Relative Value Equity Valuation Approaches: formula sheet

Key formulas

P/E

P/E = Price per share ÷ EPS

Trailing uses past 12 months EPS; forward uses expected EPS.

Justified leading P/E

P0/E1 = (1 − b) ÷ (r − g) = payout ÷ (r − g)

b is retention ratio. Requires r > g.

Justified trailing P/E

P0/E0 = payout × (1 + g) ÷ (r − g)

Equals leading P/E × (1 + g).

P/B

P/B = Price per share ÷ Book value per share

Book value per share = (common equity − preferred equity) ÷ shares outstanding.

Justified P/B

P/B = (ROE − g) ÷ (r − g)

Above 1 when ROE exceeds required return r.

P/S

P/S = Price per share ÷ Sales per share

Equivalent to market cap ÷ total sales.

Justified trailing P/S

P0/S0 = (E0/S0) × payout × (1 + g) ÷ (r − g)

E0/S0 is the current (trailing) net profit margin. This is the trailing form, paired with current sales S0.

Justified leading P/S

P0/S1 = (E1/S1) × payout ÷ (r − g)

E1/S1 is the expected net profit margin. This is the leading form, paired with expected sales S1, and has no (1 + g) factor.

P/CF

P/CF = Price per share ÷ Cash flow per share

Cash flow may be CFO, FCFE or adjusted CF (net income plus non-cash charges); state which. EBITDA belongs in EV/EBITDA, not P/CF.

PEG

PEG = P/E ÷ earnings growth rate (in percent)

Lower suggests cheaper per unit of growth.

Enterprise value

EV = Market cap + Market value of debt + Preferred stock + Noncontrolling interest − Cash and short-term investments

Exams often use book value of debt as a proxy for market value. Use the figures the question gives.

EV/EBITDA

EV/EBITDA = EV ÷ EBITDA

Numerator covers all capital providers; denominator is before interest.

EV/Sales

EV/Sales = EV ÷ Sales (revenue)

Useful when earnings are negative; ignores margin differences.

Implied EV from a peer multiple

Implied EV = Peer EV/EBITDA × Target EBITDA

Then convert to equity.

Equity value from EV

Equity value = EV − Debt − Preferred stock − Noncontrolling interest + Cash

Divide by shares outstanding for value per share.

Dividend yield

Dividend yield = D ÷ P

Use the same dividend basis (trailing or forward) for every stock you compare.

PEG ratio

PEG = (P/E) ÷ (expected EPS growth rate in %)

Growth is a whole number: 15% growth means divide by 15. Lower PEG means cheaper relative to growth.

Justified forward P/E (Gordon growth)

P0/E1 = payout ratio ÷ (r − g)

Uses next year's earnings E1 and payout = D1 ÷ E1. Requires r > g.

Justified trailing P/E (Gordon growth)

P0/E0 = payout × (1 + g) ÷ (r − g)

Equals the forward P/E times (1 + g).

Dividend growth link

g = retention rate × ROE = (1 − payout) × ROE

The sustainable growth rate, used to link payout to growth.

Justified price from multiple

Value = justified multiple × fundamental

For example justified P/E × forecast EPS.

Implied value from a multiple

Implied value per share = Benchmark multiple × Company's fundamental per share

For P/E: implied price = benchmark P/E × EPS. For P/B use book value per share; for P/S use sales per share.

Implied enterprise value

Implied EV = Benchmark EV/EBITDA × Company EBITDA

Then equity value = EV − net debt (debt minus cash and equivalents), adjusting for other claims such as preferred stock and noncontrolling interest.

Valuation conclusion

Price < implied value → possibly undervalued; Price > implied value → possibly overvalued

Only valid if the benchmark is a fair comparison and differences in growth and risk are considered.

Law of one price

Identical cash flows and risk → same price

Basis of relative valuation. Real stocks are never identical, so judgement is needed.

Justified P/E (Gordon growth, trailing)

P0/E0 = [payout × (1 + g)] ÷ (r − g)

Shows why higher r lowers P/E and higher g raises it. Requires r > g.

Justified P/E (leading)

P0/E1 = payout ÷ (r − g)

Uses next year's expected earnings. Payout = 1 − retention.

