different options return per dollar invested B u s i n e s s F i n a n c e

Question 1

NewCrest is looking to invest at most $500,000. The investment can be divided among three
options. The return on each option depends on the economic outlook, which is shown in
Table 1. For example, if the economic outlook is bright, investing $1 in option I will generate
a gain of $3, and investing $1 in option II will result in a loss of $5.
Table 1: Return per dollar invested in the different options
Return per dollar invested in option
Economic outlook I II III
Bright 3 -5 7
Gloomy -2 6 -3

(a) Axel, a business executive, proposed two alternatives to NewCrest. One is investing
$100,000 in option I, $200,000 in II and $150,000 in III. The other is investing
$60,000 in option I, $100,000 in II and $125,000 in III. NewCrest takes a
conservative approach to decision-making. That is, it chooses the alternative that
maximizes the minimum return produced by the two outcomes of the economic
outlook. Discuss among the two alternatives proposed by Axel, which one NewCrest
will choose. Please write clearly alternatives, states of nature and payoffs in a payoff
table. Please limit the answer to within one page.
(10 marks)

(b) Ben, another business executive, pointed out that NewCrest has an unlimited number
of alternatives, not just the two proposed by Axel. Which alternative is best if
NewCrest takes a conservative approach to decision-making? To answer that
question, Ben drafted,
“Define investment in option I,
investment in option II, and
investment in option III.
The objective is to
Maximize min ”.
The objective function is not linear. Please search online “tricks to maximize the min
of objective functions” or “transformations into linear programs”. Then help Ben
develop a complete Linear Programming (LP) model that represents the problem of
deciding how much to invest in each option. Please limit the answer to within one
page.
(10 marks)

(c) Use the Excel Solver to find the optimal solution to the problem in Part (b) and
summarise how NewCrest should invest. Please paste here three screenshots, (1) the
problem worksheet just before clicking the Solver command, (2) the Solver
Parameters dialog just before clicking Solve and (3) the Answer Report created by the
Solver. Please limit the answer to within three pages.
(20 marks)