Case Study: Detecting DCF Inconsistency

1. Analyst Forecast

Consider a hypothetical growth-stage technology firm with the following terminal assumptions:

Parameter	Value
Growth rate $g$	20%
ROIC	10%
Reinvestment rate $s$	60%
WACC	9%
EBITDA margin	30%

The analyst asserts $g = 20\%$ while also specifying $s = 60\%$ and $\text{ROIC} = 10\%$.

2. Growth-Reinvestment Violation

The growth-reinvestment identity requires $g = s \times \text{ROIC}$. With the forecast above:

$$g^* = s \times \text{ROIC} = 0.60 \times 0.10 = 0.06 = 6\%.$$

The implied $g^*$ is only 6%, far from the stated 20%. The feasibility gap equals:

$$\delta^*_{\text{growth}} = |0.20 - 0.06| = 0.14.$$

3. Terminal Multiple Conflict

From the conservation-consistent multiple formula:

$$\frac{EV}{\text{EBITDA}} = \frac{(1-\tau) (EBIT/EBITDA)(1 - g/\text{ROIC})}{WACC - g}.$$

Assuming $\tau = 21\%$ and $EBIT/EBITDA = 0.85$, the denominator becomes negative ($WACC - g = -11\%$), producing a nonsensical multiple. Our validator flags the configuration with an error code terminal_value_infeasible.

4. Solver Recommendation

Running scripts/validate_dcf.py on the scenario produces:

DCF Assumptions Validation
  Growth rate (g): 20.0%
  ROIC: 10.0%
  Reinvestment rate (s): 60.0%
  Feasibility gap (growth identity): 0.1400
  Recommended adjustment: reduce g to 6.0% or raise ROIC to 33.3%
  Terminal multiple: infeasible (WACC <= g)

The valuation bridge proposes two remedies:

Reduce growth — Set $g$ to 6% to maintain the reinvestment identity.
Increase ROIC — Achieve $\text{ROIC} = g / s = 33.3\%$ if 20% growth is non-negotiable.

As long as $WACC < g$, the DCF will diverge; either $g$ must drop below 9%, or $WACC$ must rise.

5. Lessons for Analysts

Seemingly attractive high-growth scenarios often violate capital conservation when reinvestment capacity is limited.
DCF models must embed the growth-reinvestment identity to avoid inflating terminal value.
Automated feasibility checks prevent inconsistent decks from advancing to investment committees.

Citations

Damodaran, A. (2012). Investment Valuation (3rd ed.). Wiley.
Koller, T., Goedhart, M., & Wessels, D. (2020). Valuation (7th ed.). McKinsey & Company.