15.2 Terminal Value and the Equity Bridge

Terminal Value Is Most of the Model

After five years of UFCF, Alder Coatings is still a going concern. The terminal value (TV) is the value of all cash flows after the explicit period, measured as of the end of the last explicit year (Year 5 for Alder). In a five-year DCF it is common for TV to contribute about 60–80% of enterprise value. That band is a typical modeling outcome, not a CFI official constant and not a target you engineer. If your TV is 95% of EV, the explicit forecast is doing almost no work and the result is a growth-and-WACC toy. If TV is 20% of EV, you may have cut growth too hard, set g too low, or modeled a fade that does not match the operating story.

CFI teaches two standard ways to set TV: the Gordon growth (perpetuity) method and the exit-multiple method. Applied DCF work runs both and reads the range. That range is the start of the football field you will finish in the comparable-valuation chapter.

Gordon / Perpetuity Growth

TV_n = FCF_n × (1 + g) / (WACC − g)

FCF_n is the last explicit UFCF (Alder Year 5 = $154 million). You grow it one more year at the perpetual rate g, then capitalize that next-year cash flow as a perpetuity growing at g, discounted at WACC. The formula is the Year-n value of the growing perpetuity that starts at Year n+1. It is not FCF_n / (WACC − g) unless you have already grown the cash flow, and it is not FCF_n × (1 + g) / g, which would ignore the cost of capital.

g must be less than WACC. If g ≥ WACC the denominator is zero or negative and the math explodes — or, worse, produces a large negative TV that looks like a sign error instead of a broken model. g should also be at or below long-run GDP / inflation for the economy in which the firm sells. A U.S. dollar DCF in 2026 typically uses g in a 2–3% neighborhood unless you have a documented reason. Using g = 5% "because the firm has been growing 8%" implies Alder outgrows the economy forever. That is a claim you must say out loud; CFI's default is that you do not make it. g can be 0% (no real growth, or a fade to inflation only). g cannot be 9% when WACC is 9%.

Alder: g = 2.5%, WACC = 9.0%.

TV_5 = 154 × 1.025 / (0.09 − 0.025) = 157.85 / 0.065 = $2,428.46 million.

Discount TV back to today at the same convention as the explicit cash flows. Year-end: divide by (1.09)^5 = 1.53862, so PV of TV = $1,578.3 million. Mid-year: if cash is earned throughout Year 5, the terminal date is the middle of Year 5, so the exponent is 4.5. (1.09)^4.5 = 1.47384, and PV of TV = $1,647.7 million. Forgetting to shift TV to 4.5 while shifting explicit years to 0.5, 1.5, … is one of the highest-frequency DCF errors on applied exams: you would understate EV by the present-value gap between year 5 and year 4.5.

Exit Multiple

TV_n = Metric_n × exit multiple

The usual core pairing is Year 5 EBITDA × an exit EV/EBITDA. You can use EBIT or revenue multiples if the peer set is built that way; keep the multiple enterprise-side if the DCF outputs EV. Applying a P/E to Year 5 net income and calling the product terminal enterprise value is a language error from Chapter 14.

Alder Year 5 EBIT = 218 and D&A = 52, so EBITDA_5 = $270 million. At an 8.0x exit EV/EBITDA (a teaching multiple, not a CFI published constant):

TV_5 = 270 × 8.0 = $2,160 million.

Year-end PV of TV = 2,160 / 1.53862 = $1,403.9 million.

Always back-solve implied g: set Gordon equal to the exit TV and solve for g so you can see whether the multiple secretly assumes the firm outgrows the economy.

154 × (1 + g) / (0.09 − g) = 2,160

154 + 154g = 194.4 − 2,160g

2,314g = 40.4

g = 1.75%

1.75% sits inside a long-run inflation/GDP band, so 8.0x is not a 6% perpetuity in disguise. If an 11x exit implied g of 6% with WACC of 9%, you would be baking in "outgrows the economy" through the multiple. That is the same trap with a different costume. Implied g above WACC from an exit multiple is a hard fail: the two methods cannot be telling a consistent story.

Full Numeric Stub DCF — Alder Coatings

Year-end convention, 9% WACC, Gordon g = 2.5%. Discount factors: 1.09^1 = 1.09, 1.09^2 = 1.1881, 1.09^3 = 1.29503, 1.09^4 = 1.41158, 1.09^5 = 1.53862.

PV of explicit UFCF = 93.58 + 98.48 + 98.84 + 101.31 + 100.09 = $492.3 million.

Enterprise value (Gordon, year-end) = 492.3 + 1,578.3 = $2,070.6 million.

TV share = 1,578.3 / 2,070.6 = 76.2% — inside the common 60–80% outcome.

Exit-multiple EV, same explicit PV plus $1,403.9 million of discounted 8.0x TV = $1,896.2 million; TV share 74.0%.

