Management Engineering - Finance Lab + Corporate FInance

Full exam

Exercise 1 PowerTin is a company finance d with equity capital and debt. The number of equity shares outstanding is equal to 6 million and the value of the shares on the market is € 9 each. The value of the debt outstanding is equal to € 16 million (annual interest rate 5%). On average, each year the operating margin of the company is equal to € 7 million. Assuming that there is no taxation on corporate income and that the net profit is distributed as a dividend each year , compute: 1. The market value of the assets and of the equity capital and the earning per share EPS 2. The expected profitabilit y of the assets ( kA) and of the equity capital (k E) 3. Show that Proposition II by M&M predicts the value of k E PowerTon is a company very similar to PowerTin: same assets, same operating margin, same employees, same cost and revenue functions. The only difference is that it is not financed with debt (but with equity capital only). 4. Find how investors on the market can ‘replicate’ a portfolio of Power Tin shares investing into Powerton shares and investing into debt (or borrowing) Just after paying a dividend, PowerTon announces to the market that starting from the following year a part of the profits each year (40%) will be ploughed back and reinvested. Assuming that the capital reinvested in the company will deliver the same percentage profitability as the other existing assets, each year, compute: 5. The new expected value of the company earnings for the next 3 years and the growth rate in the long run 6. The value of the equity capital after the announcement to the market 7. The expected value of the equity capital 12 months after the announcement (according to the information available today) Exercise 2 On the bond market the following securities are traded: - XS 11 : risk -free bond, annual coupon 1.2% paid each 12 months, time to maturity 15 months, clean price 100.871 - XS 15 : 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 interest 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: - M5S2: annual coupon 2.8% paid each 12 months, time to maturity 15 months, clean price 101.848. Compute: 4. The accrued interest and the dirty price, 5. The yield to maturity, 6. The average spread requested by the market, on the bond return. A fourth bond on the market (M5S3) is similar to M5S2 (same issuer, same coupon payments, same maturity) but it’s a callable bond. Do you think that the clean price, the accrued interest, the yield to maturity are the same? Exercise 3 Henry Sussex is launching a new energetic drink on the market. His business plan reports the following information: - Initial investment in capital expenditures, facilities and marketing: € 1.5 million (time 0) - Future expected cash flows (gross of taxes): € 0.2 million (time 1), € 0.8 million (time 2), € 1.2 million (time 3), € 2.5 million (time 4) - Cost of capital k* (unlevered): 1 2% - Risk -free rate of return on the market: 1% - Average tax rate on cash flows: 25% Assuming that the project profits are paid each year as dividends to shareholders, c ompute: 1. The net present value of the project in the unlevered case (financed with equity capital only) 2. The net present value o f the project if a part of the initial investment (€ 0.5 million) is funded by a bank (annual interest rate 7%, the principal is paid back at time 4 ) 3. The net present value of the project if a part of the initial investment is funded by a bank (annual interest rate 7% ) and the agreement is that the debt will be always equal to 50% of the total value of the project 4. The cost of capital for shareholders under assumption 3. Assume that Henry started the project following alternative 3. and invested the money. One day after, Vasco is interested in the project (i.e. 100% of the equity capital of the project) . Compute: 5. The value of a forward contract on the project, time to delivery 18 months, delivery price € 1. 6 million 6. The value of a European call option on the project, time to maturity 6 months, strike price € 1. 7 million (assume volatility of the project return equal to 18%) Academic year 20 19-20 20 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 15th 20 20