The Fairwinds Development Corporation is considering taking part in one or more different development projects-A, B, and C-that are about to be launched. Each project requires a significant investment over the next few years and then would be sold upon completion. The projected cash flows (in millions of dollars) associated with each project are shown in the table below. Year Project A Project B Project C 1 -8 -9 -13 2 -10 -10 -10 3. -12 -7 -9 4 40 -9 -9 46 -7 62 Fairwinds has $18 million cash on hand now and also expects to receive $8 million in other income at the start of each year (year 1 through year 6) that would also be available for investments (therefore, a total of $26 million is available for projects in year 1). Assume that money not spent in a given year is available in future years, and also earns 1% interest. For example, if the ending balance in year 1 is $1 million, then $1.01 million will be available for projects at the start of year 2, along with the $8 million from other income for year 2. Assume no interest earned for year 1 as it is already included in the $18 million starting balance. For simplicity, you may assume that all cash flows (including interest earned, other income received, and project cash flows) occur simultaneously at the start of each year. The company may participate in each project either fully, fractionally (with other development partners), or not at all. If Fairwinds participates at less than 100%, then all the cash flows associated with that project are reduced proportionally. For example, if Fairwinds participates in Project A at 50%, the cash flows associated with that project would be -4, -5, -6, and $20 million in years 1 through 4, respectively. Company policy requires ending each year with a cash balance of at least $700 thousand. (Interest is earned on all remaining cash, including the $700 thousand minimum balance.) Which projects should Fairwinds take part in and at what fraction of participation, so as to end year 6 with as much cash as possible? Formulate and solve a linear programming spreadsheet model.
The Fairwinds Development Corporation is considering taking part in one or more different development projects-A, B, and C-that are about to be launched. Each project requires a significant investment over the next few years and then would be sold upon completion. The projected cash flows (in millions of dollars) associated with each project are shown in the table below. Year Project A Project B Project C 1 -8 -9 -13 2 -10 -10 -10 3. -12 -7 -9 4 40 -9 -9 46 -7 62 Fairwinds has $18 million cash on hand now and also expects to receive $8 million in other income at the start of each year (year 1 through year 6) that would also be available for investments (therefore, a total of $26 million is available for projects in year 1). Assume that money not spent in a given year is available in future years, and also earns 1% interest. For example, if the ending balance in year 1 is $1 million, then $1.01 million will be available for projects at the start of year 2, along with the $8 million from other income for year 2. Assume no interest earned for year 1 as it is already included in the $18 million starting balance. For simplicity, you may assume that all cash flows (including interest earned, other income received, and project cash flows) occur simultaneously at the start of each year. The company may participate in each project either fully, fractionally (with other development partners), or not at all. If Fairwinds participates at less than 100%, then all the cash flows associated with that project are reduced proportionally. For example, if Fairwinds participates in Project A at 50%, the cash flows associated with that project would be -4, -5, -6, and $20 million in years 1 through 4, respectively. Company policy requires ending each year with a cash balance of at least $700 thousand. (Interest is earned on all remaining cash, including the $700 thousand minimum balance.) Which projects should Fairwinds take part in and at what fraction of participation, so as to end year 6 with as much cash as possible? Formulate and solve a linear programming spreadsheet model.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Transcribed Image Text:The Fairwinds Development Corporation is considering taking part in one or more different development
projects-A, B, and C-that are about to be launched. Each project requires a significant investment over the next
few years and then would be sold upon completion. The projected cash flows (in millions of dollars) associated
with each project are shown in the table below.
Year
Project A
Project B
Project C
1
-8
-9
-13
-10
-10
-10
-12
-7
-9
40
-9
-9
5
46
-7
6
62
Fairwinds has $18 million cash on hand now and also expects to receive $8 million in other income at the start of
each year (year 1 through year 6) that would also be available for investments (therefore, a total of $26 million is
available for projects in year 1). Assume that money not spent in a given year is available in future years, and also
earns 1% interest. For example, if the ending balance in year 1 is $1 million, then $1.01 million will be available
for projects at the start of year 2, along with the $8 million from other income for year 2. Assume no interest
earned for year 1 as it is already included in the $18 million starting balance. For simplicity, you may assume that
all cash flows (including interest earned, other income received, and project cash flows) occur simultaneously at
the start of each year.
The company may participate in each project either fully, fractionally (with other development partners),
or not at all. If Fairwinds participates at less than 100%, then all the cash flows associated with that project are
reduced proportionally. For example, if Fairwinds participates in Project A at 50%, the cash flows associated with
that project would be -4, -5, -6, and $20 million in years 1 through 4, respectively. Company policy requires
ending each year with a cash balance of at least $700 thousand. (Interest is earned on all remaining cash, including
the $700 thousand minimum balance.)
Which projects should Fairwinds take part in and at what fraction of participation, so as to end year 6 with
as much cash as possible? Formulate and solve a linear programming spreadsheet model.
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