Which input moves the answer

Which bar is widest? The discount rate: 81.95 to 113.24. Growth over the first ten years is a close second, 81.84 to 110.71. Terminal growth (87.47 to 105.65) and the number of growth years (87.76 to 101.31) move the value less at these settings.

Is each bar lopsided? Yes. Three of the four reach further on the high side; only growth years leans the other way. Dropping the discount rate a point lifts the value more than raising it a point cuts it, because discounting compounds: every year's cash, and the terminal value most of all, is divided by a smaller number. Lopsided bars warn you that "plus or minus one point" is not plus or minus the same amount of value.

Were the pushes fair? A tornado ranks inputs only as honestly as the low and high settings you chose. One point on the discount rate and two points on growth are the ranges the bench uses; if you think growth is far less certain than that, widen its push and the bars may swap order. Write the settings next to the chart, always.

What does the bar not show? What happens when two inputs move together. That is Part 2.

Why a higher discount rate means a lower value at all, the price of waiting, is taught in Economics Foundations session 5 ↗; here we only measure how much it moves.

Each tornado bar is computed with the other three inputs pinned at the default. Real disagreements rarely come one input at a time: a colleague who thinks P&G deserves a lower discount rate often also thinks it will grow faster, because both views come from the same belief that the business is safer and stronger than you assume. Pinned bars cannot show what that combined view does.

The effects also do not simply add. Growth matters more when the discount rate is low, because the extra cash from faster growth is shrunk less on its way back to today. You will see it directly in the grid: at 8 percent, moving growth from 3 to 7 percent adds more value than the same move at 10 percent. A tornado is the right first look and the wrong last one.

A single DCF value invites the question "is that right?", which has no answer. A grid invites a better one: "which row and column do you believe, and why?" The output to carry out of the room is the sentence, not the cell: P&G, 5.00 ten-year mean owner earnings (all-capex approximation), 10 years then 2.5 percent: 70.84 to 132.39 a share across discount rates of 8 to 10 percent and growth of 3 to 7 percent; 95.16 at 9 and 5.

Read the grid three ways. Down a column, at 5 percent growth, the discount rate alone moves the value from 113.24 to 81.95, the same swing as the tornado's top bar. Across a row, at 9 percent, growth moves it from 81.84 to 110.71. Row against row, the interaction from the self-study card shows: at 8 percent the growth row spans 96.86 to 132.39, at 10 percent only 70.84 to 94.88. Growth is worth more when the discount rate is low.

Notice also that two cells nearly tie with the centre: 96.86 (8 percent, 3 percent growth) and 94.88 (10 percent, 7 percent). A lower rate and slower growth can land almost exactly where a higher rate and faster growth do. Two analysts can agree on the value and disagree about everything underneath it.

A grid draws nine cells the same size, which quietly suggests nine equally likely outcomes. They are not. The top corner, 132.39, needs the cheapest money and the fastest growth at the same time. For P&G, whose owner earnings grew about 3.1 percent a year across its filed run, 7 percent for a decade is already a stretch before the discount rate is touched. The low corner, 70.84, needs the dearest money and the slowest growth together, and slow growth is roughly what the record shows.

Inputs are also linked by the business itself. Damodaran's relationship from Analyst session 3, growth equals reinvestment rate times return on capital, says faster growth has to be paid for with reinvestment, which lowers the owner earnings left over. The grid holds the base fixed at 5.00 in every cell, so its fast-growth column gets the growth for free. Treat the corners as boundaries for argument, not as scenarios with a probability attached. Analyst session 7 brings the base rates that tell you how often fast growth actually lasts.

The discount rate is a choice, not a fact. It is the return you require for tying money up in this business rather than somewhere safer. No filing contains it. The argument is therefore about you, not the company: what return do you need, and is P&G riskier or safer than the alternatives you would otherwise hold? The cost-of-capital machinery that formalises this is outside these sessions; the honest move is to state your rate, state why, and show the grid either side.

Growth is a claim about the business, so it can meet evidence. P&G's filed owner earnings grew about 3.1 percent a year over 14 years, nominal. Arguing for 7 percent means arguing that the next decade will look nothing like the last one, and naming why. That argument can be checked against the filings and, in Analyst session 7, against base rates for how often fast growth lasts.

Terminal growth has a hard ceiling. Damodaran's terminal value slides set the rule: the stable growth rate cannot exceed the growth rate of the economy, though it can be lower, and the riskfree rate is a simple proxy for nominal economic growth. A terminal rate above that says the company eventually becomes larger than the economy. Check your 3.5 percent push against that ceiling before you treat 105.65 as a fair high case.

Growth years are a claim about durability. Five years or fifteen is a question of how long the business keeps an edge, which is a moat treated as a valuation input. That is Analyst session 8; the economics of moats themselves live in Economics Foundations session 6 ↗.

The grid prints values to the cent, and the code needed the base to six decimals to reproduce them. That precision belongs to the arithmetic, not to the answer. A cell reading 95.16 is no more knowable than one reading 95; what is knowable is that a point on the discount rate moves it by tens of dollars. Reporting a valuation to the cent when its inputs are uncertain by whole percentage points is the error the grid exists to expose.

Carry full precision through the calculation, because rounding the base to 5.00 prints 95.19 instead of 95.16 and breaks reproducibility. Then round hard when you speak: "roughly 70 to 130, about 95 at the middle inputs" is the sentence that matches what you actually know.