Finco Investment Corp. must determine investment strategy for the firm during th

Question

Finco Investment Corp. must determine investment strategy for the firm during the next three years. At present time (time 0), $100,000 is available for investment. Investments A, B, C, D and E are available. The cash flow associated with investing $1 in each investment is given below. For example, $1 invested in investment B requires a $1 cash outflow at time 1 and returns $0.50 at time 2 and $1 at time 3. 1. Cash flow at time t ($) Investment 0.0 1.0 +0.5+1.0 0.0 10 +1.2 1.0 0.0 1.0 +0.5+1.0 0.0 0.01.9 1.0 0.0 0.0 0.0 To ensure that the company's portfolio is diversified, Finco requires that at most $75,000 be placed in a single investment. In addition to investments A-E, Finco can earn interest at 8% per year by keeping uninvested cash in money market funds. Returns from investments may be immediately reinvested. Finco cannot borrow funds. Formulate an LP to maximize cash on hand at time 3

Explanation / Answer

We define the following decision variables.

A= dollars invested in investment A,

B= dollars invested in investment B,

C= dollars invested in investment C,

D= dollars invested in investment D,

E= dollars invested in investment E,

St=dollars invested in money market funds at time t(t=0,1,2,)

Time 3 cash on hand =B+1.9D+1.5E+1.08S2

Objective Function: B+1.9D+1.5E+1.08S2

Cash available at time t= Cash invested at time t

For t=0

100000= A + C + D + S0

For t=1

0.5A + 1.2 C + 1.08 S0= B + S1

For t=2

A + 0.5 B + 1.08 S1= E + S2

Don't forget that at most $75000 can be placed in any of investments A-E.

Therefore,A75000, B75000, C75000, D75000, E75000,

Combining all with the sign restrictions yields the following LP:

Max Z= B+1.9D+1.5E+1.08S2

Subject to constraints:

A + C + D + S0=1000000.

5A + 1.2 C + 1.08 S0= B + S1

A + 0.5 B + 1.08 S= E + S2

A75000

B75000

C75000

D75000

E75000

A,B,C,D,E, S0, S1, S20

Solution: We find the optimal solution to be

z=$218500

A=60000

B=30000

D=40000

E=75000

C= S0,=S1,=S2=0

Thus, Finco should not invest in money market funds at time 3.

Finco should invest $60000 in A and $40000 in D.

Then, at time 1, the $30000 cash inflow from A should be invested in B.

At time 2, the $60000 cash inflow from A and the $15000 cash inflow from B should be invested in E.

At time 3, Finco's $100000 will have grown to $218500

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