Fundamental valuation — multiples, DCF, SOTP

Equity valuation is the art of estimating what a share of a business is worth based on its expected future cash flows. The honest practitioner uses multiple methods, triangulates between them, and reports a range rather than a point. The methods divide into two families: relative valuation (multiples vs comparable companies) and absolute valuation (discounted cash flow). The two should be cross-checks on each other, and the gap between them — when it appears — is where the most interesting analysis lives.

Price-to-earnings (P/E)

                    Price per share
  P/E   =   ───────────────────────────────
                  Earnings per share

where:
  Price per share        =  current market price of one share
  Earnings per share     =  net income attributable to common shareholders,
                            divided by the weighted-average diluted share count
                            'Trailing' P/E uses last-twelve-months EPS;
                            'Forward' P/E uses next-twelve-months forecast EPS

A P/E of 20 means investors pay $20 today for each $1 of current
annual earnings. The reciprocal — earnings yield, 1/PE = 5% — is
the direct comparison to a bond yield.

P/E is the most-cited valuation multiple because it is intuitive: $20 today for $1 of annual earnings means a 20-year payback period at current earnings, or equivalently a 5% earnings yield. Its limitations are real: earnings are affected by accounting choices (depreciation methods, stock-based comp), one-time items (impairments, gains on sales), and crucially by leverage — a more-leveraged company has lower net income because of interest expense, so its P/E looks artificially lower or its valuation looks artificially cheaper. Comparing P/E across firms with materially different capital structures or industries can mislead.

EV/EBITDA — the capital-structure-neutral multiple

                Enterprise Value
  EV/EBITDA  =  ──────────────────
                     EBITDA

where:
  Enterprise Value (EV) = Market cap of equity
                        + Market value of debt
                        + Preferred stock
                        + Minority interest
                        − Cash and cash equivalents
                        
                        Captures the value of the operating business,
                        treating the firm as if you bought it outright
                        and assumed the debt.

  EBITDA              = Operating income
                      + Depreciation
                      + Amortisation
                      
                        Approximates pre-financing cash flow from operations.
                        Pre-interest (so capital-structure-neutral),
                        pre-tax (so tax-regime-neutral),
                        pre-D&A (so capex-policy-neutral).

Because EV captures both equity and debt and EBITDA is pre-interest, EV/EBITDA is the multiple of choice for comparing companies with different leverage. The comparison is apples-to-apples — two firms with identical operating businesses but different debt loads will have very different P/E multiples but very similar EV/EBITDA multiples. Typical ranges: investment-grade industrials 8-12x EBITDA; capital-light tech 15-30x; mature slow-growth utilities and consumer staples 6-9x; cyclical commodities 4-7x at trough, 8-12x at peak. Sub-Saharan African listed corporates typically trade 4-7x on this measure.

Price-to-book (P/B) — for businesses where book matters

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

where:
  Book value per share  =  Shareholders' equity (excluding preferred)
                           divided by common shares outstanding
  Shareholders' equity  =  Total assets − Total liabilities − Preferred equity
                           Reported on the balance sheet at historical cost
                           (with some marking-to-market for trading assets)

P/B is most relevant for businesses where book value approximates economic value — banks, insurance companies, asset-heavy industrials, real-estate trusts. For a bank, P/B of 1.0 means the market values the equity at book; P/B of 2.0 implies the market sees the bank generating sustainable returns on equity well above its cost of equity, justifying a premium over book. The implicit identity: P/B should approximately equal (ROE − g) / (Ke − g) under steady-state assumptions, which is why high-ROE banks trade at P/B premiums and low-ROE banks trade at discounts.

Dividend yield and the Gordon growth model

                          D_1
  Equity value  P   =   ─────────
                          r − g

where:
  P    =  the present value of an infinite stream of growing dividends
           — the intrinsic value of the equity per share today
  D_1  =  next year's expected dividend per share, in currency units
           — typically last year's dividend × (1 + g)
  r    =  the cost of equity, decimal form (the Ke we computed in the DCF course)
           — the annual return shareholders require for bearing equity risk
  g    =  the long-run sustainable growth rate of dividends, decimal form
           — must be less than r for the formula to give a finite answer
           — typical values: 2-3% in developed markets, 4-6% in emerging
  r − g  =  the 'spread' the model is essentially dividing by
           — small changes here produce large changes in P, because
             dividing by a small number amplifies small numerator moves

The Gordon growth model is the simplest dividend discount model: value the stock as the present value of an infinite stream of dividends growing at constant rate g. For mature, dividend-paying companies (utilities, consumer staples, mature banks) it provides a clean sanity check; the limitation is that the answer is hyper-sensitive to small changes in r and g, especially when r and g are close. A change in g from 3% to 4% with r at 9% moves P from D/0.06 = 16.7×D to D/0.05 = 20.0×D, a 20% valuation change from a 1-percentage-point growth assumption. The model is a sanity check, not a precision tool, and the sensitivity itself is informative.

Free cash flow to equity discount model

Free cash flow to equity (FCFE) is the cash the business generates that is available to equity holders after capex, working-capital changes, and net debt repayments. Discounted at the cost of equity, FCFE gives an absolute valuation independent of dividend policy. This is preferred when companies don't pay material dividends (most US tech) or when dividend payout ratios are volatile.

                  N
               ─────         FCFE_t                 Terminal value
  Equity     =   ∑      ─────────────────       +     ────────────────
                t = 1     ( 1 + Ke )^t                  ( 1 + Ke )^N

                              FCFE_(N+1)
  Terminal value     =     ──────────────────
                              Ke  −  g

where:
  Equity      =  the present value of equity per share (sum of explicit forecast + terminal)
  N           =  number of years in the explicit forecast period (typically 5-10)
  t           =  year index running from 1 to N
  FCFE_t      =  free cash flow to equity in year t, in currency units
                 = Net income + Non-cash charges − Capex − ΔWorking capital + Net borrowing
  Ke          =  cost of equity (from CAPM in the DCF course)
  Terminal    =  the Gordon-growth value of all cash flows beyond year N,
   value         expressed as of year N
  FCFE_(N+1)  =  the first cash flow in the perpetual stream — year N+1 FCFE,
                 grown one more year from the explicit forecast endpoint
  g           =  long-run sustainable perpetual growth rate (typically 2-3%
                 in developed markets, 4-6% in emerging markets, never
                 exceeding the long-run nominal GDP growth rate of the
                 economy in which the firm operates)

Sum-of-the-parts (SOTP)

For diversified conglomerates, valuing each business segment separately and then summing the parts (often with a 'conglomerate discount' applied) is more accurate than valuing the whole. Berkshire Hathaway's segments — insurance, energy, railroads, manufacturing, equity holdings — each trade at different multiples in the public market. Goldman Sachs publishes SOTP analyses on multi-business conglomerates regularly. SOTP often surfaces hidden value that drives activist campaigns to spin off or break up undervalued businesses.

Forward versus trailing multiples

Forward multiples (using next-twelve-months or next-fiscal-year forecasted earnings) are typically preferred to trailing multiples (last-twelve-months actual earnings) because they reflect the market's expectations about the future. The catch: forward earnings forecasts come from sell-side analysts and consensus tends to be too optimistic in late-cycle conditions. Always check whether the multiple is trailing or forward, and what the underlying earnings number is.