A company named ElLi is a large, successful, profit$-$making business. ElLi$$s

free cash flow for the most recent fiscal year was $$5\mathrm{.}23$ billion, and this free cash flow is expected to grow at a rate of $2\%$ per annum indefinitely. Currently, ElLi$$s CEO discovered startup called $$DisplaceEL$$ and is concerned about the impact DisplaceEL can have on ElLi. In fact, if successful, DisplaceEL could significantly impact ElLi$$s business. The CEO of ElLi aims to acquire DisplaceEL to preempt this potential competition and ensure ElLi$$s continued growth as forecasted.

$1.$ If ElLi$$s CEO acquires and liquidates DisplaceEL now, the growth of ElLi$$s free cash

flow will remain as expected. Assume that if ElLi$$s CEO does not acquire and liquidate

DisplaceEL now, the opportunity to acquire this startup will never arise again, and

ElLi$$s free cash flows will grow at a rate of $-1\%$ per annum from now on indefinitely.

How much is ElLi$$s CEO willing to pay for DisplaceEL now if she is using a $12\%$

discount rate?

$2.$ After considering the cost of acquiring DisplaceEL, ElLi$$s CEO reassesses the com$-$

petitive threat posed by the startup and revises the cash flow estimates for a scenario

where DisplaceEL is not acquired. The revised estimates suggest that ElLi$$s free cash

flows will grow at a reduced rate of $1\mathrm{.}5\%$ per annum for the next ten years and then

continue to grow at an even lower rate of $1\%$ per annum starting in the eleventh year

indefinitely. Given these revised estimates, how much is ElLi$$s CEO willing to pay for

DisplaceEL now if she is using a $12\%$ discount rate?

$3.$ ElLi$$s CEO begins to consider the optimal timing for acquiring DisplaceEL. Assuming ElLi$$s CEO does not acquire and liquidate DisplaceEL$$s business now but does so in three years, ElLi$$s free cash flows are expected to grow at a rate of $1\mathrm{.}5\%$ per annum for the next three years and then continue to grow at a rate of $2\%$ per annum starting in the fourth year indefinitely. In this scenario, how much is ElLi$$s CEO willing to pay for acquiring DisplaceEL in three years if she is using a $12\%$ discount rate? Give your answer in terms of current value of the acquisition price paid in three years.