Gordon Growth Model

Halworth Systems' final projected free cash flow is $50 million, expected to grow at a 3% terminal growth rate forever thereafter. Using a 9.2% WACC, what is the terminal value (using the Gordon growth / perpetuity growth model)?

1. A.$806.5 millionWrong. This uses $50M directly instead of growing it by (1 + g) first ($50M ÷ 0.062).
2. B.$830.6 millionCorrect. $50M × 1.03 ÷ 0.062 ≈ $830.6 million.
3. C.$1,612.9 millionWrong. This divides by (WACC − g) using a WACC or growth rate different from the ones given.
4. D.$538.6 millionWrong. This does not correctly apply the perpetuity growth formula to the given inputs.

Why: Terminal Value = Final Year FCF × (1 + g) ÷ (WACC − g) = $50M × 1.03 ÷ (0.092 − 0.03) = $51.5M ÷ 0.062 ≈ $830.6 million.

In building a DCF terminal value using the perpetuity growth (Gordon growth) model, the terminal growth rate assumed must be:

1. A.Higher than the growth rate used in the explicit projection periodWrong. Terminal growth is typically set lower than near-term explicit growth, reflecting a mature, steady-state pace — not higher.
2. B.Exactly equal to the WACC used to discount the terminal valueWrong. That would make the denominator (WACC − g) zero, producing an undefined result.
3. C.Always set at exactly 0%, representing no growthWrong. Terminal growth can be any rate below WACC, including a modest positive rate reflecting long-run inflation or GDP growth; it need not be zero.
4. D.Strictly less than the WACC used to discount the terminal valueCorrect. If g equals or exceeds WACC, the (WACC − g) denominator is zero or negative, breaking the formula.

Why: The perpetuity growth formula divides by (WACC − g). If the terminal growth rate g is set equal to or above WACC, the denominator becomes zero or negative, producing an undefined or nonsensical (negative) terminal value — so g must be strictly less than WACC for the formula to produce a meaningful result.