You are considering building a large or a small facility. You need to build one $-$ not building is not an option.

Assume all costs are NPV$,$ so a cost of $X million represents a NPV of $X$,$ and revenue of $Y million represents a NPV of $Y$.$

A small facility will cost $$20$ million, and a large facility will cost $$60$ million.

After you have built your facility, you will learn what the demand is for your products made at that location.

The best estimates are that demand will be low with probability $0\mathrm{.}1,$ medium with probability $0\mathrm{.}5,$ and high with probability $0\mathrm{.}4.$

The demand is independent of how big a facility you build; people want what they want regardless of your ability to manufacture it$.$

This means each facility will face the same demand probabilities.

If you build a small facility, and demand is low, you will have revenue of $$20$ million.

If you build a small facility, and demand is medium, you will have revenue of $$50$ million.

If you build a small facility, and demand is high, you will have revenue of $$60$ million.

If you build a large facility, and demand is low, you will have revenue of $$20$ million.

If you build a large facility, and demand is medium, you will have revenue of $$50$ million.

If you build a large facility, and demand is high, you will have revenue of $$170$ million.

Sketch out a decision tree like in Figure $11\mathrm{.}4($drawing by hand is fine$)$ and compute the following numbers:

What is the expected value of the decision to build a small facility?