Management Engineering - Finance Lab + Corporate FInance

Completed exercises of the course

Divided by topic

Politecnico di Milano Corporate Finance Es. 1 Monti is an unlevered company and its market value of equity is € 50 million. The equity capital is divided into 25 million shares. The average annual operating profit (revenues less operating costs) is € 7.5 million. Compute: 1) The share price, the earning per share (EPS) and the expected profitability for shareholders kE. Assume no taxes on corporate income exist. Monti then decides to raise debt capital for an amount equal to € 10 million. The annual interest rate on debt is 6%. The capital raised will be used to repurchase part of the shares outstanding, in order to leave the book value of assets and liabilities unchanged. 2) How will this operation affect the share price, the earning per share and the expected profitability for shareholders? 3) Show how to replicate the expected profitability for the shareholders after the debt issue by investing in 4 shares of the levered company (and investing personally in debt securities). Es. 2 The market value of the assets of Livestock Inc. is equal to € 45 million. The market value of the outstanding debt is equal to € 7 million (the annual interest rate is equal to 5% and the debt is always constant). The equity capital is made up by 9 million shares. The average annual operating income (difference between revenues and operating cash costs) is equal to € 4.8 million. The tax rate on corporate income is equal to 27%. All the company profits are paid to shareholders. 1) Compute the market value of the equity capital and the equilibrium price of each share 2) Compute the annual net profit and the earning per share 3) Compute the expected return for shareholders 4) Compute the annual saving on taxes that Livestock Inc. obtains through debt financing Now, assume that Livestock Inc. changes its financial structure, increasing debt and reducing the equity capital, so that the assets remain unchanged. In detail new debt is raised (additional € 3 million and again the debt is kept constant). 5) Compute the change in the value of the assets (list all the necessary assumptions) 6) Compute the new annual net profit 7) Compute the new expected return for shareholders: does Proposition II by Modigliani & Miller hold? Politecnico di Milano Corporate Finance Class exercises 29/09/2022 Ex 1 TL is an unlevered company. The market value of the assets is equal to € 58 million. The equity capital is divided into 17 million shares. The average annual operating margin of the company (revenues net of cash costs) is equal to € 11 million. Assuming that there are no taxes on corporate income, compute: 1. The expected earning per share (EPS); 2. The expected price of the TL shares on the market; 3. The expected profitability for shareh olders Now TL is willing to restructure the composition of liabilities. Therefore an extraordinary dividend is paid now to shareholders (total amount of cash distributed € 5 million) and debt is raised for the same amount (€ 5 million). The annual interes t rate on debt is equal to 8%. Compute (assuming that the ordinary dividend related to the annual profits has also just been paid now): 4. The new expected earning per share (EPS) 5. The new price of the TL shares on the market 6. The new expected profitability fo r shareholders (show that Proposition II by Modigliani and Miller is true) 7. Find out if (and eventually how) TL shareholders could have obtained the expected profitability computed in question 6. in the case that the company did not pay the extraordinary di vidend and did not raise debt (build a replicating portfolio ). Ex. 2 Itsasin Inc. is a company financed with equity capital only. The number of shares outstanding is equal to 40 million and the share price on the market is equal to € 3. The annual operating margin on average is equal to € 20 million and every year all the profits are paid as dividends to shareholders. Assume that there is no taxation on corporate income. Compute: 1) The market value of the company assets 2) The earning -per -share (EPS) 3) The expected profitability for shareholders Gowest Ltd is a company absolutely similar to Itsasin (same assets, same products, same technology, same dividend policy) but is financed also with debt (the amount of the debt is € 30 million, the annual interest rate on debt is 5%). Compute: 4) The market value of the company assets (int roducing explicitly the needed assumptions) 5) The market value of the equity capital 6) The expected profitability for shareholders (check that Proposition II by Modigliani and Mille is right) Politecnico di Milano  Corporate Finance ‐ Class exercises 19/10/2022      Es. 1  A  financial  product  requires  monthly  payments  of  €  100  starting  from  January  1st  2012.  