Epsilon Co will buy the patents to a new camera technology for $$90$ million. There are $3$ years left on the life of the patent. Epsilon does not own production facilities, so if Epsilon decides to sell the camera it will need to outsource production to specialized production firms. In such contracts, Epsilon can choose whether to produce at the start of each year. If Epsilon decides to produce, it will need to pay $$15$ million as a fixed cost every year, and an additional $$5$ per unit produced to the production firm. These payments are due at the end of each year.

Each year, the probability that there will be high demand is $30\%,$ and the probability that there will be low demand is $70\%.$ Epsilon can determine the demand for the rest of the year at the start of each year, before making the decision to outsource production. Additionally, if there is high demand for the camera in any year, demand will be high for the remaining life of the patent.

In year $1,$ if there is high demand, Epsilon will sell $15$ million units, and if there is low demand, Epsilon will sell $2$ million units. In year $2,$ if there is high demand, Epsilon will sell $17$ million units, and if there is low demand, Epsilon will sell $4$ million units. In year $3,$ if there is high demand, Epsilon will sell $20$ million units, and if there is low demand, Epsilon will sell $6$ million units. After year $3,$ demand is always expected to be high, and Epsilon will be able to sell $25$ million units. From year $1$ to year $3,$ the unit price is $$12$ when there is high demand and $$8$ when there is low demand. From year $4$ and onwards, the unit price is $$6$ despite the high demand due to patent expiration. All cash from sales is received at the end of each year. Epsilon$$s required rate of return is $10\%.$

What is the value of the option to delay production of the camera, using the decision$-$tree method? $($Round the final answer to the nearest two digits.$)$

None of the other answers are correct

$7\mathrm{.}62$

$7\mathrm{.}87$

$6\mathrm{.}94$

$6\mathrm{.}34$