$6.$ Alcibides Inc. is considering the purchase of $2-$year racehorse named Box Spread. Information:

$$ The estimated purchase price of Box Spread at the upcoming Keenland sale is expected to be $$6$M$.$ This cost can be depreciated for $10$ years to a book value of zero.

$$ It is expected that Alcibiades Inc.$$s earnings will be sufficient that it can use all of the depreciation

$$ The estimated economic life of Box Spread $($race career and breeding$)$ is expected to be $10$ years

$$ Effective tax rate $=\mathrm{.}40$

$$ Cost of capital $=\mathrm{.}20$

$$ An economist at Xavier University$$s Equine Institute estimates the following annual revenues and operating costs and their probabilities:

Revenues:

o $$6\mathrm{.}0$M with probability of $0\mathrm{.}5$

o $$3\mathrm{.}0$M with probability of $0\mathrm{.}5$

Operating Costs:

o $$1$M with probability of $0\mathrm{.}5$

o $$2$M with probability of $0\mathrm{.}5$

Questions:

Using a decision tree, determine the Box Spread$$s expected net present value. Should Alcibiades Inc. purchase Box Spread.