Question $1$

You have a potential project for which you want to establish the value of any possible real

options. The project will have an initial cost of $$86$ million, which must be paid at the time of

investment. You realize that the project has four possible cash flows starting in year $1$ and

continuing forever. First, there is a $18\%$ chance of earning $$2$ million per year starting in year

Second, there is a $30\%$ chance of earning $$6\mathrm{.}07$ million per year starting in year $1.$ Third,

there is a $21\%$ chance the the project will earn $$5\mathrm{.}28$ million per year. Fourth, there is a

chance that the project will earn $$3\mathrm{.}9.$ These are the only four possibilities. In $3$ year$($s$),$ you

will be able to improve the quality of your manufacturing process to increase the net CFs from

the project if you would like to$.$ The cost of this will be $$62$ million, and the cash flows will

increase beginning immediately when you make this investment $($the CFs increase starting the

same year that you pay the improvement cost$)$ and will remain at the new level forever, if you

choose to 'improve' the project. The 'improvement' will increase the project's cash flows by

$120\%.$ The risk$-$free rate and appropriate discount rate for the project is $5\%.$ What is the

value today of this option to 'improve'? Hint: you can treat this the same wayyou would an

expansion option.

Input your answer in millions of dollars, rounded to the nearest $0\mathrm{.}001($e$.$g:$,,$$$19,056,129$

would be entered as $19\mathrm{.}056).$

Question $2$

For partial credit only: Refer to Question $1.$ Type out the calculation that you did $($and the

answer you calculated$)$ to determine whether to exercise the option in the highest CF case:

Type out the calculation that you did $($and the answer you calculated$)$ to determine whether to

exercise the option in the higher mid$-$CF case:

Type out the calculation that you did $($and the answer you calculated$)$ to determine whether to

exercise the option in the lower mid$-$CF case:

Type out the calculation that you did $($and the answer you calculated$)$ to determine whether to

exercise the option in the lowest CF case:

Type out the calculation or calculations that you did to value the option to 'improve' after you

did the above calculations $($do not repeat those calculations in this step$).$ You may not need all

of these blanks; just fill in the ones that you need:

Question $3$

You also have a second potential project, with a different real option. The project will have an

initial cost of $$52$ million, which must be paid at the time of investment. You realize that the

project has three possible cash flows starting in year $1$ and continuing forever. First, there is a

$14\%$ chance of earning $$1\mathrm{.}49$ million per year starting in year $1.$ Second, there is a $49\%$

chance of earning $$6\mathrm{.}97$ million per year starting in year $1.$ Third, there is a chance the the

project will earn $$3\mathrm{.}07$ million per year. These are the only three possibilities. In $3$ year$($s$),$ you

will be able to abandon the project and sell off the assets for $$37\mathrm{.}5$ million, but will give up

the cash flows starting one year after you abandon $($if you abandon in year $1,$ you receive the

year $1$ CFs but no CFs after that; if you abandon in year $2,$ you receive the year $1$ and year $2$

CFs$,$ but no CFs after that, and so on$.).$ The risk$-$free rate and appropriate discount rate for the

project is $5\%.$ What is the value today of this option to abandon? Input your answer in

millions of dollars, rounded to the nearest $0\mathrm{.}001($e$.$g:$,$ $$19,056,129$ would be entered as

$19\mathrm{.}056).$

Question $4$

For partial credit only: Refer to Question $3.$ Type out the calculation that you did $($and the

answer you calculated$)$ to determine whether to exercise the option in the highest CF case:

Type out the calculation that you did $($and the answer you calculated$)$ to determine whether to

exercise the option in the mid$-$CF case:

Type out the calculation that you did $($and the answer you calculated$)$ to determine whether to

exercise the option in the lowest CF case:

Type out the calculation or calculations that you did to value the option to abandon after you

did the above calculations $($do not repeat those calculations in this step$).$ You may not need all

of these blanks; just fill in the ones that you need: