Textbook Problem

James Judson is the financial manager in charge of the company pension fund at Armco Incorporated. James knows that the fund must be sufficient to make the payments listed in Table 4.4. Each payment must be made on the first day of each year. James is going to finance these payments by purchasing bonds. It is currently January 1 of year 1, and three bonds are available for immediate purchase. The prices and coupons for the bonds are as follows. (We assume that all coupon payments are received on January 1 and arrive in time to meet cash demands for all the year on which they arrive.)

• Bond 1 costs $980 and yields a $60 coupon in the years 2 through 5 and a $1060 payment on maturity in the year 6.
• Bond 2 costs $970 and yields a $65 coupon in the years 2 through 11 and a $1065 payment on maturity in the year 12.

Bond 3 costs $1050 and yields a $75 coupon in the years 2 through 14 and a $1075

James must decide how much cash to allocate (from company coffers) to meet the initial $11,000 payment and buy enough bonds to make future payments. He knows that any excess cash on hand can earn an annual rate of 4% in a fixed-rate account. How should he proceed?

In the pension fund model, suppose there is an upper limit of 60 on the number of bonds of any particular type that can be purchased. Modify the model to incorporate this extra constraint and then reoptimize. How much more money does James need to allocate initially?