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Valuation Range: Method

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Valuation Range: Several Methods Side by Side

What it does

No single method gives the value of a share, and every method needs an assumption that nobody knows exactly: a multiple, a growth rate, a discount rate. This page runs several common methods on the same company, each at the low end and at the high end of a range you choose, and puts the results next to each other: a table, and a chart with one horizontal bar per method that analysts call a football field. If you type a share price it is drawn as a line across the bars, and each method is also run backwards to show what it would need to return that price. The page describes what your assumptions lead to. It does not say what the share is worth.

The method

Money is in millions of one currency; the share price, earnings per share and the dividend are per share. S is the number of shares and ND the net debt (debt less cash; negative for net cash).

Price-to-earnings (P/E). V = m × EPS, where EPS is the earnings per share of the last year and m the multiple.

Enterprise multiples. Enterprise value (EV) is the value of the whole business, to lenders and shareholders together. EV = m × EBITDA (earnings before interest, taxes, depreciation and amortization), or in Advanced mode EV = m × revenue. The bridge to the shares: equity value = EV − ND, and V = (EV − ND) / S.

Price-to-book (P/B, Advanced). Book value per share BVPS = shareholders' equity / S, and V = m × BVPS.

Discounted cash flow (DCF). Free cash flow FCF0 (cash from operations less capital spending) grows at g for N years and at the terminal rate gT afterwards; r is the discount rate, the yearly return investors require on the whole business. With q = (1 + g)/(1 + r):

EV = FCF0 q (1 − qN)/(1 − q) + FCF0 (1 + g)N (1 + gT) / [(r − gT)(1 + r)N]

The first term is the present value of years 1 to N; the second is the terminal value, the Gordon growth formula applied at year N and discounted to today. Then V = (EV − ND) / S. The low case uses the low growth with the high discount rate, the high case the high growth with the low discount rate. This is the model of the Reverse DCF tool, run forward. Simple mode uses N = 10.

Dividend discount. V = D0 (1 + g) / (rs − g), the Gordon growth formula on the dividend per share D0, with g the dividend's growth for ever and rs the return shareholders require.

Overlap. All the ranges share a common part when the highest of the low values is not above the lowest of the high values; the common part runs between those two numbers.

At a typed price P. For a multiple, the multiple the price stands at is P / EPS (or (P × S + ND) / EBITDA for an enterprise multiple), and the change in the metric that would put the price at a multiple m is P / (m × EPS) − 1. For the DCF the page solves, at each end of the discount-rate range, for the growth g at which the formula above returns EV = P × S + ND. For the dividend model the growth that returns the price is g = (P rs − D0) / (P + D0).

What it assumes

  • The ranges are yours. The page checks no multiple against any market and no growth rate against any history.
  • One year's figures stand for the company: the multiples apply to the last year's earnings, EBITDA, revenue and book value, whatever was unusual in that year.
  • The DCF has two stages with constant growth in each, cash flows at year ends, and one discount rate; the dividend model has one growth rate for ever.
  • Net debt is the only item between enterprise value and the value of the shares. Leases, pensions, minority interests, preferred shares and share options are not bridged.
  • Figures loaded from the company box are annual figures as filed with the SEC, in the company's reporting currency and never converted; the share price must be typed in that currency, per ordinary share.

When it misleads

  • The bars look like evidence and are not. A bar is exactly as wide as the range typed. Narrow ranges give a tidy chart that says nothing about how uncertain the value is.
  • Overlap is not confirmation. A P/E range and a DCF range chosen by the same person in the same mood will agree. The methods also share inputs: earnings, EBITDA and free cash flow move together.
  • The low and high cases are corners. The DCF low case pairs the lowest growth with the highest discount rate; both happening together is less likely than either alone.
  • The terminal value dominates the DCF, often more than half the value, and it rests on the two rates known least well. The dividend formula is more sensitive still: at a required return of 8 % a growth of 7 % gives three times the value that 5 % gives.
  • A method can be the wrong tool for the company. A company that pays out little of its earnings looks small through a dividend model; one that has bought back most of its equity has a book value that says little; a bank has no meaningful EBITDA or net debt. Such a method is left out when its input is missing, but it is your call when the input is present and merely uninformative.
  • Loaded data can be wrong or missing. The dividend per share is not tagged by every company and is unreliable for some foreign filers; debt lines can omit parts. Check the figures against the filing.

Worked example

The default case uses Apple Inc.'s Form 10-K for the fiscal year ended 30 September 2023 (money in US$ millions): diluted EPS 6.13; EBITDA 114,301 + 11,519 = 125,820; free cash flow 110,543 − 10,959 = 99,584; dividend 0.94 a share; net debt 111,088 − 162,099 = −51,011; 15,553 million shares. The share price of 175.00 and every range are illustrative.

P/E 20 to 30: 20 × 6.13 = 122.60 and 30 × 6.13 = 183.90.

EV / EBITDA 15 to 22: EV = 15 × 125,820 = 1,887,300; equity = 1,887,300 − (−51,011) = 1,938,311; per share 1,938,311 / 15,553 = 124.63. At 22: 181.25.

DCF, growth 5 to 10 %, discount rate 8 to 10 %, terminal growth 3 %, 10 years. Low case (g = 5 %, r = 10 %): q = 1.05 / 1.10 = 0.9545; years 1 to 10 are worth 99,584 × 0.9545 × (1 − 0.954510) / (1 − 0.9545) = 777,931; FCF10 = 99,584 × 1.0510 = 162,212; terminal value 162,212 × 1.03 / 0.07 = 2,386,831, worth 920,227 today; EV = 1,698,157; equity 1,749,168; per share 112.47. High case (g = 10 %, r = 8 %): 232.67.

Dividend discount, required return 8 %, growth 5 to 7 %: 0.94 × 1.05 / 0.03 = 32.90 and 0.94 × 1.07 / 0.01 = 100.58.

Overlap. The highest low value is 124.63 (EV / EBITDA) and the lowest high value is 100.58 (dividend discount): the ranges have no common part. Apple pays out about 15 % of its earnings, so a model that values only the dividend describes a much smaller stream of cash than the other three.

At 175.00: the price is 175 / 6.13 = 28.55 times earnings; EV = 175 × 15,553 − 51,011 = 2,670,764, which is 21.23 times EBITDA; the DCF returns the price with growth of 6.33 % a year at an 8 % discount rate or 11.10 % at 10 %; the dividend formula returns it with growth of (175 × 0.08 − 0.94) / (175 + 0.94) = 7.42 % a year for ever.

A calculator for education and analysis, not investment advice.