This  amount  of  money (net of monthly fees and management costs of € 1.81) is immediately invested in a fund that yields  the 4% annually.  1) What is the future value of the payments at December, 31st 2025 (consider that the future value will be  distributed to the investors on this date)?  2) What is the net annual equivalent rate of this product?  3) How much should an investor pay each month to obtain € 25.000 at the maturity stated in point 1?  Es. 2  Elster  Inc.  wants  to  raise  money  on  the  market.  The  company  is rated  BBB  by  the  top  rating  agencies.  The  interest rate structure and the average credit spreads are reported below. Two different types of bonds will  be issued on the market:  A) Annual coupon 2%, paid annually, maturity 4 years   B) Annual coupon 1.5%, paid annually, maturity 3 years  Compute:  1. The equilibrium issue price, the duration, the expected volatility of the two bonds  4 months later, the clean price of the bonds is equal to 99.847 (bond A) and 98.843 (bond B) Compute:  2. The accrual and the dirty price of the two bonds in that moment  3. The yield to maturity (YTM) of the two bonds in that moment    Es. 3 Three risk‐free bonds are priced in the bond market:  a. Francis, which pays an annual coupon rate equal to 2% of the nominal value, its time to maturity is 1 year  and 7 months and its clean price is 100.471; b. Kaplan,  which  pays  an  annual  coupon  rate  equal  to  3%  of  the  nominal  value,  its  time  to  maturity  is  2  years and 7 months and its clean price is 101.292; c. Pelton, a zero‐coupon with a time to maturity of 1 year and 7 months and market price of 97.366  Compute:  1) The accrued interest of Francis and Kaplan  2) The term structure of interest rates 3) The yield to maturity of the three bonds 4) The duration and volatility of the three bonds. Mr.  Turbino  has  €  100,000  to  invest  among  the  three  securities, and he wants to hold a portfolio with a  duration  equal  to  2  years.  Knowing  that  the  three  bonds  all  have  the  same  nominal  value,  how  should  he  invest his money? How much would his portfolio appreciate/depreciate if the term structure of interest rates  shifted by 1% at all the maturities?  CORPORATE FINANCE – WRAP-UP EXERCISES Exam August 29th 2022 JUMP company has 10 million shares outstanding. The market value of the assets (invested in real estate properties) is equal to € 50 million. The company is financed also by debt, with annual interest rate equal to 6%. The ration between the market value of the debt and the market value of the equity capital (D/E) is equal to 0.65. 1) Compute the market value of the equity capital E and the equilibrium price of the shares p. Assuming that the annual net operating margin on average is equal to € 1.8 million, and no taxes are charged on the corporate income, compute: 2) The return on assets kA and the return on equity capital kE. 3) The earning per share. Suddenly, the company is experiencing troubles for unexpected costs in the future and decides to sell some properties (at the market value, equal to € 5 million). The cash raised is used to reduce the debt, for the same amount. Compute: 4) The changes in the equilibrium price of the share, in the return on shareholders’ capital kE and on the earning per shares, assuming that the percentage return on assets kA is unchanged after the sale of the properties. An investor, after the buyback of the debt, holds 2% of the equity capital of the company. Explain how he could have built a portfolio equivalent to this investment (i.e. with the same expected return, and the same initial investment) before the sale of the properties. Exam February 10th 2020 Buffalo Brothers is willing to raise money for new investments and is planning to issue a bond, with maturity 4 years, coupon paid each year. The total par value of the bonds will be equal to € 20 million (the company wants to raise money for the same amount). A credit rating agency issued the rating for the debt (BBB). The risk free interest rate on