Normalized earnings (historical average method)

Normalized EPS = average EPS over a full business cycle

Simple and objective but ignores changes in the firm's size and capital base.

Normalized earnings (average ROE method)

Normalized EPS = average ROE × current book value per share

Reflects current capital base. Use when the firm has grown or shrunk.

Multiples for negative earnings

Use P/S, EV/Sales, P/B or EV/EBITDA instead of P/E

A negative P/E is not meaningful. Do not average it into a peer median.

Harmonic mean of multiples

Harmonic mean = n ÷ Σ(1 ÷ multiple)

It is the average of the reciprocals of the multiples (for P/E, the earnings yields), inverted. It reduces the influence of very large multiples (outliers). It requires all multiples to be positive.

Quick revision

• P/E = price per share ÷ earnings per share; it is not meaningful when earnings are negative.
• P/B = price per share ÷ book value per share; useful for asset-heavy firms such as financial institutions, weaker for intangible-heavy ones.
• P/S = price per share ÷ sales per share; usable when earnings are negative but ignores profitability.
• P/CF is less easily manipulated than earnings but depends on which cash flow measure is used.
• EV = market value of equity + market value of debt + preferred stock − cash and short-term investments.
• EV/EBITDA is useful when comparing firms with different leverage, and it is unaffected by depreciation policy differences.
• Match numerator and denominator: equity-based price with per-share equity measures, EV with operating measures before payments to capital providers.
• Method of comparables assumes similar companies should trade at similar multiples; check growth, risk and accounting.
• Trailing multiples use past fundamentals; forward multiples use forecasts and are only as reliable as the forecast.
• Differences in accounting standards, currencies and country risk can make cross-border multiples non-comparable.
• A low multiple alone does not prove undervaluation; there may be lower growth or higher risk.
• Quickly eliminate options that confuse equity value with enterprise value.

Common mistakes

• Using trailing and leading P/E formulas interchangeably. Fix: Leading pairs with E1 and has no (1 + g). Trailing pairs with E0 and includes (1 + g).
• Using retention ratio in place of payout. Fix: Always compute 1 − retention first and write it down.
• Adding cash instead of subtracting it when computing EV. Fix: Cash is subtracted from EV (it offsets the purchase price). It is added when going from EV back to equity value.
• Dividing price or market cap by EBITDA. Fix: Match numerator and denominator: EV goes with EBITDA, EBIT or sales; price or market cap goes with earnings after interest.
• Entering growth as a decimal in the PEG ratio Fix: For PEG, use 12 for 12%. Divide P/E by 12.
• Using the justified forward P/E formula for a trailing P/E Fix: Forward P/E = payout ÷ (r − g). Trailing P/E multiplies the numerator by (1 + g).
• Treating a lower multiple than peers as proof of undervaluation. Fix: Ask whether growth, risk or accounting differences justify the gap. The law applies only to truly similar assets.
• Forgetting to subtract net debt when using EV/EBITDA. Fix: EV is the value of the whole firm. Subtract debt, add cash, then divide by shares.
• Concluding a stock in a high-P/E country is overvalued from the multiple alone. Fix: Check growth, interest rates and risk first. A higher justified P/E can come from higher g or lower r.
• Using a P/E for a firm with negative earnings or averaging it into the peer group. Fix: Treat negative P/E as not meaningful. Use P/S, EV/Sales, P/B or EV/EBITDA, or normalized earnings.

Exam tips

• Read whether the question gives E0 or E1 before choosing the formula.
• Memorise the pairing of each multiple with the situations where it fails: P/E with negative earnings, P/B with intangibles, P/S with weak margins, P/CF with working capital changes.
• Direction questions are common: higher g or lower r raises P/E and P/B.
• Many items are conceptual. Match the multiple's weakness to the company described.
• With no penalty for wrong answers, always answer; eliminate the option with the wrong direction first.
• Expect questions that test why EV/EBITDA beats P/E when comparing firms with different leverage.
• Always check whether the question gives book or market value of debt and use what is given.
• With three options, test direction first: extra cash lowers EV; extra debt raises it.