Arch Capital Group Ltd. (ACGL) valuation

1 · Enterprise-value target (what the DCF must match)

Market cap   = price × diluted shares
             = $96.19 × 359.0M
             = $34.53B

EV target    = market cap + total debt − cash & equivalents
             = $34.53B + $156.0M − $993.0M
             = $33.70B
            

2 · Starting NOPAT (base year 0)

GAAP EBIT          = $5.16B   (25.9% of revenue)
× (1 − tax rate)  = × (1 − 14.7%) = × 0.8527
= NOPAT₀            = $4.40B
            

3 · Invested capital & starting ROIC

Invested capital = total debt + book equity − cash
                 = $156.0M + $24.21B − $993.0M
                 = $23.37B

Raw ROIC₀        = NOPAT₀ / Invested capital
                 = $4.40B / $23.37B
                 = 18.8%
(no cap applied; raw value is within the 40.0% ceiling)
            

4 · Growth path construction

Source       = analyst consensus: Y1 = -15.6%, Y2 = 2.8%
Clamp        = [2.5%, 60%] (no sub-terminal or 60%+ starts)
Plateau rate = 2.8% (Y2 — held from year 2 through end of plateau)
Tier         = 3 years (rule: plateau rate < 15% → 3y, < 25% → 5y, else 7y)
Plateau      = 3 years
Fade         = linear from effective Y2 to terminal 2.5% across the remaining 7 years

Effective Y1 growth after solver bumps = -15.6%
Effective Y2 growth after solver bumps = 2.8%
Growth by year:
  Y1 = -15.6%
  Y2 = 2.8%
  Y3 = 2.8%
  Y4 = 2.7%
  Y5 = 2.7%
  Y6 = 2.6%
  Y7 = 2.6%
  Y8 = 2.6%
  Y9 = 2.5%
  Y10 = 2.5%
            

5 · Margin path construction

Starting margin (Y0) = 25.9%   (source: latest FY EBIT margin (GAAP))
Target margin (Y10)  = 14.1%   (solver output, normal band)
Year-t margin        = starting + (target − starting) × (t / 10)
Margin by year:
  Y1 = 24.7%
  Y2 = 23.5%
  Y3 = 22.4%
  Y4 = 21.2%
  Y5 = 20.0%
  Y6 = 18.8%
  Y7 = 17.7%
  Y8 = 16.5%
  Y9 = 15.3%
  Y10 = 14.1%
            

6 · ROIC path construction

The capex heuristic compares latest-period CapEx ($44.0M) against the Normalized CapEx (3-yr mean) of $49.0M — mean of the last three annual CapEx values. When the latest is above 1.4× that mean and CapEx is at least 5% of revenue, we treat the filer as capital-intensive and mid-investment, hold ROIC flat for a 5-year harvest phase, and only then fade to terminal ROIC. The 3-yr mean does not feed the DCF directly — it only gates this flag.

Capex-heuristic inactive (latest CapEx 0.90× the 3-yr mean of $49.0M — below the 1.4× / 5%-of-revenue gates).
Fade from Y1: ROIC_t = ROIC₀ + (ROIC_terminal − ROIC₀) × (t / 10)
ROIC₀ = 18.8%; ROIC_terminal = 11.0%

ROIC by year:
  Y1 = 18.0%
  Y2 = 17.3%
  Y3 = 16.5%
  Y4 = 15.7%
  Y5 = 14.9%
  Y6 = 14.1%
  Y7 = 13.3%
  Y8 = 12.6%
  Y9 = 11.8%
  Y10 = 11.0%
            

7 · Solver iterations

Each row is one bisection attempt. The solver sweeps Y1 growth bumps 0pp → +20pp across the plateau ladder inside the normal margin bracket, then — if nothing reconciles — repeats the same sweep in a widened margin band ([-10%, 80%]). The first feasible attempt is the one the page uses. If no combination reconciles, the page shows the attempt whose PV sits closest to the target EV so both levers are balanced.

8 · Terminal value derivation

NOPAT_{N+1}         = NOPAT_{10} × (1 + g_terminal)
                    = $2.56B × (1 + 2.5%)
                    = $2.63B

ΔNOPAT              = NOPAT_{N+1} − NOPAT_{10}
                    = $64.0M
Reinvestment_{N+1}  = ΔNOPAT / ROIC_terminal
                    = $64.0M / 11.0%
                    = $582.2M

FCF_{N+1}           = NOPAT_{N+1} − Reinvestment_{N+1}
                    = $2.63B − $582.2M
                    = $2.04B

Terminal value (TV) = FCF_{N+1} / (WACC − g_terminal)
                    = $2.04B / (9.0% − 2.5%)
                    = $31.44B

PV(TV)              = TV / (1 + WACC)^10
                    = $31.44B / 2.367
                    = $13.28B
            

9 · Reconciliation check (DCF PV vs. the market)

This isn't a fair value — it's the inverse check. The solver built the scenario so that DCF PV reproduces the current enterprise value; if the normal bracket worked the delta below is ~0 by construction. A non-zero delta only appears when the solver fell through to the widened margin band.

Σ PV(FCF_1..10) = $20.41B
+ PV(TV)          = $13.28B
= Enterprise value = $33.70B   (≈ EV target $33.70B by construction)
− Total debt      = $156.0M
+ Cash            = $993.0M
= Equity value    = $34.53B
÷ Diluted shares  = 359.0M
= DCF PV / share  = $96.19

Market price      = $96.19
Reconciliation Δ  = +0.0%   (≈ 0 by construction — the solver anchored on this price)