# solution

A major retail clothing store is considering whether to open a
new store on the other side of town or wait one year and then open
the store. In the meantime, they have paid \$10,000 for a one year
option on a building. If they open the store now it will cost
\$140,000 to refurbish it, but it will cost \$160,000 if they wait
one year.

?

They expect sales to
depend on the economy in the area at the time they open the store.
If they go ahead now, there is a 50% chance the economy will go up,
30% it will stay the same, and 20% it will go down. They then
expect the following returns: if the economy goes up \$200,000;
stays the same \$160,000; and goes down -\$20,000.

?

If they wait one
year, they can either open the store then or not open the store and
let the option expire. If the option expires, they will lose the
\$10,000. One year from now they expect there is a 40% chance the
economy will go up, 30% stay the same, and 30% go down. The returns
they expect to get would then be: if the economy goes up \$180,000;
stays the same \$160,000; and goes down -\$30,000.

?

a. Using decision tree analysis,
what is the expected value of opening the store now?

b. Using decision tree analysis,
what is the expected value of waiting one year to open the
store?

c. What should the company do and what is the
expected value of that decision?