How do you derive a justified P/E ratio from fundamentals, and how is it different from a trailing P/E?

Question

AcadiFi · Accepted Answer

A justified P/E ratio is derived from a fundamental valuation model rather than from market prices. It tells you what P/E the stock *should* trade at given its fundamentals, which you can then compare to the actual P/E to assess mispricing.

**Deriving Justified Leading P/E from GGM:**

Starting with the Gordon Growth Model:

$$
P_0 = \frac{D_1}{r - g}
$$

Since D1 = E1 x (1 - b) where b is the retention rate:

$$
P_0 = \frac{E_1 	imes (1 - b)}{r - g}
$$

Divide both sides by E1:

$$
\frac{P_0}{E_1} = \frac{1 - b}{r - g}
$$

This is the **justified leading P/E**.

**Deriving Justified Trailing P/E:**

$$
\frac{P_0}{E_0} = \frac{(1 - b)(1 + g)}{r - g}
$$

**Worked Example: Westbrook Industries**

| Input | Value |
|---|---|
| Required return (r) | 11% |
| Sustainable growth (g) | 5% |
| Payout ratio (1 - b) | 45% |
| Current EPS (E0) | $5.20 |
| Current stock price | $52.00 |

**Justified Leading P/E:**
= 0.45 / (0.11 - 0.05) = 0.45 / 0.06 = **7.50x**

**Justified Trailing P/E:**
= 0.45 x 1.05 / 0.06 = 0.4725 / 0.06 = **7.875x**

**Actual Trailing P/E:**
= $52.00 / $5.20 = **10.0x**

**Interpretation:** Westbrook's actual P/E (10.0x) exceeds its justified P/E (7.875x), suggesting the stock is **overvalued** relative to fundamentals.

**What Drives the Justified P/E:**

| Factor | Effect on Justified P/E | Intuition |
|---|---|---|
| Higher growth (g) ↑ | P/E increases ↑ | Faster growth justifies higher price |
| Higher payout (1-b) ↑ | P/E increases ↑ | More cash returned to shareholders |
| Higher required return (r) ↑ | P/E decreases ↓ | Higher risk = lower valuation |

**Justified P/E vs. Market Comparables:**

| Approach | Justified P/E | Market Comparable P/E |
|---|---|---|
| Source | Fundamental model | Peer group averages |
| Advantage | Firm-specific, grounded in theory | Simple, market-based |
| Limitation | Sensitive to input assumptions | Assumes peers are fairly valued |
| Best for | Intrinsic value assessment | Quick relative check |

**Exam Tip:** If a CFA Level II question gives you growth rate, payout ratio, and required return, calculate the justified P/E and compare it to the actual. If justified > actual, the stock is undervalued. If justified < actual, overvalued.

Master justified multiples with our CFA Level II equity materials on AcadiFi.

How do you derive a justified P/E ratio from fundamentals, and how is it different from a trailing P/E?

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