Disclaimer: The characters in this problem are fictitious. Any similarity between these and persons either living or dead is purely coincidental. Oliver South is a loyal and innovative employee of the Never Say Can't Corporation (NSC), the world's leading manufacturer of gag gifts and door prizes. Recently South contracted with I. O. Tola, the chief of the society of Involuntary Revenue Allowing Negotiators (figure out the acronym yourself). In exactly one year I. 0. Tola will accept a 30 million dollar shipment of some of the best gag gifts from the NSC cata- logue. At the time of delivery Tola will deposit 30 million dollars in a special account that South maintains to make payment especially convenient for his customers. Now South has one problem. He has a particular investment project that he would like to finance. (There is a bit of controversy in NSC concerning the Net Present Value of this project, but this is not important for this problem.) Unfortunately, South can only start this project in three years, two years after he receives the money from I. O. Tola. What can he do with the 30 million dollars over those two years? South calls up a banker friend of his in Switzerland (the same place he has the convenient account for easy payment). He asks the banker for some advice and the banker suggests that he loan the money forward. South is somewhat bewildered by this idea, but he likes the sound of it. Encouraged by South's response, the banker gives his bank's current rates. If South wants to borrow money for one year, the bank will charge an annualized rate of interest (with continuous compounding) equal to .14 (14%). If South wants to borrow for two years, the rate is .15 (15%). For a three year loan, the borrowing rate is .17 (17%). Finally, the rate quoted for a four year loan is .19 (19%). (All loans are to be repaid with a single payment at the termination of the loan period.) At the same time South can deposit money in the bank if he chooses. The annualized, continuously compounded rate earned on a one year CD (certificate of deposit) is .08 (8%). The rate on a two year CD is .10 (10%) and the rate on a three year CD is .13%. The four year CD rate is .15 (15%). Remember all rates are Chapter 9: Forward Contracts, Questions Page 451 Adventures in Debentures annualized with continuous compounding. Also, for any amount over 10,000 dollars deposited with the bank for a year or more, South will receive a toaster. The prospect of getting a toaster sells South on the idea. He decides to loan the 30,000,000 dollars forward, the forward loan starting one year hence and ending three years from now. Explain exactly what South must do to create the forward loan. How much money will he have in three years? What is the forward rate he faces? (In making this calculation ignore the value of any toasters received.) Disclaimer: The characters in this problem are fictitious. Any similarity between these and persons either living or dead is purely coincidental. Oliver South is a loyal and innovative employee of the Never Say Can't Corporation (NSC), the world's leading manufacturer of gag gifts and door prizes. Recently South contracted with I. O. Tola, the chief of the society of Involuntary Revenue Allowing Negotiators (figure out the acronym yourself). In exactly one year I. 0. Tola will accept a 30 million dollar shipment of some of the best gag gifts from the NSC cata- logue. At the time of delivery Tola will deposit 30 million dollars in a special account that South maintains to make payment especially convenient for his customers. Now South has one problem. He has a particular investment project that he would like to finance. (There is a bit of controversy in NSC concerning the Net Present Value of this project, but this is not important for this problem.) Unfortunately, South can only start this project in three years, two years after he receives the money from I. O. Tola. What can he do with the 30 million dollars over those two years? South calls up a banker friend of his in Switzerland (the same place he has the convenient account for easy payment). He asks the banker for some advice and the banker suggests that he loan the money forward. South is somewhat bewildered by this idea, but he likes the sound of it. Encouraged by South's response, the banker gives his bank's current rates. If South wants to borrow money for one year, the bank will charge an annualized rate of interest (with continuous compounding) equal to .14 (14%). If South wants to borrow for two years, the rate is .15 (15%). For a three year loan, the borrowing rate is .17 (17%). Finally, the rate quoted for a four year loan is .19 (19%). (All loans are to be repaid with a single payment at the termination of the loan period.) At the same time South can deposit money in the bank if he chooses. The annualized, continuously compounded rate earned on a one year CD (certificate of deposit) is .08 (8%). The rate on a two year CD is .10 (10%) and the rate on a three year CD is .13%. The four year CD rate is .15 (15%). Remember all rates are Chapter 9: Forward Contracts, Questions Page 451 Adventures in Debentures annualized with continuous compounding. Also, for any amount over 10,000 dollars deposited with the bank for a year or more, South will receive a toaster. The prospect of getting a toaster sells South on the idea. He decides to loan the 30,000,000 dollars forward, the forward loan starting one year hence and ending three years from now. Explain exactly what South must do to create the forward loan. How much money will he have in three years? What is the forward rate he faces? (In making this calculation ignore the value of any toasters received.)
