What is the 'growth of growth rates' concept and why does it matter for terminal value?

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AcadiFi · Accepted Answer

This is a subtle but critical point about terminal value sensitivity. The Gordon formula V = D₁/(r − g) has a first derivative with respect to g of D₁/(r − g)², meaning the sensitivity increases as g approaches r. But more importantly, when you're forecasting, small revisions to your terminal g estimate — say from 3% to 3.5% — can appear benign yet dramatically shift valuation because of the convex relationship. Consider a firm with D₁ = $2 and r = 10%: - g = 2.0% → V = $25.00 - g = 2.5% → V = $26.67 (+6.7%) - g = 3.0% → V = $28.57 (+14.3% vs 2%) - g = 3.5% → V = $30.77 (+23.1%) - g = 4.0% → V = $33.33 (+33.3%) The marginal impact of each 50bps of g grows — that's the 'growth of growth rates' effect: valuation is increasingly sensitive at the high end of plausible terminal g. ```mermaid flowchart LR A[g plus 50bps] --> B[Lower g
Small Impact] A --> C[Higher g
Large Impact] C --> D[Convexity
in V] ``` Practical discipline: (1) tie terminal g to nominal GDP × (corporate share of GDP), typically capping at 4-5%; (2) stress-test ±50bps around base g and report the valuation range; (3) when doing sum-of-parts, don't assume different segments can all grow at the upper end — aggregate cannot exceed macroeconomic ceiling; (4) be especially skeptical when DCFs require terminal g near r to 'work'. That's when sensitivity is highest and your edge is lowest.

What is the 'growth of growth rates' concept and why does it matter for terminal value?

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