the market is equal to 0.2%. Compute: 1. The annual coupon that the company should pay (see the Table for spread values) 2. The duration of the bond at the issuance 3. The volatility of the bond price 4. The coupon that the company could have decided, if it was paid each quarter, instead of each year Assuming that the tax rate on corporate income is 23%, compute: 5. The tax saving that Buffalo Brothers will obtain each year 6. The present value of the financing (i.e. the present value of future tax savings) Now assume that Buffalo Brothers is introducing the option to reimburse the bond any time in the future, before maturity, at its own discretion. In order to raise the same amount of money at time 0, should the coupon be larger or lower? Table: Rating and Bond spreads AAA - AA +0.8% A +1.2% BBB +1.75% BB +2.5% B +3.2% CCC +4.3% Politecnico di Milano Corporate Finance Class exercises 10 /1 1/202 2 Exercise 1 Silvio just retired from work and is analyzing a stock traded on the Exchange. His favoured share just paid a dividend equal to € 0.4 per share that corresponds to 70% of the earning per share realised in the last 12 months. At the moment, the book value of the equity capital is equal to € 40 million, divided into 20 million shares. The market e xpects that the accounting return of the equity capital ROE (return on equity) in the future (comprising the next 12 months) will be equal to 23%, and the company will pay -out each year a portion of the earnings comprised between 60% and 80%. The annual eq uity cost of capital k is equal to 15%. 1. Determine the payout ratio that the company must promise to shareholders so that they evaluate the share price € 3.87 €. 2. Determine the present value of growth opportunity (PVGO) related to the price ahead . Assume now that the payout ratio is the one determined before , but the accounting equity return ROE will be equal to 23% only for three years (starting from the next 12 months), and that thereafter it will decrease immediately to 16%. 3. Determine the equili brium market share and the present value of growth opportunity under these assumptions. 4. Determine the expected price of the share at time t=1 assuming that expectations will be confirmed and be stable in the future. 5. Silvio buys the shares and then (confirm ing the expectations before) he wonders if we can define a ‘duration’ for his investment... can you help him? Exercise 2 Orthodoxa shares are soaring on the stock exchange and Francesco is curious to analyze them. The equity capital is made up by 40 mi llion shares. The accounting value of the equity capital is equal to € 250 million. The expected future profitability, defined by the ROE index (return on equity, ratio between annual net profit and accounting value of the equity capital at the beginning o f the year) should be: (i) first year = 16%, (ii) second year = 18%, (iii) third year = 20%. In the following years we expect the ROE index to be equal to 20%. Assuming that the company is willing to pay 70% of the earnings as dividends, and that the annua l cost of capital k is equal to 15%, compute: 1. The earning per share EPS expected in the next 4 years 2. The theoretical equilibrium price of the share today 3. The present value of growth opportunity PVGO 4. The theoretical price of the share at time 1, with stationary conditions, just after the payment of the dividend. Francesco thinks that maybe someone on the market has different information, as the current market price today is equal to € 13.1. 5. Holding constant the other parameters, find out the long -term profitability ROE, starting from time 4, that can justify the current price. 6. A financial columnist argues on her blog that the current price (€ 13.1) is ‘fair’ since ‘the company has a profitability potential that could push the ROE up to 30% and ensure th e payment of a future minimum annual dividend equal to € 1.8’. How would you reply? Politecnico di Milano  CORPORATE FINANCE Exercise 1  Mela and Ambra are planning to establish a new venture in Perth in order to produce pure mango juice.  The business plan submitted to the bank highlights that: ‐ the initial investment in assets and inventories is equal to $ 500,000 ‐ each year they expect revenues equal to $ 1,200,000 and operating cash costs equal to $ 900,000;  the tax rate on corporate income is equal to 26%;  ‐ the project will generate cash flows for 10 years, and thereafter it will not generate any significant  cash flow; ‐ the cost of capital requested by the two investors is equal to 20%, if they are the only financers.  