Learn about terminal value and growth assumptions

What is Terminal Value?

Two approaches exist:

1. Perpetuity Growth Method (Gordon Growth Model)
2. Exit Multiple Method (using comparable multiples)

We'll focus on the perpetuity growth method, as it's grounded in fundamental assumptions about long-term economics.

The Perpetuity Growth Formula: Derived from First Principles

Where:

• $TV_n$ = Terminal value at end of year $n$
• $FCF_{n+1}$ = Free cash flow in the first year after forecast period
• $WACC$ = Weighted average cost of capital (discount rate)
• $g$ = Perpetual growth rate

Let's derive this. Suppose at year $n$, the company generates $FCF_{n+1}$ in year $n+1$, then grows at rate $g$ forever:

$\text{Year } n+1: FCF_{n+1}$ $\text{Year } n+2: FCF_{n+1}(1+g)$ $\text{Year } n+3: FCF_{n+1}(1+g)^2$ $\vdots$

The present value (at time $n$) of this infinite series is:

$TV_n = \frac{FCF_{n+1}}{(1+WACC)} + \frac{FCF_{n+1}(1+g)}{(1+WACC)^2} + \frac{FCF_{n+1}(1+g)^2}{(1+WACC)^3} + \cdots$

Factor out $FCF_{n+1}$:

$TV_n = FCF_{n+1} \left[ \frac{1}{1+WACC} + \frac{1+g}{(1+WACC)^2} + \frac{(1+g)^2}{(1+WACC)^3} + \cdots \right]$

Let $r = \frac{1+g}{1+WACC}$. This becomes a geometric series:

$TV_n = FCF_{n+1} \cdot \frac{1}{1+WACC} \left[ 1 + r + r^2 + \cdots \right]$

Why this step? Geometric series with first term $a$ and ratio $r$ (where $|r| < 1$) sums to $\frac{a}{1-r}$.

Here, $a = 1$ and $r = \frac{1+g}{1+WACC}$:

$TV_n = FCF_{n+1} \cdot \frac{1}{1+WACC} \cdot \frac{1}{1 - \frac{1+g}{1+WACC}}$

Simplify the denominator:

$1 - \frac{1+g}{1+WACC} = \frac{(1+WACC) - (1+g)}{1+WACC} = \frac{WACC - g}{1+WACC}$

Why this step? We're combining fractions to get a cleaner form.

Therefore:

$TV_n = FCF_{n+1} \cdot \frac{1}{1+WACC} \cdot \frac{1+WACC}{WACC - g} = \frac{FCF_{n+1}}{WACC - g}$

Key insight: This formula only works when $g < WACC$. The geometric series only converges when $r = \frac{1+g}{1+WACC} < 1$, i.e., when $g < WACC$. If $g = WACC$, then $r = 1$ and the infinite sum diverges to $+\infty$. If $g > WACC$, then $r > 1$ and the sum does not converge at all (the negative number the formula spits out is mathematically meaningless). Either way, the result is economically impossible.

Growth Rate Assumptions: The Critical Choice

What is a Reasonable Growth Rate?

No company can grow faster than the economy forever. Here's why:

• If a company grows at 5% and GDP grows at 2%, the company eventually becomes larger than the entire economy (impossible)
• Typical ranges:
  • Conservative: 2-2.5% (roughly long-term GDP growth)
  • Mature companies: 2-3%
  • Industry leaders in growing sectors: 2.5-3.5%
  • Never use: >4% (unless you can justify why this company will dominate the world)

Step 1: Calculate $FCF_6$ $FCF_6 = FCF_5 \times (1 + g_{5 \to 6}) = 100 \times 1.04 = \$104M$

Why this step? Terminal value uses the first cash flow in the terminal period.

Step 2: Calculate terminal value at Year 5 $TV_5 = \frac{104}{0.08 - 0.025} = \frac{104}{0.055} = \$1,891M$

Why this step? We're valuing all cash flows from Year 6 onward, discounted back to Year 5.

Step 3: Discount TV to present value (assume we're valuing at Year 0) $PV(TV) = \frac{1,891}{(1.08)^5} = \frac{1,891}{1.469} = \$1,287M$

Why this step? Terminal value is stated at Year 5; we need its value today.

Why this matters: A 1.5% growth difference creates a 33% valuation difference. This is why analysts argue endlessly about terminal growth rates.

