learn-value-investing-with-phoebe / Analyst session 10 of 10
Learn Value Investing with Phoebe · Analyst session 10 of 10

The intrinsic value bench

Nine sessions have built one machine. Tonight you run it. The bench reads four companies' real annual figures, stands in a past year, forecasts the years that followed with five different rules, and checks every forecast against what the filings later showed. Then it values each company today on the rule you pick, prints the value as a range, and measures a margin of safety against a price you type. There is an anti-lever, the rule a hopeful analyst reaches for, and it misses by two orders of magnitude. There is a break button that sets terminal growth equal to the discount rate, where the arithmetic has no answer and the bench says so. Educational, not investment advice.

🔴 Bench night Analysts, and anyone who has to defend a valuation in a room Browser only, no code needed 45 min
0-3 · Welcome 3-14 · Reading the ladder 14-40 · The bench, then the sentence 40-45 · Q&A
Part 0

Where we start

A valuation you cannot break is one you do not understand. Everything on the bench is computed in your browser from the same four companies' 10-K facts that Analyst session 1 read: net income, depreciation and amortisation, capital spending and shares, fifteen to nineteen fiscal years each. Nothing is stored output. Move a control and the engine recomputes; pick the anti-lever and watch the miss; press the break button and watch the value disappear.

🎫 Clear all three quiz questions to stamp your passport Live = presented in the 45 minutes Self-study = the full depth, after class ★ Bench = every number computed in your browser

Educational, not investment advice. The bench never shows a market price. The only price on it is one you type, and the value it prints depends on four inputs you choose. A value per share from this bench is an exercise in reasoning, not a recommendation about any company.

★ What you walk out with tonight. A ladder you have checked against real outcomes, with the finding stated as the data gave it; the anti-lever you can now name when somebody proposes it; the reason a terminal growth rate at or above the discount rate has no value; and one sentence for a meeting that carries a range, the growth a price implies, and what would prove you wrong.

Part 1 · covers the five rungs and what the filings later showed

Reading the ladder

8 min live

Stand in fiscal 2020 (2021 for Procter & Gamble, whose year ends in June), with only the years before. Forecast average owner earnings per share for the next five years with each rule, then compare with what the filings showed. The miss is the forecast minus the outcome, as a share of the outcome, averaged across the four companies without signs.

FIVE RULES, ONE HELD-OUT FUTURE mean miss across four companies, last five fiscal years held out · the bench recomputes these 1 · last year's earnings 70.4% 2 · five-year owner earnings 47.4% 3 · ten-year owner earnings 50.2% 4 · ten-year, growth fading 47.7% best year's growth, compounded 19,614.8% WHAT THE DATA SHOWED Normalising beat last year's earnings, mostly because 2020 was a bad year to start from: Exxon lost money. Every honest rung undershot. Owner earnings for all four rose after 2020, and no average of the past saw it. Hold out four years instead of five and last year's earnings win. The ranking depends on where you stand. The best single year is a rebound, and a rebound is not a trend.
🔍 Click to zoom - the brass rung won this hold-out by a hair; the red one lost by a factor of four hundred
LiveWhat each rung assumes, and why the anti-lever explodes4 min▶

Rung 1 takes last year's net income per share and holds it flat: no normalising, no capex. Rung 2 holds the five-year average of owner earnings flat. Rung 3 holds the ten-year average flat, usually a whole cycle. Rung 4 starts from rung 3 and grows at half the business's own past growth, fading to 2.5 percent over five years: the conservative growth fade from Analyst session 7.

The anti-lever starts from last year's owner earnings and compounds the single best year-on-year growth of the previous ten. On these filings the best year is always a rebound from a trough: Johnson & Johnson's 2018 over its 2017 (+409.7 percent), Procter & Gamble's 2020 over 2019 (+271.7 percent), Caterpillar's 2018 over 2017 (+179.4 percent), Exxon Mobil's 2016 over 2015 (+82.3 percent). Compounding a rebound for five years produces forecasts tens or hundreds of times the outcome. Nobody types "+409.7 percent" into a model on purpose; they type "the growth we saw last year" after a good year, and it is the same mistake at a smaller scale.

Self-studyWhy the honest finding is "it depends on where you stand"3 min▶

Hold out three years and the five-year rung wins again (28.4 percent mean miss, against 39.7 for last year's earnings). Hold out four and last year's earnings win (26.8 percent, against 42.1 for the five-year rung), because the starting year becomes 2021, a strong one. The ten-year rung is never best on these four companies: its average drags in the 2015 to 2017 slump. Four companies and three hold-outs is a small sample, and it is a sample from a period when large-company earnings rose. The defensible lesson is narrower than "normalise and you win": starting from one year makes you hostage to that year, and averaging protects you from a bad start without telling you anything about the future.

