It is currently the beginning of 2010. Gotham City is trying to sell municipal bonds to support improvements in recreational facilities and highways. The face values of the bonds and the due dates at which principal comes due are listed in the file P06_84.xlsx. (The due dates are the beginnings of the years listed.) The Gold and Silver Company (GS) wants to underwrite Gotham City’s bonds. A proposal to Gotham for underwriting this issue consists of the following: (1) an interest rate of 3%, 4%, 5%, 6%, or 7% for each bond, where coupons are paid annually; and (2) an upfront premium paid by GS to Gotham City. GS has determined the set of fair prices for the bonds listed in the same file. For example, if GS underwrites bond 2 maturing in 2013 at 5%, it would charge Gotham City $444,000 for that bond. GS is allowed to use at most three different interest rates. GS requires a profit of at least $46,000, where its profit is equal to the sale price of the bonds minus the face value of the bonds minus the premium it pays to Gotham City. To maximize the chance that GS will get Gotham City’s business, GS wants to minimize the total cost of the bond issue to Gotham City, which is equal to the total interest on the bonds minus the premium paid by GS. For example, if the year 2012 bond (bond 1) is issued at a 4% rate, then Gotham City must pay two years of coupon interest: 2(0.04)($700,000) = $56,000. What assignment of interest rates to each bond and upfront premium ensure that GS will make the desired profit (assuming it gets the contract) and minimize the cost to Gotham City?
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