A.3.4 Terminal Value & the EV→Equity→Per-Share Bridge

Basic Prerequisites: 03 · Cost of Capital.

---

1. Intuition & Practical Objective

You cannot forecast 100 years of cash by hand, so you forecast an explicit window (typically 5–10 years) and then collapse everything after it into a single number: the terminal value. This page builds that number and completes the valuation by walking from enterprise value down to value per share.

Two facts to internalise:

• The terminal value is most of the value. In the worked two-stage example below it is $74.6\%$ of the total. A DCF is therefore mostly a statement about the stable, long-run economics of the business, dressed up with detail about the next five years.
• A discounted-cash-flow valuation must end with a discounted cash flow, not a multiple. Plugging an exit EV/EBITDA into a DCF imports relative-valuation assumptions into an absolute-value model (see page 06) - the only consistent terminal assumptions are a stable-growth (Gordon) perpetuity or a liquidation value.

The one-sentence essence. ”${\text{TV}}_n=\frac{{\text{CF}}_{n+1}}{r-g_n}$, then $\text{Equity}=\text{EV}+\text{Cash}-\text{Debt}-\text{other claims}$, then divide by diluted shares - and check what fraction of value is terminal before you believe any of it.”

---

2. Mathematical Ground Truth & Derivations

2.1 The Gordon terminal value

If cash flows beyond year $n$ grow at a constant $g_n<r$,

$${\text{TV}}_n=\sum _{t=n+1}^{\infty }\frac{{\text{CF}}_n(1+g_n{)}^{t-n}}{(1+r{)}^t}=\boxed{\frac{{\text{CF}}_{n+1}}{r-g_n}}$$

with the flow and rate matched: discounting FCFF uses $K_c=\text{WACC}$; discounting FCFE (or dividends) uses $k_e$. Discount ${\text{TV}}_n$ back by $(1+r{)}^n$ and add the explicit-window PVs.

2.2 Consistency conditions on stable growth (Damodaran Ch 12)

The stable-growth assumption is only coherent if three things line up:

1. $g_n\le$ the growth rate of the economy (nominal if the discount rate is nominal). A firm cannot grow faster than its economy forever. Rule of thumb: $g_n$ should not exceed the risk-free rate.
2. Reinvestment consistent with growth: $\text{RR}=g_n/\text{ROC}$. If you assume stable growth but keep a boom-era reinvestment rate, the cash flow is inflated or deflated arbitrarily.
3. Risk normalised: the beta should be close to one and the cost of capital should reflect a mature firm, not the high-growth firm you just forecast.

2.3 The enterprise-to-equity-to-per-share bridge

$$V_{\text{equity}}=V_{\text{operating assets}}+\text{Cash \& marketable securities}-\text{Debt}-\text{other claims (minority, preferred)}.$$

Then

$$\text{value per share}=\frac{V_{\text{equity}}}{\#\text{diluted shares}},$$

where diluted shares include options/RSUs, and the option value is best handled by subtracting the estimated option value (a Black–Scholes / treasury-stock-method charge) rather than by raw share counts. Getting the bridge wrong is as damaging as getting the cash flows wrong - a large cash pile or an off-balance-sheet claim can move per-share value by double digits.

---

3. Computational Implementation - terminal value and the full bridge

Stdlib only. Part A values Tube Investments end-to-end (Damodaran Illustration 15.1); Part B runs a two-stage DCF and measures how much of the value is terminal.

Part A reproduces Damodaran exactly: operating assets $\approx \text{Rs}2002$ million (his rounded figure; computed $2001.9$), equity $\text{Rs}1560$ million, $\text{Rs}63.36$/share (the stock traded at $\text{Rs}92.70$ - so this firm looked expensive on these inputs). The variant shows how one assumption - whether the firm can earn its cost of capital on new investment - moves the value from $\text{Rs}63.36$ to $\text{Rs}103.03$ (Damodaran: $103.04$). Part B makes terminal dominance concrete: $74.6\%$ of the $1478.6 enterprise value is the perpetuity.

---

4. Failure Modes & First-Principles Breakdowns

1. Terminal-value dominance. With $\sim 75\%$ of value in the perpetuity, the model’s real content is $g_n$ and $K_c$. A $1\%$ change in $g_n$ can move value by $20\%+$ (page 05’s sensitivity grid). Treat any DCF as a bet on the stable-state assumptions.
2. $g_n$ above the risk-free rate. Growth faster than the economy forever is impossible; it also risks $g\to K_c$, where the formula explodes. Cap $g_n$ at the risk-free rate, and never assume $g_n\ge K_c$.
3. Terminal multiple smuggling. Using an exit EV/EBITDA as “terminal value” makes the DCF relative in its most influential term - the two methods can disagree wildly, and you have silently re-imported the comps’ mispricing.
4. Reinvestment inconsistency. Keeping an explicit-window reinvestment rate into stable growth overstates growth or understates cash. Enforce $\text{RR}=g_n/\text{ROC}$.
5. Bridge errors. Omitting net debt, minority interests, preferred stock, pension deficits, or option dilution mis-states equity value. Cash is added, debt is subtracted, and shares must be diluted.

---

5. References

• Damodaran, Investment Valuation
• Koller et al. (McKinsey), Valuation
• Pinto et al. (CFA Institute), Equity Asset Valuation
• Penman, Financial Statement Analysis and Security Valuation

---

6. Connected Graph Bridges

• Back: 03 · Cost of Capital · Index Hub
• Forward: 05 · Failure Modes & Practice → 06 · Relative Valuation & Advanced Extensions
• Risk: Stress Testing & Scenario Analysis (sensitivity of the terminal term)