Calculation for 3.0% case: $TV_5 = \frac{104}{0.08 - 0.03} = \frac{104}{0.05} = \$2,080M$ $PV(TV) = \frac{2,080}{1.469} = \$1,416M$

Why it feels right: Recent performance is tangible and observable. It's tempting to extrapolate.

The fix: Terminal growth must reflect steady-state maturity, not current high-growth phase. A 15% perpetual growth rate implies the company will eventually be larger than all global economies combined. Instead:

1. Use the explicit forecast period (Years 1-5) to model high growth
2. Assume the company matures by Year 6
3. Terminal growth should approach GDP growth (2-3%)

Better approach: "The company grows at 15% for 5 years (explicit period), then matures to 2.5% terminal growth."

Why it feels right: "The company is high-quality and will grow almost as fast as our required return."

The fix: This creates a near-infinite valuation because the denominator approaches zero. Economically, it means you believe cash flows will compound at almost the same rate you require for taking risk—implying nearly risk-free doubling forever. Reality check: Maintain at least 2-3% spread between WACC and $g$. If you truly believe $g$ is that high, you need to justify why (and likely extend your explicit forecast period instead).

WACC vs. Growth Rate: The Relationship

Think of it like real interest rates: if inflation is 3% and your bond pays 5%, your real return is ~2%. Similarly, if cash flows grow at 2% and you require 8%, your real value capture is 6%.

Connecting to the Full DCF Model

Where:

• First term = PV of explicit forecast cash flows
• Second term = PV of terminal value

Typical proportions:

• Explicit period value: 20-40% of total EV
• Terminal value: 60-80% of total EV

Why this matters: Your terminal assumptions drive most of the value, making them the highest-leverage inputs.

Step 1: PV of explicit cash flows $PV_{explicit} = \frac{50}{1.09} + \frac{60}{1.09^2} + \frac{70}{1.09^3} + \frac{82}{1.09^4} + \frac{95}{1.09^5}$ $= 45.87 + 50.50 + 54.05 + 58.08 + 61.73 = \$270.23M$

Step 2: Terminal value at Year 5 $TV_5 = \frac{100}{0.09 - 0.025} = \frac{100}{0.065} = \$1,538.46M$

Step 3: PV of terminal value $PV(TV) = \frac{1,538.46}{1.09^5} = \frac{1,538.46}{1.5386} = \$1,000M$

Step 4: Enterprise value $EV = 270.23 + 1,000 = \$1,270.23M$

Proportion check:

• Explicit period: $270.23 / 1,270.23 = 21.3\%$
• Terminal value: $1,000 / 1,270.23 = 78.7\%$

This demonstrates why terminal assumptions are critical—they represent nearly 80% of the value.

Exit Multiple Method (Alternative Approach)

Instead of assuming perpetual growth, you assume the company is sold at Year $n$ for a multiple of its earnings.

Example: If Year 5 EBITDA = 150M and comparable companies trade at 8x EBITDA: $$TV_5 = 150 \times 8 = \1,200M$$

Pros: Simple, grounded in market reality Cons: Circular logic (you're using market multiples to determine if the market price is right), assumes comparables remain valid

We focus on perpetuity growth because it's theoretically cleaner and forces explicit assumptions about long-term economics.

So here's the trick: you say, "Okay, starting next summer, my lemonade stand will make a little more money each year—maybe 2% more because I'm getting better at it. And it'll keep doing that forever." Terminal value is a math formula that takes "forever money" and figures out what it's worth today.

The tricky part? If you assume it'll grow super fast forever (like 10% every year), the formula says your stand is worth a bazillion dollars. But that's impossible—you'd eventually own all the lemonade in the world! So we have to be realistic and use a small number like 2-3%, which is about how fast the whole economy grows.

The reason this matters so much is that most of your lemonade stand's value comes from all those future years, not just this summer. So if you mess up that growth number even a little bit, you might think your stand is worth $100 when it's really worth$150—that's a big mistake!

Connections

• Discounted Cash Flow (DCF) Model - Terminal value is the final component
• Weighted Average Cost of Capital (WACC) - The discount rate in the denominator
• Free Cash Flow (FCF) Calculation - What we're projecting into perpetuity
• Gordon Growth Model - Alternative name for perpetuity growth method
• Sensitivity Analysis in Valuation - Testing how growth assumptions affect value
• GDP Growth and Economic Indicators - Ceiling for terminal growth rates
• Exit Multiple Valuation - Alternative terminal value method

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Hinglish (regional understanding)