DCF with Terminal P$/$E

There are many ways to value an asset. Valuation is a science, but it is also an art. Each method may not provide identical answers, and they can sometimes be far off.

A DCF model that incorporates using multiples and free cash flow is shown on slides $38-42$ for Tesla. Using a similar approach to slides $38-40,$ value a stock with the following information.

Assume

FCFE per share in time $0=$$$1\mathrm{.}00$

FCFE per share in time $1=$$$1\mathrm{.}10$

FCFE per share in time $2=$$$1\mathrm{.}20$

FCFE per share in time $3=$$$1\mathrm{.}30$

FCFE per share in time $4=$$$1\mathrm{.}40$

FCFE per share in time $5=$$$1\mathrm{.}50$

FCFE per share in time $6=$$$1\mathrm{.}60$

FCFE per share in time $7=$$$1\mathrm{.}70$

Assume change in capital $($net fixed assets and net operating working capital$)$ in time $7$ are $$0\mathrm{.}50$ per share.

Assume the P$/$E in time X ${?}^3$ is $18$

Assume the cost of equity $($the discount rate or $r)$ is $10\%.$

What is this stock worth?

Note: Enter your answer with two decimals and without the $ sign. That is$,$ if your answer is $$50\mathrm{.}514$ then enter $50\mathrm{.}51.$

Trick $1$: You must remember that FCFE $=$ net income $-$ investment. Investment is also called change in capital. It is change in net fixed assets $+$ change in net operating working capital.

Trick $1$: This is a two$-$stage model using the the P$/$E $*$ E for the terminal value. See slide $38$ for an example. You need to determine the present value of each FCFE, and then add the present value of the terminal value $($P$/$E in time $7^{**}E$ in time $7).$ Note that the test I will not give you so many hints.