Management Engineering - Finance Lab + Corporate FInance

Full exam

Exercise 1 The market value of the assets held by the software company XFEX is equal to € 146 million. The company is financed with debt (market value € 38 million, annual interest rate 6% - the company is willing to keep the amount of the debt constant in the future). The average annual operating margin (difference between revenues and operating costs) is equal to € 12 million. The corporate tax rate is equal to 25%. The equity capital is made up by 73 million shares. Compute: 1. The equilibrium price of XFEX shares on the market 2. The earning-per-share (EPS) 3. The expected return for shareholders 4. The asset value if the same company was unlevered, under proper assumptions 5. The expected return for shareholders, in the unlevered case One shareholder discovers that investing into 5% of the equity of the ‘levered’ company delivers the same expected return as investing into 5% of the equity of the ‘unlevered’ company and borrowing € 1.425 million at the 6% interest rate. Is that true? Are the two portfolios equivalent and replicating? Finally, find out the ‘optimal’ financial structure if we assume that raising debt originates bankruptcy costs and agency costs, equal (in € million) to 0.004*D 2 (D is the value of the total debt in € million). Exercise 2 The following bonds are traded on the market: - A: maturity 10 months, annual coupon 0.5%, may be considered risk-free; - B: maturity 12 months, annual coupon 1.5% (payment each semester), risky, rating BBB; Given the information displayed in the following, compute: 1. The theoretical equilibrium price of the two bonds (dirty price and clean price) 2. The accrual, as at today 3. The yield to maturity of the two bonds (considering the theoretical price) 4. The duration of the two bonds 5. The volatility of the price of the two bonds Compute the value of a forward contract on bond B, time to delivery 5 months, delivery price X 100.111. Should the price of that forward contract be different on the market, can we build an arbitrage portfolio? (and how, for example?) Term structure of interest rates (risk-free) Requested spread for rating notches AAA - AA 0.1% A 0.4% BBB 0.8% BB 1.3% B 1.5% CCC 2.3% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Months Exercise 3 Tony just graduated in Management Engineering and had the brilliant idea to open a startup company. The company is developing an App to book a seat in the most prestigious beaches in Apulia, in July and August. The initial investment required to start the business is equal to € 2 million. Expectations about future operating cash flows, gross of taxes, are as follows: Year 1 = € 100,000 Year 2 = € 1 million Year 3 = € 2 million Year 4 = € 2 million The terminal value of the project is negligible. The corporate tax rate is equal to 27%. The unlevered cost of equity capital k* is equal to 20%. Compute the value created by the project under these financing options: 1. Equity capital provided 100% by the founders 2. Part of the initial investment (€ 400,000) financed by a bank loan, annual interest rate 10%, the principal is paid back each year (€ 100,000 every year) starting from year 1 3. Same as 2. but the bank keeps the right to call back the loan if the project will not be profitable in the future (i.e. the company might be forced to pay back the debt in any time, if the bank asks) 4. Part of the initial investment financed by a bank loan, annual interest rate 10%, the bank requires that the ratio L between debt and value of the project is kept equal to 30% 5. The founders invest € 1 million in the project, and € 1 million is raised through an equity crowdfunding campaign on the Internet (the crowdfunding portal requires a 6% fee on the capital raised, that is deductible from the taxable income) Compute the cost of capital for shareholders in cases 2. and 4. 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 – January 23rd 2018 0,9% 0,8% 0,7% 0,6% 0,5% 0,4% 0,3% 0,2% 0,1%