Finco Investment Corporation must determine an investment strategy for the firm during the next three years. Currently (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 in Table. For example, $1 invested in investment B requires a $1 cash outflow at time 1 and returns 50¢ at time 2 and $1 at time 3. To ensure that the company's portfolio is diversified, Finco requires that at most $75,000 be placed in any single investment. In addition to investments A-E, Finco can earn interest at 8% per year by keeping uninvested cash in money market funds. Returns from investments may be immediately reinvested. For example, the positive cash flow received from investment C at time 1 may immediately be reinvested in investment B. Finco cannot borrow funds, so the cash available for investment at any time is limited to cash on hand. Formulate an LP that will maximize cash on hand at time 3. Cash Flow ($) at Time* 0 2 A -1 B 0 с -1 Ꭰ -1 0 E 0 0 = *Note: Time 0 = present; time 1 from now. 1 year from now; time 2 = 2 years from now; time 3 = 3 years INV 1 0.5 -1 1.2 1 0.5 0 0 -1 Decision variables, x₁ = dollars invested in investment A x₂ = dollars invested in investment B x3 = dollars invested in investment C X4 = dollars invested in investment D X5 = dollars invested in investment E St=dollars invested in money market funds at time t (t = 0, 1, 2) 3 0 1 0 1.9 1.5 The mathematical model max Z = x₂ + 1.9x4 + 1.5x5 +1.08S₂ s.t. x₁ + x3 + X4+ So = 100,000 0.5x₁ + 1.2x3 +1.08So=x2 + S₁ x₁ +0.5x₂ +1.08S₁ = x5 + S₂ X₁ ≤ 75,000 X₂ ≤ 75,000 X3 ≤ 75,000 X4 ≤ 75,000 X5 ≤ 75,000 X1, X2, X3, X4, X5, So, S₁, S₂ 20
Finco Investment Corporation must determine an investment strategy for the firm during the next three years. Currently (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 in Table. For example, $1 invested in investment B requires a $1 cash outflow at time 1 and returns 50¢ at time 2 and $1 at time 3. To ensure that the company's portfolio is diversified, Finco requires that at most $75,000 be placed in any single investment. In addition to investments A-E, Finco can earn interest at 8% per year by keeping uninvested cash in money market funds. Returns from investments may be immediately reinvested. For example, the positive cash flow received from investment C at time 1 may immediately be reinvested in investment B. Finco cannot borrow funds, so the cash available for investment at any time is limited to cash on hand. Formulate an LP that will maximize cash on hand at time 3. Cash Flow ($) at Time* 0 2 A -1 B 0 с -1 Ꭰ -1 0 E 0 0 = *Note: Time 0 = present; time 1 from now. 1 year from now; time 2 = 2 years from now; time 3 = 3 years INV 1 0.5 -1 1.2 1 0.5 0 0 -1 Decision variables, x₁ = dollars invested in investment A x₂ = dollars invested in investment B x3 = dollars invested in investment C X4 = dollars invested in investment D X5 = dollars invested in investment E St=dollars invested in money market funds at time t (t = 0, 1, 2) 3 0 1 0 1.9 1.5 The mathematical model max Z = x₂ + 1.9x4 + 1.5x5 +1.08S₂ s.t. x₁ + x3 + X4+ So = 100,000 0.5x₁ + 1.2x3 +1.08So=x2 + S₁ x₁ +0.5x₂ +1.08S₁ = x5 + S₂ X₁ ≤ 75,000 X₂ ≤ 75,000 X3 ≤ 75,000 X4 ≤ 75,000 X5 ≤ 75,000 X1, X2, X3, X4, X5, So, S₁, S₂ 20
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Transcribed Image Text:Finco Investment Corporation must determine an investment strategy for the firm during the next
three years. Currently (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 in Table.
For example, $1 invested in investment B requires a $1 cash outflow at time 1 and returns 50¢ at
time 2 and $1 at time 3. To ensure that the company's portfolio is diversified, Finco requires that
at most $75,000 be placed in any single investment. In addition to investments A-E, Finco can
earn interest at 8% per year by keeping uninvested cash in money market funds. Returns from
investments may be immediately reinvested. For example, the positive cash flow received from
investment C at time 1 may immediately be reinvested in investment B. Finco cannot borrow funds,
so the cash available for investment at any time is limited to cash on hand. Formulate an LP that
will maximize cash on hand at time 3.
Cash Flow ($) at Time*
0
2
A
-1
B
0
с
-1
Ꭰ
-1
0
E
0
0
=
*Note: Time 0 = present; time 1
from now.
1 year from now; time 2 = 2 years from now; time 3 = 3 years
INV
1
0.5
-1
1.2
1
0.5
0
0
-1
Decision variables,
x₁ = dollars invested in investment A
x₂ = dollars invested in investment B
x3 = dollars invested in investment C
X4 = dollars invested in investment D
X5 = dollars invested in investment E
St=dollars invested in money market
funds at time t (t = 0, 1, 2)
3
0
1
0
1.9
1.5
The mathematical model
max Z = x₂ + 1.9x4 + 1.5x5 +1.08S₂
s.t.
x₁ + x3 + X4+ So = 100,000
0.5x₁ + 1.2x3 +1.08So=x2 + S₁
x₁ +0.5x₂ +1.08S₁ = x5 + S₂
X₁ ≤ 75,000
X₂ ≤ 75,000
X3 ≤ 75,000
X4 ≤ 75,000
X5 ≤ 75,000
X1, X2, X3, X4, X5, So, S₁, S₂ 20
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