That is the same lesson Analyst session 7 draws from the Base Rate Book: forecasts drawn from the past are too narrow, and the honest response is a wider range, not a cleverer average.

Build-along · the bench

Value four companies, and try to break it

★ 20 min · the main event

Work it in order. In panel A, pick each rung for each company and read the forecast against the filings, then press the anti-lever and read the miss. Change the hold-out from five years to four and watch the winner change. In panel B, keep rung 3 and read the value and its range at the default inputs: 9 percent discount rate, 10 growth years, 5 percent growth, 2.5 percent terminal growth. Press the break button. In panel C, type a test price of your own and read the margin of safety and the growth that price implies. Say out loud what changed each time.

Read the tags. Readouts marked "computed" come straight from the filings: owner earnings, outcomes, misses. Readouts marked "modelled" are arithmetic under inputs you chose: values, ranges, margins, implied growth. A modelled number is only as good as the four sliders under it.

WHY THE TAIL CARRIES MOST OF THE VALUE, AND WHEN IT HAS NONE a value: growth years, then a tail each later year worth less today years 1 to 10: 43% the tail: 57% every year after the break: terminal growth = discount rate each year worth exactly as much as the last no value: the sum never stops the bench prints the reason, not a number At 9 percent, 10 years of 5 percent growth, then 2.5 percent: 57.0 percent of any base's value comes from beyond year 10.
🔍 Click to zoom - most of a value lives in the years nobody can forecast, and at the break there is no value at all
LiveWhat the break button proves4 min▶

Press it. Terminal growth jumps to equal the discount rate, and panel B stops printing a value. The tail of a two-stage model is a growing perpetuity, worth next year's cash divided by the gap between the discount rate and the growth rate. As the gap closes the value climbs without limit, and at zero gap the formula divides by zero. Above it, the formula would return a negative number, which a careless spreadsheet happily displays. The bench refuses both and says why.

The lesson goes beyond arithmetic. Damodaran's rule for the stable period is that growth there cannot exceed the growth of the economy, and the riskfree rate is a simple proxy for the economy's nominal growth. A terminal growth rate near the discount rate is a claim that the business outgrows the economy forever. Slide terminal growth to 4.5 and 6.5 percent before pressing the button and watch the value run away first: the model was already telling you something was wrong.

Self-studyWhy the anti-lever's values run to millions a share2 min▶

Pick the anti-lever, then look at panel B. The growth slider is replaced by the best year's growth, and Caterpillar's value at the defaults is about 3,756,447.17 dollars a share, with over 90 percent of it in the tail. It is not a bug. It is ten years of +179.4 percent compounding, followed by a perpetuity on the result. The bench shows it so that the next time a model's growth input is "last year's", you can ask which last year.

Part 2 · covers the range and the price you type

From one value to the sentence

6 min live

On rung 3 at the default inputs the bench values Procter & Gamble at about 95.16 dollars a share, with a range of 70.84 to 132.39 when the discount rate moves one point either way and growth two points either way. The range is the honest output. The price you type turns it into a question: what would the business have to do to be worth this?

PROCTER & GAMBLE, RUNG 3, DEFAULT INPUTS test prices you type are not market prices; these two are half and double the value $0 $200 70.84 132.39 95.16 the range: rate +/- 1 point, growth +/- 2 test price 47.58 implies -4.31% a year test price 190.33 implies +14.17% a year for 10 years
🔍 Click to zoom - the reverse is scale-free: any rung-3 base doubles to 14.17 percent and halves to -4.31 at these inputs
LiveThe margin of safety against the low end, not the middle3 min▶

Panel C prints two margins. The first is against the central value. The second, against the low end of the range, is the one Owner session 3 asks for: the case you must survive. A price can carry a comfortable margin against the middle and none against the low end, and the bench colours the verdict accordingly.

The third readout, the growth the price implies, is the reverse discounted cash flow from Analyst session 5. Instead of asking what the business is worth, it asks what growth would make your typed price fair, with the discount rate, the growth years and terminal growth held where you set them. Doubling the price asks for 14.17 percent a year for ten years against the 5 percent the central value assumed. Analyst session 7's base rates say how often large companies have managed that.

Self-studyWhy every rung 3 base gives the same implied growth2 min▶

Value is proportional to the starting owner earnings when the other inputs are fixed. Doubling the price relative to the value therefore asks for the same growth whichever company you pick: 14.17 percent at these inputs, and -4.31 percent for half. That is why the reverse question is useful across businesses of different sizes, and why it is only as good as the starting point it multiplies.

