Financiad Economics ECN134 Midterm 1 Winter 2009 Prof Farshid Mojaver 20 pts 1 Some Financial Terms and Ideas a What is securitization Securitization is the process of taking an illiquid asset or group of assets and through financial engineering transforming them into a security b What is financial engineering Creating new financial instruments by combining other derivatives or more generally by using derivatives pricing techniques c What is Credit Default Swap CDS A CDS is a contract in which one party the protection seller agrees to reimburse another party the protection buyer against a default on a financial obligation by a third party the reference entity d How might CDS have contributed to the current financial crisis The protection seller needs to cover its position when the reference entity is in high risk of default One way to do this is to short the securities of the reference entity But this will reduce the stock price of the reference entity leading to it collapse When the reference entity goes bankrupt the position of all those institutions that hold its share becomes weaker People that hold shares of these institutions buy CDS to cover this risk The protection seller shorts the shares of these companies leading to their faster collapse That is one event cascades to the other leading to a systematic collapse of the entire financial market 11 pts 2 Derivation of the formula for Growing Annuity Show that the present value of a growing annuity that pays a stream of cash flows C and grows at a constant rate g for a fixed number of periods T can be simplified to PV 12 pts 3 Annuity C r g 1 g T 1 1 r Weak consumer spending has led automobile manufacturers to offer zero interest financing or cash back options to stimulate sales Suppose you can buy the car of your choice for its negotiated price of 16 200 less 500 cash back or you can finance the entire 16 200 car cost for 36 months at zero interest You have the cash necessary to pay for the car in an account that earns a stated annual interest rate of 4 compounded monthly You will either finance it or pay cash depending on which is the best deal a What is the cost of the financed car to you right now b Should you pay cash or finance the car and why c Now suppose the manufacturers offer 2 rather than zero percent financing Should you pay cash now or finance the car and why Answer a The monthly financed car payment with no interest is 16 200 36 450 C 1 PV r 1 1 r T 450 0 04 12 1 36 1 0 04 1 12 PV 15 241 84 b Finance it By financing we will actually make profit of 458 16 15 700 15 241 84 c First we need to find monthly payment when price is 16 200 ND financing is 2 PV C ArmT PV 16 200 ArmT 1 1 34 9 1 36 0 02 12 1 02 12 1 1 1 mT A r m 1 r m C 16 200 34 913 464 01 Now we need to calculate the PV of a constant stream of income using SAIR of 4 This is the true value of the financing offer to us PV 464 1 1 0 04 12 1 04 12 36 15 716 34 This is 16 only better than the cash price I would be nearly indifferent between the two 6 pts 4 Annuity Pure Discount Bond Suppose that you have a pure discount bond that pays 1 000 at maturity with 6 years remaining until payoff in order to yield a 7 return a How would you price the bond b Suppose the day after you buy the bond interest rate falls to 2 What are your capital gain loss and the new yield to maturity Answer F 1 r T F b PV 1 r T a PV 1000 666 342 1 07 6 1000 887 97 profit 143 YTM 2 1 02 6 8 pts 5 Effective versus Stated Annual Rates In all cases give the formulas you used in obtaining the answers a Suppose the stated annual interest rate SAIR is 8 compounded quarterly what is the quarterly effective rate b Suppose the SAIR is 8 compounded quarterly what is the effective annual interest rate EAIR c Suppose the EAIR is 8 what is the 3 month effective rate d Suppose the EAIR is 8 what is the SAIR which when compounded continuously produces an 8 EAIR Answer a EQIR 8 2 4 b EAIR 1 02 4 1 8 2432 1 4 E 3 monthIR 1 08 1 1 927 c EAIR 8 r r e 1 0 08 e 1 08 r 7 6961 d EAIR 8 12 pts 6 Stock Valuation and Growth Opportunities The stock of Nogro Corporation is currently selling for 10 per share Earnings per share in the coming year are expected to be 2 The company has a policy of paying out 50 of its earnings each year in dividends The rest is retained and invested in projects that earn a 20 rate of return per year This situation is expected to continue indefinitely a Assuming the current market price of the stock reflects its intrinsic value as computed using the constant growth DDM what rate of return do Nogro s investors require b By how much does its value exceed what it would be if all earnings were paid as dividends and nothing were reinvested c If Nogro were to cut its dividend payout ratio to 25 what would happen to its stock price What if Nogro eliminated the dividend Answer a k D1 P0 g D1 0 5 2 1 g b ROE 0 5 0 20 0 10 Therefore k 1 10 0 10 0 20 20 b Since k ROE the NPV of future investment opportunities is zero PVGO P0 c E1 10 10 0 k Since k ROE the stock price would be unaffected by cutting the dividend and investing the additional earnings 15 pts 7 Stock valuation and Intrinsic Value The digital Electronic Quotation System DEQS Corporation pays no cash dividends currently and is not expected to for the next five years Its latest EPS was 10 all of which was reinvested in the company The firm s expected ROE for the next 6 years is 20 per year and during this time it is expected to continue to reinvest all of its earnings Starting 6 years from now the firm s ROE on new investment is expected to fall to 15 and the company is expected to start paying out 40 of its earnings in cash dividends which it will continue to do forever after DEQS s market capitalization rate is 15 discount rate per year a What is your estimate of DEQS s intrinsic value per share b Assuming its current market price is equal to its intrinsic value what do you expect to happen to its price over the next year The year after c …