Justified P/E ratio

Now decompress each multiple. The derivations are worth doing yourself. Once you've derived P/B = (ROE−g)/(r−g), you can never again say "cheap at 0.8× book" without asking what the ROE is. Throughout, r is the cost of equity you built earlier and g is the stable growth rate, subject to the g ≤ economy-growth cap from the terminal-value work. The firm is in steady state. The single-stage results come first. The two-stage arithmetic that premium multiples need is in India's premium multiples.

Justified P/E

Start from Gordon: P0 = D1/(r−g). Dividends are earnings times the payout ratio: D1 = E1 × payout. Divide both sides by forward earnings E1:

Forward (leading) P/E  =  P0/E1  =  payout / (r − g)
Trailing P/E           =  P0/E0  =  payout × (1+g) / (r − g)

But payout isn't free. The sustainable-growth identity from the DCF forecasting work chains it to growth: g = retention × ROE, so retention = g/ROE and:

payout = 1 − g/ROE
Forward P/E = (1 − g/ROE) / (r − g)

Put some numbers through it. Take an Indian consumer firm with ROE 20%, stable growth 6% and r 12%. Payout = 1 − 6/20 = 0.70. Forward P/E = 0.70/0.06 = 11.7×, and trailing = 0.70 × 1.06/0.06 = 12.4×. Now move the same business to US market parameters: ROE 20%, g 4%, r 8.5%. It pays out 0.80 and justifies 0.80/0.045 = 17.8× forward. It's the same quality of business. The rate regime alone moves the fair multiple six points. Hold on to that, because it comes back when we get to India's premium multiples.

What does the justified P/E formula tell you?

Two results inside this formula are worth more than the formula:

Result 1: growth is only worth paying for if ROE exceeds r. Set ROE = r and watch growth vanish from the price. Let ROE = r = 12%. At g = 2%, payout = 1 − 2/12 = 0.833 and P/E = 0.833/0.10 = 8.33×. At g = 8%, payout = 1 − 8/12 = 0.333 and P/E = 0.333/0.04 = 8.33×. Identical. Algebraically, ROE = r makes forward P/E collapse to 1/r for any g, because the extra growth needs just as much retained capital as the growth is worth.

So growth is a multiplier on the ROE−r spread, with no value of its own. That's the deepest idea in Phase 3, and it just fell out of a P/E formula. When you get to value drivers and capital allocation, you'll see the general version: growth destroys value when returns are below the cost of capital.

Result 2: the stable-growth ceiling. Now let ROE grow without limit, which describes a business that needs no capital at all. Payout tends to 1 and forward P/E tends to 1/(r−g). With India's r ≈ 11.5% and the terminal-g cap of ~5%, the ceiling is 1/0.065 ≈ 15.4×. With US parameters, r 8.5% and g 4%, it's 1/0.045 ≈ 22×. No steady-state business on earth justifies 50× forward earnings, not even one with infinite ROE. Every multiple above the ceiling is a claim about a high-growth phase: its rate, its length, its returns. That's the door you'll walk through when we reach India's premium multiples.

Justified P/B: the full derivation

P/B has the cleanest driver algebra of all the multiples. The banks module will hand you a banking sector priced almost entirely on it, so derive it fully and never forget it.

Start again from Gordon, P0 = D1/(r−g), and express D1 in terms of book value. Define ROE on beginning-of-year book equity, so next year's earnings are E1 = ROE × B0. Dividends are earnings times payout, and payout = 1 − g/ROE:

D1 = E1 × payout = ROE × B0 × (1 − g/ROE) = B0 × (ROE − g)

P0 = B0 × (ROE − g) / (r − g)

P0/B0 = (ROE − g) / (r − g)

Three lines, and everything a bank analyst needs is inside them:

