Why the Gordon Growth Terminal Value Starts with Next Year’s Cash Flow
Summary
The discussion explains a common timing error when adding a Gordon growth terminal value to a discounted cash flow valuation. The terminal value at the end of the explicit forecast period represents cash flows beginning in the following period. The first projected cash flow in the perpetuity is therefore the last forecast cash flow grown by the perpetual growth rate, rather than a repeated copy of the last forecast amount.
To combine the terminal value with cash flows valued today, discount that end-of-period value back across the forecast horizon. The answer also shows that the perpetuity’s geometric series begins one period after the valuation date and that its timing must be consistent with the explicit forecast. The example algebra assumes a constant growth path and uses a discount rate above the growth rate; the exchange does not address broader forecasting uncertainty or how to choose those inputs. Its central lesson is to align the first perpetuity payment, terminal-value date, and present-value discounting.
Key ideas
- A Gordon growth terminal value is measured at the end of the explicit forecast period.
- The first perpetuity cash flow occurs one period after that terminal-value date.
- The first perpetuity payment is the final forecast cash flow grown by the perpetual rate.
- Discount the terminal value back to the present over the full explicit forecast horizon.
- A consistent timeline prevents double counting projected cash flows.
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# Logic behind Gordon Growth Model in a DCF analysis?
# Logic behind Gordon Growth Model in a DCF analysis?
Sorry, I wanted to ask this on the finance/money forum, but they don't support LaTeX there.
Let's say we are valuing a company using the DCF methodology with a 5-year projection period.
We project free cash flows of $F_{1},\ldots,F_{5}$. Then if $w$ is the WACC of this company and $g$ is the perpetual growth rate from year 5 forward, the sum of the future cash flows discounted at $w$ is
$$V_{1}:=F_{1}(1+w)^{-1}+\ldots+F_{5}(1+w)^{-5}+F_{5}\sum_{t=6}^{\infty}\frac{(1+g)^{t-5}}{(1+w)^{t}}.$$
This formula for the Gordon Growth model replaces the infinite sum with the easily computed geometric series $$F_{5}\sum_{t=1}^{\infty}\frac{(1+g)^{t}}{(1+w)^{t}}=F_{5}\frac{1+g}{w-g},$$ and therefore (basically) DOUBLE COUNTS (!!) the cash flows $F_{1},\ldots,F_{5}$ to get $$\begin{align*} V_{2}&:=F_{1}(1+w)^{-1}+\ldots+F_{5}(1+w)^{-5}+F_{5}\sum_{t=1}^{\infty}\frac{(1+g)^{t}}{(1+w)^{t}}\\ &=F_{1}(1+w)^{-1}+\ldots+F_{5}(1+w)^{-5}+F_{5}\frac{1+g}{w-g}\\ &\gg V_{1}.\end{align*}$$
What am I missing here?
EDIT
Even if you could convince me of the legitimacy of $F_{5}(1+g)^{t-5}\mapsto F_{1}(1+g)^{t}$ in order to get a uniformly indexed sum (and hence a geometric series), i.e. $F_{5}$ equals the 6-fold growth of $F_{0}$ before we first start to sum it, I would still be very hard to convince of the legitimacy that we should also not truncate the series and re-index the sum at $t=1$.
## Answer by Matt B. (score 1)
https://quant.stackexchange.com/a/14058
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 discount that to the present, you need to multiply by $\frac{1}{(1+r)^5}$. If you think that $F_5 = (1+g) ^5 F_0$ and the same for the previous ones, you easily demonstrate that
$ V_{1}:=F_{1}(1+r)^{-1}+\ldots+F_{5}(1+r)^{-5}+F_{5}\sum_{t=6}^{\infty}\frac{(1+g)^{t-5}}{(1+r)^{t}} = \sum_{t=1}^{5} F_0 (\frac{1+g}{1+r})^t + F_0 (\frac{1+g}{1+r})^5\frac{(1+g)}{(r-g)} = F_0 \frac{1+g}{r-g}$
## Answer by UnknownUser (score 0)
https://quant.stackexchange.com/a/14417
What you're missing in your interpretation is what the sixth payment actually is. It is not the fifth cash flow or even the value of the fifth cash flow. It is the value of an annuity at t5 whose first payment occurs in one years/time periods time and is F5*(1+g). Or the last known dividend grown by one years worth of the growth rate. It is important to remember that the value of a annuity is calculated based on the assumption that the first payment occurs at t+1 and not t.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.