The DCF Where the Terminal Growth Exceeds the Economy
You are building a discounted cash flow for a software-enabled logistics business. Five-year projections show revenue growing 22%, 18%, 15%, 12%, and 10%, with EBITDA margins expanding from 14% to 19%. FCFF in year 5 is $6.8M. You are asked to apply a 3.5% perpetuity growth rate and a WACC of 9.0%. The risk-free rate is 4.2%, the equity risk premium is 5.5%, beta is 1.35, the pre-tax cost of debt is 6.5%, the tax rate is 25%, and the target capital structure is 30% debt / 70% equity. The company has $12M of debt and $3M of cash. A partner reviews the model and says the terminal value "looks too high" but cannot say why.
1. Recompute the WACC and check whether the 9.0% input is defensible.
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Cost of equity (CAPM): 4.2% + 1.35 × 5.5% = 4.2% + 7.425% = 11.63%.
After-tax cost of debt: 6.5% × (1 − 0.25) = 4.875%.
WACC: (0.70 × 11.63%) + (0.30 × 4.875%) = 8.14% + 1.46% = 9.60%.
The stated 9.0% is too low - it understates the discount rate by ~60 bps, which inflates value. Recompute using 9.60%. Note also: beta of 1.35 for a logistics/software hybrid is plausible but should be checked against a relevered peer set; if the 1.35 is an unlevered beta mistakenly used as levered, the error compounds.
2. Evaluate the terminal value. Is 3.5% growth consistent with a 9.6% WACC, and what is the implied terminal multiple?
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Terminal value (Gordon growth): TV = FCFF₅ × (1 + g) / (WACC − g) = $6.8M × 1.035 / (0.096 − 0.035) = $7.038M / 0.061 = $115.4M.
Implied terminal EV/EBITDA: We need year-5 EBITDA. If FCFF₅ = $6.8M and we approximate EBITDA₅ ≈ FCFF₅ / (1 − tax rate) adjusted for capex/WC... more directly, if margins are 19% on year-5 revenue, and revenue is not given, we can back into it only with assumptions. Flag this: the model must show year-5 EBITDA explicitly. Assuming EBITDA₅ ≈ $9.0M, implied multiple = $115.4M / $9.0M ≈ 12.8x - high but not absurd for a growing software-enabled business.
The real problem: 3.5% perpetuity growth is at or above long-run nominal GDP growth (~4–5% nominal, ~2–2.5% real). A 3.5% real growth rate in perpetuity is not credible for a logistics business. If 3.5% is nominal, it is defensible only if inflation is ~2% and real growth is ~1.5%. State which it is. If it is real, cut it to 2.0–2.5% and recompute: TV = $6.8M × 1.025 / (0.096 − 0.025) = $6.97M / 0.071 = $98.2M - a ~15% reduction in TV.
Also check: the 22%→10% fade is steep but plausible; however, terminal growth must not exceed the growth rate used to normalize capex and working capital. If capex is held at a fixed % of revenue while growth is 3.5%, the terminal FCFF is inconsistent.
3. The partner says the terminal value "looks too high." What diagnostics would you run to find the error?
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Diagnostics, in order:
- WACC check - recompute from inputs (done: 9.60%, not 9.0%). A 60 bps error alone moves TV by ~10%.
- Growth vs. WACC spread - (WACC − g) is the denominator. At 9.0% − 3.5% = 5.5%, the spread is thin; at 9.6% − 3.5% = 6.1%, better. Small denominator errors swing TV enormously.
- Terminal multiple sanity check - compute implied EV/EBITDA and compare to market comps. If it implies 15x+ for a logistics business, something is off.
- Normalized terminal year - is year-5 FCFF a sustainable figure? If margins are still expanding at year 5, the terminal year is not steady-state. Either extend the fade or normalize margins.
- Capex vs. D&A - in perpetuity, capex should roughly equal D&A plus growth capex. If capex is understated, FCFF is overstated.
- Working capital - a growing business consumes WC. If terminal growth is 3.5% but WC is held flat, FCFF is overstated.
- Mid-year convention - if applied inconsistently, discounting is off.
The most likely culprit here is the combination of an understated WACC and a growth rate at the edge of credibility, compounded by a terminal year that has not been normalized to steady state.