• ROE = r ⇒ P/B = 1. A firm that earns its cost of equity, and no more, is worth its book value, and no more. Accounting book and economic value coincide when there are no excess returns. That's your anchor. P/B is a market-priced verdict on the ROE−r spread.
• ROE > r ⇒ P/B > 1, and growth amplifies it. With ROE 18%, r 12% and g 5%, P/B = (18−5)/(12−5) = 13/7 = 1.86×. Raise g to 7% and it's 11/5 = 2.20×. Growth multiplies a positive spread.
• ROE < r ⇒ P/B < 1, and growth makes it worse. With ROE 10%, r 12% and g 5%, it's 5/7 = 0.71×. Push growth to 7% and you get 3/5 = 0.60×. A bank earning below its cost of equity that grows its loan book faster becomes worth less of its book, because it's manufacturing negative-NPV assets at scale. So "cheap at 0.6× book" now reads correctly, as priced for value destruction. Don't ask "how far below book?" Ask "is the market's ROE verdict right?" That's an asset-quality question, and valuation won't answer it.

One identity ties the family together. Divide the P/B formula by the forward P/E formula and you get P/B = ROE × forward P/E. Check it with ROE 18%, g 5% and r 12%. Forward P/E = (1 − 5/18)/0.07 = 0.722/0.07 = 10.32×, and times ROE 0.18 that's 1.86×, the same answer as before. One firm, one value, several shirts. If your P/E and P/B verdicts on the same stock disagree, your inputs are inconsistent somewhere.

P/FCF: the owner's multiple

For a steady firm, P0 = FCFE1/(r−g), so forward P/FCFE = 1/(r−g). That's the ceiling multiple again. FCFE is what's left after reinvestment, so no payout ratio appears. With US parameters (r 8.5 to 9%, g 4%), fair P/FCFE ≈ 20 to 22×, which is an FCF yield of ~4.5 to 5%. For India (r 11.5 to 12%, g 5%) it's ≈ 14 to 15×, an FCF yield of ~6.5 to 7%. The practical form is FCF yield + g ≈ expected return, holding the multiple constant. It's the fastest sanity check in the toolkit. A stock on a 2% FCF yield needs ~7% perpetual FCF growth to earn a US cost of equity, and you can judge that claim in seconds.

In practice you compute P/FCF as market cap ÷ (CFO − capex). Two cautions carry over from the free-cash-flow work. Capex is lumpy, so average 3 to 5 years or the multiple whipsaws. And growth capex depresses FCF just when the business is at its best. A heavily reinvesting compounder looks expensive on P/FCF while it builds its future, and Amazon spent a decade "expensive" this way. Separate maintenance from growth capex before you trust the ratio, or use owner earnings. Phase 6 formalizes Buffett's version.

PEG: the false precision machine

PEG = (P/E) ÷ (expected EPS growth × 100). Lynch popularized it ("fairly priced at PEG = 1") and screens love it. It fails first-principles inspection on four counts:

1. It assumes P/E is linear in g through the origin. The justified-P/E formula is convex in g and doesn't pass through zero. A zero-growth firm is worth payout/r ≈ 8 to 11× earnings, nowhere near 0×. Dividing by g punishes low-growth firms for a value floor they legitimately have.
2. It ignores r and ROE entirely. Two firms with identical P/E and g but different risk or capital intensity get the same PEG. They shouldn't get the same price.
3. Its g is undefined. Is it next year's growth, a five-year CAGR, or whoever's estimate you happened to open? Move the horizon and the ranking reshuffles.
4. "PEG < 1 = cheap" has no derivation. It's folklore with a decimal point.

Some numbers make it vivid. Here are four firms, all with ROE 18% and r 9%, and all fairly priced by construction on the justified formula:

Every one of these is at fair value, yet PEG runs from 3.7 to 6.9 and anoints the 6% grower "cheapest." So PEG isn't comparable even across correctly priced firms, and among mispriced ones it's noise. If you use it at all, use it as a coarse screen within a set of same-risk, same-ROE, same-horizon firms. Then do the real algebra before you act.