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Assuming you mean $P_t=S_T$, that you are pricing under the risk neutral measure $\mathbb{Q}$ and introducing a discount factor $e^{-\int_0^T{r(t)dt}}$, your equation can be rewritten $-$ where $\{\mathcal{F}_n\}_{n\geq0}$ is an appropriate filtration:
$$ \begin{align}
\mathbb{E}^{\mathbb{Q}}\left[V_T|\mathcal{F}_0\right]=\mathbb{E}_0^{\mathbb{Q}}\left[V_T\...
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There's plenty of resources on the internet but I used to use during a banking internship:
https://corporatefinanceinstitute.com/resources/templates/excel-modeling/dcf-model-template/
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The discount rate (for interbank trades) is broadly treated as the risk free rate. So at worst you could obtain this rate for no risk, making it the minimum rate of return. No instrument should yield less than this.
NPV is not about how the universe evolves, it's about the fair value of something today. If you were to dispose of an asset, or make a price, ...
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You should use whatever currency in which the debt is denominated. Specifically, since it is the EUR currency and interest rate risk associated with the debt, some sort of EUR curve should be used.
Theoretically, if you are looking for the present value in USD, although the debt is denominated in EUR, you could convert future payments at the forward ...
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Under GGM dividends are used, under the assumption of constant growth. You're given FCF under the assumption of constant growth. So you could use FCFF or FCFE models. Since the question is asking for the value of the corporation, you will want to use the FCFF model
$Firm Value = \frac{FCFF_1}{(WACC-g)}=\frac{FCFF_0(1+g)}{(WACC-g)}$
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Your last cash flow is not correctly expressed as you forgot the $(1+r)^{-5}$ when you reinjected.
A $t= 5$ (in 5 years), your PV of the remaining cash flows is: $F_5 \sum_{k=1}^\infty (\frac{1+g}{1+r})^k$. That is the formula for receiving a cash-flow $F_5$ growing at $1+g$, discounted at $(1+r)$ each year, receiving the first cash-flow in year 6.
Now ...
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