Assuming that the Bank of Fremantle is available to finance immediately a part of the project with a  loan of $ 250,000, with an annual interest rate on the debt equal to 9%,  Determine:  1) the net present value (NPV) of the project in the ‘unlevered’ case (i.e. financed only with equity capital); 2) the ‘adjusted’ present value (APV) of the project in  the ‘levered’ case (i.e. financed also with debt);the  debt is constant and will be totally paid back at time 10; 3) the minimum price that the two investors should charge to sell 100% of the shares of the project at time  5, under the assumptions referring to 1) and 2)  4) the ‘adjusted’ present value of the project in the ‘levered’ case assuming that half of the debt ($ 125,000)  will be paid back at time 5, and the remaining part will be paid back at time 10; 5) the weighted average cost of capital (WACC) in the case that the debt initially equal to $ 250,000 will be  adjusted (and thus reduced) in the future in order to keep constant the ratio L between debt outstanding  and value of the project 6) the net present value of the project in the ‘unlevered’ case, assuming that the State of Western Australia  will initially pay a subsidy equal to $ 100,000 in order to help the investors, half with no reimbursement,  and half reimbursed in constant payments each year, up to time 10, with no interests.  Exercise 2 Cimaglia Inc. is planning to open a new ‘smart casual’ fast‐food in Dubai. The initial investment is equal to $  800,000. Expected operating cash flows, gross of taxes, are as follows (assume a conventional tax rate on  cash flows equal to 18%):  Year 1: $ 20,000; Year 2: $ 45,000; Year 3: $ 350,000; Year 4: $ 950,000; Year 5: $ 1,250,000 The required cost of capital k* is equal to 18% (if the project is financed only by Cimaglia’s own resources).  1) Compute the net present value (NPV) of the project in the ‘base case’  2) Compute  the  NPV  in  the  case  that  Cimaglia  borrows  $  300,000  from  the  Arab  Bank,  that  charges  an  annual interest rate equal to 5% (interests are deductible from the taxable income); the debt is paid back  at time 5   3) Compute  the  NPV  in  the  case  that  Cimaglia  borrows  $  300,000  from  the  Arab  Bank,  that  charges  an  annual interest rate equal to 5% (interests are deductible from the taxable income); the debt is paid back  half at time 3, half at time 5   4) Compute the NPV in the case that Cimaglia borrows money from the Arab Bank, that charges an annual  interest rate equal to 5% (interests are deductible from the taxable income), and wants to keep the ratio  L between debt and value of the project equal to 50%, each year  5) Compute the amount of debt that should be borrowed from the bank in case 4, now.   6) Compute the expected profitability for shareholders (namely the cost of equity capital) k E in cases 2. and  4.  Politecnico di Milano Corporate Finance Exercises on Forward Contracts Exercise 1 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): 12% - Average tax rate on cash flows: 25% Assumin g that the project profits are paid each year as dividends to shareholders, compute: 1. The net present value of the project in the unlevered case (financed with equity capital only); 2. The net present value of 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 wil l 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 Exercise 2 The Suburbia Stock Exchange (SSE) is introducing derivatives on sunflower seeds. On the market today the price of sunflower seeds is equal to $ 20 / cwt (*). The annual risk free interest rate is equal to 2%, the volatility of the price of the seeds is equal to 30% and if you store the seeds the cost of carry is equal to $ 0.25 per cw t, to be paid at the end of each quarter. Can you support the SSE analysts to find out: 1) The forward price of sunflower seeds at the maturity of 3, 6, 9 months 2) The value of a forward contract (maturity 9 months, delivery price $ 20 / cwt) 3) How we can build up an arbitrage portfolio if the price of the contract mentioned at the previous question is equal to zero (be careful!) Exercise 3 Romeo manages a chain of coffee houses in Verona and is worried about the recent jump in the price of coffee on the market. Today the wholesale price is US$ 2.55 per pound, while just 6 months ago it