Equity calculus / one assumption

Why can PEG = 1 feel like fair value?

Begin with one canonical equity earning $0.25 every quarter. Choose one constant growth rate, then watch cumulative earnings fill the PEG-one purchase price.

Turn growth into a price

The quarter-dollar company earns $0.25 each quarter, or $1.00 per year. At 25% growth, PEG = 1 treats the growth number 25 as a 25× earnings multiple: $25 per share.

4 × $0.25 = $1 EPS → 25 × $1 = $25

Hold growth constant

Every quarter grows from the prior quarter at the same compounded rate. Nothing fades and no second assumption intervenes. The experiment asks what that single growth rate implies if carried forward.

E(t) = E₀(1 + g)ᵗ

Watch the earnings refill the price

Add each quarter to the cumulative pile. At the canonical 25% rate, the pile crosses the $25 PEG-one price after roughly eight and a half years. This similar-feeling payback window is PEG-one’s intuitive appeal.

C(T) = ∫₀ᵀ E(t)dt → find C(T) = price

Constant-growth lab

Two inputs. One century.

Assume the same growth rate continues for 100 years. This is intentionally unrealistic: it isolates the PEG-one payback intuition.

Annualized earnings now$1.00four current quarters

PEG-one price$25.0025× current earnings

Naive payback8.5 yearswhen cumulative earnings refill the price

Collected by year 100$22.62Bthe compounding thought experiment

02 / Cumulative earnings

How much has the company earned for you?

The curve adds every quarter for 100 years. Both axes are literal: years across, cumulative dollars up.

PEG-one price $25.00Payback 8.5y

X · Year10

Y · Cumulative earnings$38.30

The whole mechanism

Price is a line. Earnings are an area.

Grow one flowE(t) = E₀(1 + g)ᵗ

A constant growth rate bends the earnings stream upward.

Add the flowC(T) = ∫₀ᵀ E(t)dt

The integral is simply every future quarter added to one pile.

Find the crossingC(T) = E₀ × 4 × 100g

The crossing year is the naive time needed to earn back the PEG-one price.

The honest conclusion

PEG = 1 is a payback intuition, not a valuation law.

What the model reveals

Across common positive growth rates, PEG-one prices tend to imply a similar nominal earnings-payback period. That regularity is why the rule feels sensible.

What the model assumes

Growth continues unchanged for a century, and every dollar of EPS behaves like cash available to the owner. The enormous year-100 result makes the unreality visible.

The unit trick

PEG uses growth as a whole-number percent: 25, not 0.25. The equality is a market convention, not a dimensionless law of finance.

What reality adds back

Competition, reinvestment, dilution, cyclicality, debt, taxes, growth fade, and the value of time can all break the shortcut.