FLATBUSH Iris Yu Ting Hsueh Wen Shan Li
FLATBUSH Iris Yu Ting Hsueh Wen Shan Li Jong Won Baek Sung Pae BY SMART BRUINS
Objective • Find the optimal combination of government bonds (zero coupon and regular) to minimize the total cost and cover the required annual clean-up expenditure • Can buy fractional bonds Note: virtual bonds are created in the calculation, but we set the prices in such a way that these bonds do not affect our answers
Zero Coupon • Zero coupon bond does not pay annual coupon payments • Income from bond is simply the face value at maturity date (this is the principle we would receive at maturity) • Calculation of total income: (# of bonds) x (face value) • Face value = $1000
Regular Bonds • Regular bond pays annual coupon payments based on the coupon rate and face value. Total income from bond is the sum of all the coupon payments and the face value at maturity date • Calculation of total income from one regular bond: coupon payments+ income from maturing bond = ∑(coupon rate x face value x # of bonds) + (face value x # of bonds) • Face value = $1000
Total Income from All Regular Bonds Example: Bought two $1000 7% bonds maturing in 1 -year and one $1000 10% bond maturing in 3 -years • Total income @ end of year 1 = coupon payment of all 3 bonds + principle received from the two 1 -year maturity bonds 2*1000*0. 07+1000*0. 1+2*1000= $2240 • Total income @ end of year 2 = coupon payment of the one 3 - year bond • Total income @ end of year 3 = coupon payment and principle received from the 3 -year bond
Cash • Cash earns 4% annual interest • The cash left over after paying the expenditure is carried forward to the next year (No cash in beginning of year 1) Constraints • Year 1 -14: cash carried forward cannot exceed $4, 000. 00 per year • Year 15: cash carried forward cannot exceed $25, 000. 00
Total Fund Available • This is the amount of money Flatbush uses to pay off the annual expenditures • Calculation: cash left over + total income from regular bonds + total income from zero coupon bonds
Total Cost • The total cost for Flatbush is the cost for all the bonds it buys in order to pay off the annual clean-up expenditure • Calculation: (# of zero coupon bonds)(price of zero coupon bonds) + (# of regular bonds)(price of regular bonds) • Can minimize cost by purchasing the optimal combination of bonds that will satisfy all the requirements &constraints
Solution • Using Solver in Excel, we found the cost minimizing combination to be the following: Bond Type Price per 1000 # of Bonds to Purchase Z 10 $600 645. 73 B 1 $1100 2268. 31 B 5 $1100 4008. 10 B 8 $900 6952. 57 B 12 $840 1292. 76 B 15 $760 2559. 84 • Total Cost = $16, 580, 197. 87 • Cash Left in year 15 = $25, 000. 00
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