How do you derive the justified trailing P/E ratio from the Gordon Growth Model?

Question

AcadiFi · Accepted Answer

The justified P/E ratio tells you what P/E a stock **should** trade at based on fundamentals. It is derived directly from the Gordon Growth Model.

**Derivation of Justified Trailing P/E:**

Start with the Gordon Growth Model:

> V_0 = D_1 / (r - g)

Rewrite D_1 as:
> D_1 = E_1 x (payout ratio) = E_0 x (1 + g) x p

where p = dividend payout ratio

Substitute into GGM:
> V_0 = E_0 x (1 + g) x p / (r - g)

Divide both sides by E_0 (trailing earnings):

> **Justified Trailing P/E = P_0/E_0 = p x (1 + g) / (r - g)**

**Justified Leading (Forward) P/E:**

Divide V_0 by E_1 instead:
> **Justified Leading P/E = P_0/E_1 = p / (r - g)**

The only difference is the (1 + g) factor in the numerator.

**Worked Example:**

Northstar Manufacturing has:
- Trailing EPS (E_0) = $5.00
- Payout ratio (p) = 40%
- Required return (r) = 12%
- Sustainable growth (g) = 5%

**Justified Trailing P/E:**
= 0.40 x (1.05) / (0.12 - 0.05)
= 0.42 / 0.07
= **6.0x**

**Justified Leading P/E:**
= 0.40 / (0.12 - 0.05)
= 0.40 / 0.07
= **5.71x**

If Northstar trades at a trailing P/E of 8.0x, it appears **overvalued** relative to the justified 6.0x.

**Sensitivity Analysis:**

| Scenario | r | g | p | Justified Trailing P/E |
|---|---|---|---|---|
| Base case | 12% | 5% | 40% | 6.0x |
| Lower risk | 10% | 5% | 40% | 8.4x |
| Higher growth | 12% | 7% | 40% | 8.6x |
| Higher payout | 12% | 5% | 60% | 9.0x |

**Key relationships:**
- Higher growth → higher justified P/E
- Lower required return → higher justified P/E
- Higher payout ratio → higher justified P/E (holding g constant)

**When to use each:**
- **Trailing P/E** when you have reliable actual earnings and want to compare to the current market P/E
- **Leading P/E** when you want to compare to forward estimates from analysts
- On the CFA exam, pay attention to whether the question gives E_0 or E_1 — this determines which formula to apply

Practice justified multiple calculations in our CFA Level I equity question bank.

How do you derive the justified trailing P/E ratio from the Gordon Growth Model?

Master Level I with our CFA Course

Related Questions

Practice Questions