The Zephyr Software Company in Manchester currently has an option to purchase the rights

to a new piece of software with advanced AI capabilities. It is now May $1$st$,$ and the current

price is $2\mathrm{.}2$ million. Zephyr does not actually need the software until the beginning of July,

but its top executives fear that another company might buy the rights between now and the

beginning of July. They assess that there is a $5\%$ chance that a competitor will buy the rights

during May. If this does not occur, they assess that there is a $10\%$ chance that the competitor

will buy the rights during June. If Zephyr does not take advantage of its current option, it can

attempt to buy the software rights at the beginning of June or the beginning of July, provided

they are still available.

Zephyr$$s incentive for delaying the purchase is that its financial experts believe there is a good

chance that the price will fall significantly in one or both of the next two months. They assess

the possible price decreases and their probabilities in Tables $1$ and $2.$ Table $1$ shows the

probabilities of the possible price decreases during May. Table $2$ lists the conditional

probabilities of the possible price decreases in June, given the price decrease in May. For

example, it indicates that if the price decrease in May is $60,000,$ then the possible price

decreases in June are $0,30,000,$ and $60,000$ with respective probabilities $0\mathrm{.}6,0\mathrm{.}2,$ and $0\mathrm{.}2.$

Table $1$: Distribution of Price Decrease in May

Price Decrease Probability

$00\mathrm{.}5$

$60,0000\mathrm{.}3$

$120,0000\mathrm{.}2$

Table $2$: Distribution of Price Decrease in June

Price Decrease in May

$060,000120,000$

June

Decrease

Probability June

Decrease

Probability June

Decrease

Probability

$00\mathrm{.}300\mathrm{.}600\mathrm{.}7$

$60,0000\mathrm{.}630,0000\mathrm{.}220,0000\mathrm{.}2$

$120,0000\mathrm{.}160,0000\mathrm{.}240,0000\mathrm{.}1$

If Zephyr purchases the software rights, it believes it can generate $3$ million in revenue from

the new capabilities. But if it does not purchase the rights, Zephyr believes it can make

$650,000$ from alternative software investments. What should the company do$?$

PLease help with creating payoff table with values for above problem.