On January $1,20$X$1,$ Pujols Industries has the opportunity to invest in a project with an uncertain

outcome. The product might be a hit and highly profitable, or it might not. To put specific numbers to

it$,$ there is a $50$ percent chance that the payoffs will be an annuity of $$1,500$ per year for three years.

There is also a $50$ percent chance that the payoffs will be an annuity of $$500$ per year for three years.

The payoff on December $31,20$X$1$ is when Pujols discovers whether the product is a hit or not. If the

payoff is $$1,500,$ then management expects the other two years will also be $$1,500.$ If the payoff is

$$500,$ then management expects the other two years will also be $$500.$

Because Pujols does not know whether the product will be a hit or not, Pujols assigns $50/50$ chances to

the $$1,500$ and the $$500.$

The alternative use of money is to invest it at $10$ percent.

Required

a$.$ What is the expected present value of the project as of January $1,20$X$1?$

b$.$ As it happens, the land, building, and equipment have alternative uses, which means that anytime

during the project, Pujols could stop the project and turn to an alternative project $($project $2).$ This

alternative project, project $2,$ would only be a choice if the original project was turning out poorly, say,

after the results of the original project were known on December $31,20$X$1.$ If numbers were put to it$,$

Pujols anticipates that this alternative project, project $2,$ would last the remaining two years and have a

present value of $$1,600$ as of December $31,20$X$1.$ Were Pujols to switch on December $31,20$X$1,$ Pujols

would have the new project $($project $2)$ worth $$1,600$ plus the $$500$ from the first year of the the original

project $($total of $$2,100).$

Now, think back to January $1,20$X$1.$ With the opportunity to switch, Pujols has a $50$ percent chance of

the three year annuity of $$1,500.$ Pujols also has a $50$ percent chance of $$2,100$ in one year.

What is the present value as of January $1,20$X$1$ when Pujols has an opportunity to switch?

c$.$ What is the value at January $1,20$X$1,$ of being able to opt out of this first project if it turns out to have

a low payoff? The value of this option is the increase in present value of part b$.$ compared to part a$.$ I

think this is sometimes called the value of the abandonment option.