Lesson 5 of 6
Solving for what the price needs
Run the model backwards. Take the market value, subtract book value, and read off the residual income growth the price already requires.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- Forwards, the model needs a forecast. Backwards, it needs a price, and it returns the forecast the price contains.
- Market value less book value is the present value of all future residual income that the price implies.
- The output is a condition you can test against filed history, not a verdict on the price.
A valuation run forwards produces a number you then compare with the price, and the comparison is only as good as your forecast. Run backwards, the model takes the price as given and hands back the expectations inside it. That output can be checked against ten years of filings, which a forecast cannot.
What the price is made of, at a chosen cost of equity
Paid for by the price today
- Book value on the balance sheet$32,169m8.5%
- Present value of future residual income implied by the price$347,731m92%
Already on the balance sheet
Total$379,900m
The arithmetic, in three lines
Solving for the implied growth rate
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Take the stored market capitalisation: 381,700 million dollars. Subtract book value of 32,169. The difference, 349,531, is what the price pays for everything above the charge.
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Take this year's residual income at an 8 percent cost of equity: 11,119 million dollars.
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A stream growing at a constant rate forever has a present value of the first year divided by the rate less the growth. So 349,531 equals 11,119 divided by 0.08 minus g. Solving, g is 4.8 percent.
Reading the answer
The price requires residual income to grow at about 4.8 percent a year, forever, at an 8 percent cost of equity. Change the charge and the condition changes with it, which is why the rate is quoted next to the answer and never left implied.
Turning it into something testable
The value of this output is that it is a claim about the world with a date on it. Residual income growing at 4.8 percent a year forever, with book value compounding underneath it, is a statement you can hold against what the company has actually filed for ten years, and against the return it earns on each new dollar it retains.
That is the useful form of the question. Not "is this price right", which nobody can answer, but "what would have to keep being true", which the filings can speak to. It is also the shape a written thesis takes: a condition, a level, and a way to know when it has stopped holding.
Two checks make the condition concrete. The first is arithmetic: residual income can only grow if book value grows, if the return on that book stays high, or both, so an implied growth rate is also an implied statement about reinvestment and the return earned on it. The second is historical: compute residual income for each of the last ten filed years and look at the rate it actually grew at. If the price requires 4.8 percent and the filed decade produced something far from that, you have not found a mistake in the market. You have found the exact question to go and answer, which is usually a question about the business rather than about the arithmetic.
One warning about the stability of this output. The subtraction that starts it takes a small number away from a large one, so both halves matter. Book value here is 8 percent of market value, and a fall of a third in the share price would leave the implied stream needing roughly a third less. An implied growth rate is therefore a reading taken on a date, and it belongs next to that date whenever it is quoted or written into a thesis.
Check yourself
What does market value less book value represent in this model?
- The company's goodwill
- The present value of all future residual income that the price implies
- The accumulated dividends
Show the answer
Answer: B.
Book value is the anchored first term. Everything the market pays above it is payment for earnings above the charge, discounted.At a 9 percent cost of equity instead of 8 percent, the growth the same price requires moves from 4.8 percent to what?
- 3.7 percent
- 5.9 percent
- It does not move
Show the answer
Answer: B.
A higher charge lowers this year's residual income and raises the discount rate, so the same price requires faster growth: 5.9 percent.What is the honest use of an implied growth rate?
- Deciding whether to buy the share
- Stating a condition that can be tested against filed history and watched afterwards
- Forecasting next year's share price
Show the answer
Answer: B.
The output is a condition, not a verdict. Its value is that a filing can speak to it, and that you can write down when it stops holding.Sources
- The Coca-Cola Company, Form 10-K for fiscal 2025, filed 2026-02-20, accession 0001628280-26-010047. Net income and equity read from the SEC XBRL company facts API on 2026-09-13.
- This site's company catalogue, built 2026-09-16 from prices last stored on 2026-09-15, for the market capitalisation.
- Mauboussin and Rappaport, Expectations Investing, 2001, on solving for the expectations already in a price.
What this leaves out
- A constant growth rate forever is a modelling convenience. No company grows at one rate forever, and a fading stream gives a different implied number.
- The market capitalisation is a stored figure from the date shown, not a live quote. Prices move and the implied condition moves with them.
- The cost of equity is chosen. Every implied growth rate on this page is conditional on it.
- This is arithmetic on a price, not a view on a security, and nothing here is advice.