Management Engineering - Finance Lab + Corporate FInance

Full exam

Exercise 1 Industrial Inc. is an unlevered company. The market value of the assets today is equal to € 360 million, and there is no financial debt. The equity capital is divided into 20 million shares. The annual operating margin on average is equal to € 40 million. Assuming that there is no taxation on corporate income, compute: 1. The expected earning per share (EPS) 2. The expected profitability for shareholders 3. The theoretical price of the shares on the market The company announces a new investment. The net present value of the project NPV is equal to € 4 million; the initial investment required I is equal to € 10 million (it’s the cash necessary now to buy new assets) and is totally financed with a new equity issuance. The risk of the project is the same as the average risk of the other existing assets. Again, there is no taxation on corporate income. 4. Compute the new market value of the assets after the equity issuance and the investment 5. Compute the expected increase in the annual operating margin caused by the new investment (assuming that such increase is permanent, forever) 6. Find out the changes in the expected profitability for shareholders 7. Find out the changes in the operating margin, in the share price and in the expected profitability for shareholders if the initial investment of the project is totally financed with a debt issuance (on the market there is a unique annual interest rate on debt, equal to 5% and the debt is kept constant in the future, forever) 8. Show that Proposition II by Modigliani & Miller predicts the change in the expected profitability for shareholders Exercise 2 Stark Enterprises released its industrial plan for the future, and analysts expect the following figures for the company: Year 1 Year 2 Year 3 Year 4 and thereafter Return on equity (ROE) ROE 1=18% ROE 2=16% ROE 3=14% ROE LT=12% Payout ratio (PR) PR 1=60% PR 2=65% PR 3=70% PR LT=70% The last dividend (€ 0.25 per share) has just been paid. The book (accounting) value of the equity capital is now equal to € 50 million. The return on equity ROE is the ratio between annual earnings and the book value of equity at the beginning of the year. The equity capital is made up by 25 million shares. Assuming that the annual cost of capital required by shareholders is equal to 10%, compute: 1. The expected dividends per share at time 1, 2, 3, 4 2. The long-run growth rate of the dividends 3. The theoretical equilibrium price of the shares, today 4. The theoretical present value of the growth opportunity Draw a qualitative graph of the theoretical equilibrium price of the shares (y axis) as a function of the long-term expected ROE LT (x axis), with the other variables valued as before. Show the changes in the graph if PR LT=40%. Since the real market price of the shares on the market is now € 2.32, find out (other expectations being the same as in the table) the value of ROE LT expected by the market, instead of 12%. Exercise 3 Tesqua Motors manufactures electric cars. The managers are worried about the risk that the price of lithium (a metal that is needed for batteries) could soar up on the market. Today, the lithium spot price is equal to $ 22 per kilo. The price one year ago was $ 14 per kilo. Experts on the market say that the price of lithium could be equal to $ 25 per kilo at time 4 months, or $ 21 per kilo. The risk-free rate on the US dollar market is equal to 1%. 1. Compute the value of a forward contract on the lithium (time-to-delivery 4 months, delivery price $ 23 per kilo) 2. Compute the forward price of lithium, delivery 4 months 3. A metal broker is offering to Tesqua the opportunity to buy lithium at time 4 months, at a predetermined price equal to $ 22 per kilo, with no other charge. Show that there is an arbitrage opportunity (show how we can build such arbitrage) 4. Adjust the answers to 1. and 2. assuming that there is a cost of carry on lithium equal to $0.01 per kilo each month 5. Compute the value of a European call option on lithium, time-to-maturity 4 months, strike price $ 24 per kilo (do not consider the costs of carry) 6. Compute the value of the corresponding European put option 7. Explain if the price of the European put option could be equal to $ 24 per kilo at time 2 months Tesqua has to hedge against the risk of the lithium price on 50,000 kilos. Explain which type of derivatives could be efficiently used to protect the company, and the costs/benefits associated. Academic year 2017-2018 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 13 th 2018