A money manager for a university endowment has received a $$10$ million donation to

invest. The intent is to establish a cash flow stream for the next $25$ years. The goal is to

have an annual payout that begins at $$50,000$ and grows by $3\%$ per year. The manager

has identified a list of $50$ different bonds to invest in$.$ The manager$$s goal is to determine

which bonds to purchase now so as to maximize the total discounted return while

guaranteeing the bond$$s pay out the required annual funds. The manger has specified a

limit of $2,500$ units of any individual bond.

The data on tab $3$ lists the $50$ bonds available for purchase annual payout for each of the

next $25$ years. The data includes the payout each year based on the bond$$s coupon and

maturity date. The investment column contains a place to identify the number of bonds

purchased of each type.

First, complete the model.

$$ Calculate the cash flow in each year as the $($sum$)$ product of the Investment

column and the appropriate bond cash flow column.

$$ Calculate the cash flow required based on the Initial Cash Required and the

Annual Increase fields.

$$ Calculate the Disc Cash Flow as the product of the Cash Flow and discount Factor

column.

Now specify the optimization model.

$$ Define the Investment column as the decision variables.

$$ Define the Disc Cash Flow as the Objective. $($max$)$

$$ Establish the constraint that the Cash Flow must exceed the Cash Required field.

$$ Establish a constraint that limits the Investment to be less than the Available

Funds.

$$ Constrain the Investments to be non$-$negative integers and less than the Max per

Bond setting.

$$ We wish to solve the model using the standard LP $/$Quadratic engine to

guaranteed optimality $(0\%$ tolerance$).$

$$ Set the engine to Standard LP $/$Quadratic$.$ Do not have Automatically Select

Engine checked.

Now solve the model.

$$ Create a graph of the Cash Flow per year and paste it into your template.

$$ What is the total Disc Cash Flow?

$$ How many bonds were invested in$?$

$$ Filter your data to show the bonds that were selected, including the number

purchased and the Bond characteristics. Paste this data into your template.