was US$ 1.82 per pound. Analysts think that the price at time 6/12 can further increase to US$ 2.95 per pound, or go down to US$ 2.45 per pound. Assuming that the annual risk free rate in the Euro area is 0.2% and in the USA is 0.4%, compute: 1. The forward price of coffee, at 6/12 2. The value of a forward con tract to buy coffee at 6/12, delivery price US$ 2.5 per pound 3. How do the previous answers change if we consider that there is a cost of carry on coffee equal to US$ 0.01 per pound per quarter EXERCISES ON OPTIONS *(from Exam February 3rd, 2021) The Suburbia Stock Exchange (SSE) is introducing derivatives on sunflower seeds. On the market today the price of sunflower seeds is equal to $ 20 / cwt (*). The annual risk free interest rate is equal to 2%, the volatility of the price of the seeds is equal to 30% and if you store the seeds the cost of carry is equal to $ 0.25 per cwt , to be paid at the end of each quarter. Can you support the SSE analysts to find out: 1) The forward price of sunflower seeds at the maturity of 3, 6, 9 months 2) The value of a forward contract (maturity 9 months, delivery price $ 20 / cwt) 3) How we can build up an arbitrage portfolio if the price of the contract mentioned at the previous question is equal to zero (be careful!) 4) The value of a European call option and a European put option on the seeds (strike price $ 18 / cwt, time to maturity 1 year, in this case only neglect the costs of carry ) 5) Which type of companies could be interested in call options on sunflower seeds The SSE analysts are trying to fill the graph on the right, which describes the value today of a forward contract long f L on sunflower seeds, delivery price $ 20 / cwt , as a function of the maturity T, other things described above being equal. Can you help them? (*) = 1 cwt (hundredweight) is equal to 100 pounds, i.e. approximately 50 kg ** (f rom Exam February 13th, 2019) Farmers in Sardinia are worried about the price of goat milk on the wholesale market. Today, the goat milk price is equal to € 0.6 per litre. The price one year ago was € 1.3 per litre . Experts on the market say that the price of goat milk could be equal to € 0.5 per litre at time 6 months, or € 1.0 per litre . The annual risk -free rate is equal to 2%. 1. Compute the value of a forward contract on the milk (time -to-delivery 3 months, delivery price € 0.5 per litre ) 2. Compute the forward price of goat milk , delivery 3 months 3. A cheese producer is offering to farmers the opportunity to purchase their milk at tim e 3 months , at a predetermined price equal to € 0.6 per litre , 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 milk equal to € 0.01 per litre each quarter 5. Compute the value of a European call option on goat milk , time -to-maturity 6 months, strike price € 0.75 per litre (do not consider the costs of carry) 6. Compute the value of the corresponding European put option Farmers owning goats want to hedge against the risk of the volatility of the goat milk price on the wholesale market . Explain which type of derivatives could be efficiently used to protect them , and the costs/benefits associated. *** (f rom Exam February 13th, 2019) An oil field in Abu Dhabi (largely unexploited) is eval uate d 2 billion US$ as at today . Depending on the dynamics of the oil price on the market, the market value can change, with an annual volatility equal to 20%. Sheikh Mamaluk wants to obtain a European put option on the field, expiration 2 years, with stri ke price equal to 2.5 billion US$. The annual risk free rate in the US is equal to 1% , in Europe it is equal to 0.5% while in Abu Dhabi is equal to 3% . 1) Determine the value of the European put option 2) What can we say about the value of the American put option (with same parameters)? 3) Find out if it is possible to build an arbitrage portfolio if the value of the European option on the market is equal respectively to 1.4 billion US$ or 0.4 billion US$. If it is possible, show how… 4) Will the European put option be more or less valuable, considering that the oil field will absorb annual costs for insurance and managem ent equal to 1 million US$ per year ? (qualitative answer) 5) Compute the value of a forward contract (short and long) on the oil field, expiration 2 years, with delivery price equal to 2.1 billion US$ 6) Compute the value of the forward contract mentioned in Question 5) considering the costs mentioned in Question 4) fL T 0