# Model 26: Investment Planning

Winston-Salem Development Management (WSDM) is trying to complete is
investment plans for the next three years. Currently, WSDM has 2 million
dollars available for investment. At six month intervals over the next three
years, WSDM expects the following income stream from previous investments:
$500,000 (6 months from now), $400,000; $380,000; $360,000; $340,000;
and $300,000 (at the end of third year). There are three development
projects in which WSDM is considering participating. The Foster City
Development would, if WSDM participated fully, have the following cash flow
stream (projected) at six month intervals over the next three years
(negative numbers represent investments, positive numbers represent income):
-$3,000,000; -$1,000,000; -$1,800,000; $400,000; $1,800,000;
$1,800,000; $5,500,000. The last figure is its estimated value at the end
of three years. A second project involves taking over the operation of some
old lower-middle income housing on the condition that certain initial
repairs to it be made and that it be demolished at the end of three years.
The cash flow stream for this project if participated in fully would be:
-$2,000,000; -$500,000; $1,500,000; $1,500,000; $1,500,000; $200,000;
-$1,000,000.
The third project, The Disney-Universe Hotel, would have the following cash
flow stream (six-month intervals) if WSDM participated fully. Again the last
figure is the estimated value at the end of the three yeras: -$2,000,000;
-$2,000,000; -$1,800,000; $1,000,000; $1,000,000; $1,000,000;
$6,000,000. WSDM can borrow money for half-year intervals at 3.5 percent
interest per half year. At most, 2 million dollars can be borrowed at one
time, i.e., the total outstanding principal can never exceed 2 million. WSDM
can invest surplus funds at 3 percent per half-year.

Formulate the problem of maximizing WSDM's net worth at the end of
three years as a linear program. If WSDM participates in a project
at less than 100 percent, all the cash flows of that project
are reduced appropriately.