward price of crude oil at 1 year 2. The value of a forward contract on crude oil at 1 year, delivery price $ 60 per barrel 3. The value of a European call option on crude oi l, strike price $ 75 per barrel, time to maturity 1 year 4. The value of the corresponding European put option Show that if the value of the European call option (question 3.) is equal to $ 72 it is possible to build an arbitrage opportunity. Do we have the s ame opportunity if the market value of the European call is $ 69? Melissa is studying a financial product placed by Nolimits Bank, that will pay $ 1,000 to investors if the price of crude oil at time 12 months will be equal to $ 40, and $ 1,200 if the price of crude oil at time 12 months will be equal to $ 80. What should the ‘right’ fair value of this product be on the market today? Now consider that the costs of carry associated to crude oil are equal to $ 0.2 per barrel per semester and advice Melissa on how the answers to questions 1. and 2. will change. 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 – September 9th 20 21