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# quantitative week 7

Homework 4

1. The Samsung is considering taking part in one or more of tree different development projects – A, B, and C – that are about to be launched. Each project requires a significant investment over the next few year, 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 1 2 3

4 5 6

Project A -4.5 -6.8 -6.3

21 0

Project B Project C

-6 -14 -8 -8 -3 -8 -2 -7 25 -4

0 0 38

Samsung has $10 million available now and expects to receive $6 million from other projects by the end of each year (1 through 6) that would be available for the ongoing investments the following year in projects A, B, and C. By acting now, the company may participate in each project either fully, fractionally (with other development partners), or not at all. If Samsung participates at less than 100 percent, then all the cash flows associated with that project are reduced proportionally. Company policy requires ending each year with a cash balance of at least $2 million.

Solve this model using Excel Solver (keep in mind that you must set up a linear programming model in Excel Solver). In other words, what would be the (1) maximum ending balance, and (2) optimal level of participation rate for each project? Explain using at least 250 words.

How would the results in part a change if Samsung has $11 million available now and expects to receive $7 million from other projects by the end of each year? In other words, what would be the maximum ending balance and optimal level of participation rate for each project in a new situation?

(Now, you must run a new linear programming model by replacing $10 million (current starting balance) by $11 million (new starting balance) and $6 million (current value of other project) by $7 million (new value of other project). Explain using at least 250 words, focusing on why the participation rates in part b is different from those in part a.

2. Discuss biblical principles that could be related to concepts or theory you learned from this chapter, using at least 100 words. (This is an open-ended question, and there is no definite answer)