When investing in fixed income securities, to provide for future expenses, a higher yield is better. Setting aside considerations of risk and only considering maturities, the problem is that a longer maturity may not provide the funds when they are needed.

Suppose you need to provide funds in 3-5 years from now. In this case $1,000 at the beginning of each of those years.

Assume that you can hold cash (equivalently 1-year bonds) and 2-year bonds. Suppose that there are no transaction costs and that the yields on cash and 2-year bonds are 5% and 9%, respectively.

The cash flows will look like the following:

Once the last payment of $1,000 in 5 years is made, there will be no further obligations. The questions to be answered are as follows:

• What is the minimum investment to accomplish this?
• For periods 1-4, how do you re-invest the proceeds of maturing bonds?

The decision variables areand, where C_nis the amount invested in the short-term bond in year n, and D_nis the amount invested in the long-term bond in year n.

Due to new costs at the bank, there is a rule that bonds may only be bought in multiples of $100. With this restriction and using the solver ability to include an integer constraint, what is the minimum amount that must be invested at time 0 to achieve the required payments of $1,000 in years 3-5?

Hints:

• Set up decision variable for the number of bonds of each kind to buy.
• Keep a running cash balance. It can never fall below 0.
• Make an initial deposit before time 0. Use that to fund the purchases.
• The initial deposit is also a decision variable.
• The initial deposit is what should be minimized.

How much does requiring bonds to be purchased in round lots increase the cost? Round to the nearest hundredth percent.