1. FLATBUSH by Smart bruins
Iris Yu Ting Hsueh
Wen Shan Li
Jong Won Baek
Sung Pae

2. 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

3. 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

4. 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

5. Total Income from All Regular Bonds
Example:
Bought two $1000 7% bonds maturing in 1-year and one $ % bond maturing in 3-years
Total end of year 1 = coupon payment of all 3 bonds + principle received from the two 1-year maturity bonds
2*1000* *0.1+2*1000= $2240
Total end of year 2 = coupon payment of the one 3-year bond
Total end of year 3 = coupon payment and principle received from the 3-year bond

6. 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, per year
Year 15: cash carried forward cannot exceed $25,000.00

7. 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

8. 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

10. Solution
Using Solver in Excel, we found the cost minimizing combination to be the following:
Total Cost = $16,580,197.87
Cash Left in year 15 = $25,000.00
Bond Type
Price per 1000
# of Bonds to Purchase
Z 10
$600
645.73
B 1
$1100
B 5
B 8
$900
B 12
$840
B 15
$760