Subject: Business / Finance
QuestionFinancial Engineering and Risk Management1.Lottery paymentsA major lottery advertises that it pays the winner $10 million. However this prize money is paid at the rate of $500,000 each year (with the first payment being immediate) for a total of 20 payments. What is the present value of this prize at 10% interest compounded annually?1point 2.Sunk Costs (Exercise 2.6 in Luenberger)A young couple has made a deposit of the first month’s rent (equal to$1,000) on a 6-month apartment lease. The deposit is refundable atthe end of six months if they stay until the end of the lease.The next day they find a different apartment that they like just as well,but its monthly rent is only $900. And they would again have to put adeposit of $900 refundable at the end of 6 months.They plan to be in theapartment only 6 months. Should they switch to the new apartment? Assumean (admittedly unrealistic!) interest rate of 12% per month compounded monthly.StaySwitch1point 3.Relation between spot and discount ratesSuppose the spot rates for 1 and 2 years are s1=6.3% and s2=6.9% with annual compounding. Recall that in this course interest rates are always quoted on an annual basis unless otherwise specified. What is the discount rate d(0,2)?1point 4.Relation between spot and forward ratesSuppose the spot rates for 1 and 2 years are s1=6.3% and s2=6.9% with annual compounding. Recall that in this course interest rates are always quoted on an annual basis unless otherwise specified. What is the forward rate, f1,2 assuming annual compounding?1point 5.Forward contract on a stockThe current price of a stock is $400 per share and it pays no dividends. Assuming a constant interest rate of 8% per year compounded quarterly, what is the stock’s theoretical forward price for delivery in 9 months?1point 6.Bounds using different lending and borrowing rateSuppose the borrowing rate rB=10% compounded annually. However,the lending rate (or equivalently, the interest rate on deposits) isonly 8% compounded annually. Compute the difference between the upperand lower bounds on the price of an perpetuity that pays A=10,000$ peryear.1point 7.Value of a Forward contract at an intermediate timeSuppose we hold a forward contract on a stock with expiration 6months from now. We entered into this contract 6 months ago so that when we entered into the contract, the expiration was T=1 year. The stock price$ 6 months ago was S0=100, thecurrent stock price is 125 and the current interest rate is r=10%compounded semi-annually. (This is the same rate that prevailed 6 months ago.) What is the current value of our forward contract?