Joan Newton is a property owner, who owns several apartments. Joan is considering

refurbishing her apartments and is faced with a difficult decision. She has narrowed down her

choices to three options A$,$ B and C$,$ as described below:

A large$-$scale investment $($A$)$ to improve her flats. This could produce a substantial pay$-$off

in terms of increased revenue net of costs but will require an investment of $1,400,000.$ After

extensive market research it is considered that there is a $40\%$ chance that a pay$-$off of

$2,500,000$ will be obtained, but there is a $60\%$ chance $($probability$)$ that it will be only

$800,000.$

A smaller scale project $($B$)$ to re$-$decorate her premises. At $500,000$ this is less costly but

will produce a lower pay$-$off. Research data suggests a $30\%$ chance $($probability$)$ of a gain of

$1,000,000$ but a $70\%$ chance $($probability$)$ of it being only $500,000.$

Continuing the present operation without change $($C$).$ It will cost nothing, but neither will it

produce any pay$-$off. Clients will be unhappy, and it will become harder and harder to rent the

flats out when they become free.

$($i$)$ Help Joan unscramble these written procedures by preparing a Decision Tree

$(8$ marks$)$

$($ii$)$ Calculate the Expected values and Net Expected values for each of the three options

described above, using the following formulas:

Expected Value $=$ Outcomes $*$ Probability

Net Expected Value $=$ Expected Value $$ Cost

$(7$ marks$)$

Hint: Consider a tree, that starts from a decision node to branch from the Root for each option:

a large$-$scale investment $($A$),$ a smaller scale project $($B$),$ and without change $($C$).$ Then for

each of them branching for whether the choice will yield a $($High return, Low return$).$ The

outcomes should be an action result, presented to the most right$-$hand side of the tree for each

branch.