Mid-year Gordon EV ≈ 2,070.6 × 1.04403 = $2,161.8 million. Equivalently, discount each UFCF at 0.5, 1.5, 2.5, 3.5, 4.5 and TV at 4.5 — same result if you are consistent. Applying mid-year only to the five UFCF years and leaving TV at year 5 would drop EV to about $2,092 million and silently understate value.

Steady-state checks before you trust TV: Year 5 growth has faded to 4% (heading toward 2.5% g, not stuck at 8%); EBIT margin has leveled at 16.3%; capex (55) is close to D&A (52). If Year 5 still needed $200 million of growth capex, Gordon on $154 million of UFCF would capitalize a cash-flow level the firm cannot sustain.

The Equity Bridge and a Football-Field Preview

A UFCF-at-WACC DCF outputs enterprise value, the value of core operations to all capital providers. CFI's arriving-at-equity-value step — the equity bridge — is:

Equity value = EV − debt − preferred − NCI + surplus cash + non-core investments

Equivalently, subtract net debt (interest-bearing debt minus surplus cash) and still subtract preferred and NCI, then add non-core investments if they were not already inside cash. Then:

Value per share = equity value / fully diluted shares

Fully diluted shares include in-the-money options, warrants, and convertibles (treasury-stock method for options), the same count Chapter 14 used to build market cap.

Worked Bridge from Alder's Gordon Year-End EV

Start with EV = $2,071 million (rounded from 2,070.6).

Diluted shares = 50.0 million. Implied value = 1,301 / 50 = $26.02 per share. Current market cap of $1,200 million on the same 50 million shares is $24.00, so this DCF sits about 8% above the market — a view, not a fact. Mid-year Gordon EV of $2,162 million bridges to equity of $1,392 million, or $27.84. The 8.0x exit EV of $1,896 million bridges to $1,126 million, or $22.52.

Double-counting cash. This stub used gross debt of $800 million in WACC (D/V = 40% of $2,000 million) and adds the $90 million of surplus cash in the bridge. If you instead subtracted net debt of $710 million in the bridge, you must not add the $90 million again. Netting cash in the WACC weights and adding it in the bridge treats the same cash twice and overstates equity. Pick one convention and stick to it.

Preferred and NCI. Preferred is a fixed claim on the enterprise; NCI is the outside owners' share of a consolidated subsidiary whose EBITDA sat in UFCF. Skipping either overstates common equity. Alder's $50 million of preferred is small relative to V, which is why it was left out of the 9% WACC and handled in the bridge. If preferred were hundreds of millions, Chapter 3's extended WACC — (P/V) × Rp with no tax shield — would apply as well. You still subtract preferred when you go from EV to equity. You never subtract it twice.

Non-core investments (a minority stake, excess marketable securities beyond operating cash) were not in UFCF, so they are not in EV. Add them to get to equity. Do not also leave their dividends or asset sales inside UFCF — that is the other form of double-counting.

Football-Field Preview

A football field is a range chart of implied value per share (or EV) across methods. The bar chart in this section is a preview using Alder's diluted 50 million shares. Chapter 16 fills trading-comps and precedent-transaction bars; those relative methods often sit near the market, and precedents often sit higher because deal prices embed a control premium.

CFI's professional habit is to triangulate, not to average blindly. A DCF at $28 next to an exit-multiple DCF at $23 is a prompt to re-check g, WACC, the exit multiple, and whether mid-year is justified — not a license to pick the number you like. Sensitivity tables on WACC and g (Chapter 13's data-table skill) belong next to this page in a live model; a 50-basis-point WACC move on a Gordon TV that is 76% of EV is a large dollar move, which is why CFI drills CAPM, WACC, DCF, and mid-year as a single cluster rather than as trivia.

Exam Traps for Section 15.2

• Mixing levered FCF with WACC. FCFE discounted at WACC double-counts the debt claim in the rate while already deducting interest in the cash flow (or the reverse mismatch). Core pairing: UFCF + WACC = EV; FCFE + Re = equity.
• g ≥ WACC. The Gordon formula breaks. Even g slightly below WACC with an aggressive 5%+ perpetual growth is an "outgrows the economy forever" claim unless you disclose it.
• Forgetting mid-year on TV. Explicit years at 0.5, 1.5, … and TV at n (not n − 0.5) understates EV.
• Double-counting cash. Netting cash in WACC weights or in net debt and then adding cash again in the bridge.
• Calling EV a per-share value without the bridge and diluted shares.
• Treating 60–80% as a target to engineer rather than a diagnostic.
• Exit multiple on net income while reporting the product as enterprise terminal value.
• Building an LBO exit waterfall; that elective is not on the final.

The DCF you can defend on exam day is the one with paired cash flows and rates, a g that does not outgrow the economy, TV discounted on the same clock as the explicit years, and an equity bridge that subtracts every non-common claim once.