Management Engineering - Finance Lab + Corporate FInance

Full exam

Exercise 1 On the financial market we find the following bonds: - XS47: risk -free bond, annual coupon 1.2% paid each 12 months, time to maturity 15 months, clean price 100 .871 - XS33: risk -free bond, annual coupon 1.0% paid in two parts each 6 months, time to maturity 9 months, clean price 100. 600 We know that the annual i nterest rate at the maturity of 3 months is 0%. Compute: 1. The accrued interest (accrual) and the dirty prices of the two bonds , 2. Other points of the interest rate term structure , 3. The duration of the two bonds and the estimated volatility . On the market we find also a risky bond: - M5SX: annual coupon 2.8% paid each 12 months, time to maturity 15 months, clean price 10 1.848 . 4. Compute: The accrued interest and the dirty price , 5. The yield to maturity , 6. The average spread requested by the market , on the bond return . Captain Findus invests 10% of his savings in the first bond, 25% in the second bond and 65% in the third bond. Find out: 7. The yield to maturity of the portfolio , 8. The duration of the portfolio . Exercise 2 Analysts are studying the business plan of a company listed on the Stock Exchange. Expectations are as follows: Year 1 Year 2 Year 3 Year 4 and thereafter Return on equity (ROE) ROE 1=8% ROE 2=12% ROE 3=14% ROE LT=10% Payout ratio (PR) PR 1=30% PR 2=20% PR 3=20% PR LT=50% 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 60 million sh ares and the book value per shares is today 1.8 €. The return on equity of the last year has been 10%. The annual cost of equity capital kE is equal to 9%. 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) Assume now that the company decides to buyback some shares , retire (=cancel) them and borrow for the same amount. The annual interest rate on debt is equal to 5%. The tar get payout ratios will be the same as before. 4. Should we expect the ROE to increase, decrease, or be the same? Why? 5. Should we expect the cost of capital k E to increase, decrease, or be the same? Why? 6. Should we expect the price of the shares to increase, decrease or be the same? Why? (be careful!) Exercise 3 Electro + produces electrical equipment and cables. The company buys copper on the global market and wants to hedge against the risk of the price volatility on the market (see the Graph). The price of copper on the market is now US$ 2.72 per pound. The risk free interest rate in the US is equal to 0.9%. Compute: 1. The forward price of copper, delivery 6 months 2. The value of a forward contract, to sell copper at the delivery price equal to $ 2 .8 per pound, delivery 6 months 3. Show that if the value of the contract of question 2. is equal to $0.0 5 per pound we can have an arbitrage portfolio 4. The change in answers 1. and 2. I i we consider costs of carry equal to $ 0.0 1 per pound per quarter 5. The value of a European call option , strike price $ 2.5, time to maturity 6 months (assume volatility  equal to 30%) 6. The value of the European put option (same parameters as above) 7. The change in answers 5. and 6. if we consider the costs of carry (if you do not have time just explain if we expect lower or larger values) Advise the company on the right derivatives to be used (among the ones listed before) to hedge against the risk. As suming that the company is willing to hedge against the risk of 1 million pound s of copper, estimate the costs of the strategies. Academic year 20 18-201 9 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 – January 23rd 20 19 Price of copper in the last 12 months ($/pound)