$($Decision Tree$)$

The Yoran Yacht Company $($YYC$),$ a prominent sailboat builder in Newport, may design a new

$30-$foot sailboat based on the "winged" keels first introduced on the $12-$meter yachts that

raced for the America's Cup.

First, YYC would have to invest $$10,000$ at $t=0$ for the design and model tank

testing of the new boat. YYC$\text{'}$s managers believe there is a $60\%$ probability that this phase

will be successful and the project will continue. If Stage $1$ is not successful, the project will

be abandoned with zero salvage value.

The next stage, if undertaken, would consist of making the molds and producing two

prototype boats. This would cost $$500,000$ at $t=1.$ If the boats test well, YYC would go into

production. If they do not, the molds and prototypes could be sold for $$100,000.$ The

managers estimate the probability is $80\%$ that the boats will pass testing and that Stage $3$

will be undertaken.

Stage $3$ consists of converting an unused production line to produce the new design.

This would cost $$1$ million at $t=2.$ If the economy is strong at this point, the net value of

sales would be $$3$ million; if the economy is weak, the net value would be $$1\mathrm{.}5$ million.

Both net values occur at $t=3,$ and each state of the economy has a probability of $0\mathrm{.}5.$

YYC$\text{'}$s corporate cost of capital is $12\%.$

a$)$ Assume this project has average risk. Construct a decision tree and determine the

project's expected NPV$.$

b$)$ Find the project's standard deviation of NPV and coefficient of variation of NPV$.$ If

YYC$\text{'}$s average project had a CV of between $1\mathrm{.}0$ and $2\mathrm{.}0,$ would this project be of high,

low, or average stand$-$alone risk?