SECTION 2: HOMEWORK 7: STATEMENT Problem # 1 (Pension planning, Baker pg 102, [/25]) Casey's Famous Roast Beef employs mostly high-school and college-age workers. However, a few employees have been with the company for a long time, and owner Casey Carangelo has calculated that he will need the following cash flows to pay his loyal pensioners over the next 14 years. (This year is considered to be ear 0.) 01 02 03 04 05 Cash (000s) 8 10 12 14 Year 08 09 10 11 06 07 12 13 14 15 16 17 18 20 22 23 24 25 26 Mr. Carangelo does not believe in modern portfolio theory, with its emphasis on diversification, His brief foray into the market during 2008 ended disastrously. The only investments he trusts are US government bonds. His accountant has recommended three currently available bonds. Current Price () Annual Coupon (S) Years to Maturity Face Value (S 1000 Bond 1 Bond 2 980 50 5 970 55 11 1000 Bond 3 990 60 14 1000 All bonds will pay their face value when they mature. Their current price is what it costs to buy the bond at the end of this year. Each bond pays its annual coupon (interest, in effect every December 31, starting the next year). At maturity, each bond repays its face value plus the final coupon payment for that year on December 31 Cash that is carried over from one year to the next (as well as any cash in the portfolio at the start) will be placed in an interest-bearing savings account that eurrently earns 3% per year. Mr Carangelo believes that this rate will remain stable. Mr Carangelo wants the pension fund, once started, to be self-sustaining over the next 14 years. In other words, he plans to make a single withdrawal from corporate sources and invest it such that the income from his bonds, plus savings interest, will cover the pension payments each year. In effect, the following events will happen each December 31, starting next year. Mr. Carangelo withdraws all the savings account funds, with interest. He receives all bond payments. He pays required pension benefits. He deposits any remaining funds back into the saving account to earn interest over the following year. Ideally, there should be no money left at the end of the 14-year period. Mr. Carangelo, who knows very little about investments, and nothing about linear programming, has asked you to help him figure out how to set-up the pension fund. 1. Write a linear programming model for this problem. 2. Solve this model using GAMS. SECTION 2: HOMEWORK 7: STATEMENT Problem # 1 (Pension planning, Baker pg 102, [/25]) Casey's Famous Roast Beef employs mostly high-school and college-age workers. However, a few employees have been with the company for a long time, and owner Casey Carangelo has calculated that he will need the following cash flows to pay his loyal pensioners over the next 14 years. (This year is considered to be ear 0.) 01 02 03 04 05 Cash (000s) 8 10 12 14 Year 08 09 10 11 06 07 12 13 14 15 16 17 18 20 22 23 24 25 26 Mr. Carangelo does not believe in modern portfolio theory, with its emphasis on diversification, His brief foray into the market during 2008 ended disastrously. The only investments he trusts are US government bonds. His accountant has recommended three currently available bonds. Current Price () Annual Coupon (S) Years to Maturity Face Value (S 1000 Bond 1 Bond 2 980 50 5 970 55 11 1000 Bond 3 990 60 14 1000 All bonds will pay their face value when they mature. Their current price is what it costs to buy the bond at the end of this year. Each bond pays its annual coupon (interest, in effect every December 31, starting the next year). At maturity, each bond repays its face value plus the final coupon payment for that year on December 31 Cash that is carried over from one year to the next (as well as any cash in the portfolio at the start) will be placed in an interest-bearing savings account that eurrently earns 3% per year. Mr Carangelo believes that this rate will remain stable. Mr Carangelo wants the pension fund, once started, to be self-sustaining over the next 14 years. In other words, he plans to make a single withdrawal from corporate sources and invest it such that the income from his bonds, plus savings interest, will cover the pension payments each year. In effect, the following events will happen each December 31, starting next year. Mr. Carangelo withdraws all the savings account funds, with interest. He receives all bond payments. He pays required pension benefits. He deposits any remaining funds back into the saving account to earn interest over the following year. Ideally, there should be no money left at the end of the 14-year period. Mr. Carangelo, who knows very little about investments, and nothing about linear programming, has asked you to help him figure out how to set-up the pension fund. 1. Write a linear programming model for this problem. 2. Solve this model using GAMS