Real world

Exxon Mobil, three starting points. Last year's net income per share was 6.70 dollars, the five-year owner earnings average 8.87, the ten-year 6.16. At the default inputs those give values of 127.56, 168.83 and 117.34 dollars a share. The five-year average sits highest because it includes 2022's 14.60, the best year in the run. Which starting point is right is not a calculation; it is a judgment about which years were normal, and Analyst session 2 is where it is argued.

Part 3 · covers the sentence for the meeting

One sentence that can be proved wrong

5 min live

A valuation reaches a meeting as one sentence. The sentence that survives carries a range, the starting point and why, the growth a price implies, and what would prove it wrong. It does not carry a value to the cent, and it does not carry a recommendation.

THE SENTENCE, AND WHERE EACH PART CAME FROM 1 · the starting point ten-year owner earnings, $5.00, because one year is a hostage 2 · the range $70.84 to $132.39 at 9 percent, 5 percent growth for ten years 3 · what a price implies a test price at double the value needs 14.17 percent a year 4 · what proves it wrong owner earnings below the ten-year average for 3 years panel A panel B panel C the memo, A9 Procter & Gamble on rung 3 as the worked case. The fourth box is a judgment you write, not a bench output.
🔍 Click to zoom - three of the four parts come off the bench; the brass one is yours, and it is the one that makes the sentence testable
LiveWrite it for one company, out loud3 min▶

Pick one company on the bench. Say: "Starting from ten-year owner earnings of x, because reason, the business is worth between low and high at inputs. A price of p would need g percent growth for ten years. I would change my mind if kill criterion." Every blank except the reason and the kill criterion comes off the bench. The reason and the kill criterion are what the memo in Analyst session 9 is for.

Self-studyWhat the bench cannot tell you2 min▶

It cannot tell you which years were normal, how much of capex was growth, whether a moat will hold, what discount rate fits the risk, or whether cheap-looking companies as a group beat dear ones. That last question is genuinely disputed: Fama and French found the value premium much lower after 1991 than before but could not statistically distinguish the two periods (reported), and others argue the shortfall came from value stocks simply getting cheaper (reported). The bench is a reasoning tool for one business at a time. It makes no claim about any strategy.

Homework

After the bench

30 min
  1. Run every rung for every company at the five-year hold-out and write down which rung missed least for each one. Is the overall winner the winner for each company?
  2. Find the input that moves value most for one company: move each slider one step from the default and record the value. Rank the four.
  3. Type three test prices for one company, below the low end, inside the range and above the high end, and write the margin and implied growth for each.
  4. Write the sentence for one company with all four parts, including a kill criterion you would actually check next year.
Check yourself

Three questions

Clear all three and Analyst session 10 gets stamped in your passport.

1 · With the last five fiscal years held out, the five-year owner-earnings rung missed by 47.4 percent on average and last year's earnings by 70.4 percent. What is the honest reading?

The ranking depends on where you stand, and all honest rungs were far too low because owner earnings for all four companies rose after 2020. The narrow lesson is that one year makes you hostage to that year.

2 · You set terminal growth equal to the discount rate. Why does the bench print no value?

Each later year would be worth as much today as the one before, forever. Damodaran's cap, stable growth no faster than the economy, keeps a model well away from that edge.

3 · On rung 3 at the default inputs, a test price equal to twice the central value implies 14.17 percent growth a year for ten years. What does that tell you?

A reverse discounted cash flow turns a price into an expectation you can test. It forecasts nothing; it tells you what you would be betting on.

Sources covered

What this session teaches, and where it came from

✓Every bench number: the ladder at three hold-outs, the per-company misses, values, ranges, implied growthComputed in the browser from SEC EDGAR XBRL company facts (read from a public mirror, spot-checked against the SEC's API); a Python reference agrees with the browser engine on 562 values
✓Owner earnings, and its approximation hereBuffett, W., Berkshire Hathaway shareholder letter, 1986, appendix (read at source); all-capex approximation labelled
✓Stable growth cannot exceed the growth of the economyDamodaran, A., valuation class slides, terminal value session, NYU Stern, 2023 (read at source)
◐Reverse discounted cash flowMauboussin, M. and Rappaport, A., "Expectations Investing" (reported); the arithmetic is standard
◐Value versus growth as a strategyFama and French 2020 (reported) and Arnott et al. 2021 (reported); taught as a disagreement, not claimed

Every fact on this page, and its verification tier, is recorded in the course's source map.

Analyst session 10 cheat sheet · pin this

Check rules against outcomesStand in the past, forecast, compare with what the filings showed.
Where you stand decides the winnerFive-year won at 3 and 5 years held out; last year's won at 4.
The best year is a reboundCompounding it missed by 19,614.8 percent on average.
Most value is in the tail57.0 percent beyond year 10 at the defaults. At g = r, none at all.
Margin against the low endThe case you must survive, not the middle.
The four-part sentenceStarting point and why, range, implied growth, what proves it wrong.