What a share price implies: running a valuation backwards
A valuation normally turns forecasts into a price. A reverse valuation does the opposite: it takes the price as given and asks what the business must deliver for that price to be fair. This lesson solves for the growth Apple's market value implies, shows how much the answer depends on the discount rate, and compares it with what Apple has actually done.
- Level
- Beginner
- Reading time
- About 26 minutes
- Know this first
- Valuation multiples
By the end you will be able to:
- solve for the growth that makes discounted cash flows equal a market value
- explain why the answer depends on the discount rate and long-run growth
- compare implied growth with a company's record and say what the comparison can and cannot show
- use a reverse valuation to turn a price into a testable claim
Reading a price as a set of expectations
Most valuation runs forwards. An analyst forecasts a business, discounts the cash flows and arrives at a value, which is then set beside the market price. That sets one opinion, the analyst's, against another, the market's, and the opinions are hard to compare because the market never explains itself. A reverse discounted cash flow runs the same valuation backwards. It takes the market price as given, holds the discount rate and the long-run assumptions fixed, and solves for the growth that makes the cash flows add up to the price. The answer is a statement of what the price expects of the business.
That turns a price from a number to argue about into a claim to check. It does not say the market is right or wrong. It says what has to come true if the market is right, and that can be set against what the company has actually done. This lesson runs the method on Apple, shows how much the answer depends on the discount rate, and compares it with Apple's record.
The method
The forward valuation of the previous lesson takes a set of inputs and produces a value. The reverse method keeps every input but one, growth in the five forecast years, and asks for the value of that one that makes the output equal the market's enterprise value. There is no tidy formula to solve for it, because growth enters the value through five compounding years and a terminal value. The solution is found by trial: try a growth rate, see whether the value is above or below the price, and adjust until the two agree. A spreadsheet's goal seek does this, and so does the calculator below, which tests 200 successive halvings of the range between −50% and 100% a year.
The same trick works on any input. Hold growth at a figure from the company's record and solve for the discount rate, and the answer is the rate at which the market is willing to pay the price for that growth. Hold both and solve for long-run growth, and the answer is what the market assumes about the business after the forecast.
The steps, then, are these: fix the cost of capital, the reinvestment needed, the long-run growth and the return on new investment, as in the discounted cash flow lesson; set the target at the market enterprise value; solve for yearly growth in after-tax operating profit for five years. For Apple the target is the enterprise value of $3,219,668 million from the multiples lesson, which is $3,219.7 billion, and the starting profit is the $112.3 billion of after-tax operating profit for fiscal 2025.
Solve for the growth in the price
Set the market value of the business and the assumptions held fixed. The left page shows the growth that is needed in each of five years, and what it does to profit. The right page shows what the price rests on: the value the business would have with no growth in the five years, and the share of the value that comes from after year 5. If no growth rate between −50% and 100% a year can make the numbers meet, the ledger shows n/a.
To be worth $3,220 billion with a cost of capital of 8.9%, after-tax operating profit has to grow 18.7% a year for five years, from $112.3 billion to $264.3 billion. With no growth in those five years the business would be worth $1,482 billion.
Six experiments. First, at the starting settings, an 8.9% discount rate, 3% growth for ever and new investment earning 20% after year 5, the market value of $3,219.7 billion requires growth in after-tax operating profit of 18.7% a year for five years. Profit rises from $112.3 billion to $264.3 billion, 2.35 times today's. Second, look at the right-hand page. With no growth at all in the five years the business would still be worth $1,481.9 billion at these settings, 46% of the market value, and 79.5% of the value comes from the years after year 5. Third, lower the discount rate to 7%. The growth needed falls to 8.9% a year, and at 10% it rises to 23.4%. Fourth, raise long-run growth to 4% and the rate to 7%: the growth needed falls to 4.4%. Fifth, set the return on new investment after year 5 to 50%, which makes growth cheaper: the needed growth falls to 16.6%. Sixth, lower the market value to $2,000 billion and the growth needed becomes 6.9%.
The discount rate does most of the work
The table repeats the exercise for Apple's market value across a range of discount rates and long-run growth. Each cell is the yearly growth in after-tax operating profit, for five years, that makes the discounted cash flows equal $3,220 billion.
| Discount rate | Long-run growth 2% | Long-run growth 3% | Long-run growth 4% |
|---|---|---|---|
| 7% | 12.4% | 8.9% | 4.4% |
| 8% | 17.1% | 14.4% | 10.9% |
| 8.9% | 20.9% | 18.7% | 15.9% |
| 10% | 25.2% | 23.4% | 21.3% |
The same price implies very different things depending on the rate. At a 7% discount rate with 4% growth for ever, five years of growth of 4.4% a year does it. At 10% with 2% growth for ever, it takes growth that few businesses of this size have managed. So the claim made by a price is really a pair: a rate and a growth path. A reader who disagrees with the growth should check whether the real disagreement is about the rate.
Comparing the price with Apple's record
The implied growth means little until it is set beside what the company has done. Apple's net sales were $383,285 million in fiscal 2023 and $416,161 million in fiscal 2025, a rise of 4.2% a year. Products, at $307,003 million, grew 4.1% in fiscal 2025, and services, at $109,158 million and 26% of sales, grew 13.5%. Operating income grew 8.0% in fiscal 2025.
After-tax operating profit grew faster, by 20.0%, from $93,532 million to $112,281 million. But that increase is flattered by tax. The fiscal 2024 effective rate was 24.1% because it included the one-time State Aid charge, against 15.6% in fiscal 2025, so a good part of the rise is a lower tax bill, not a larger business. The operating income figure is the cleaner guide.
Against that record, the starting settings require growth of 18.7% a year for five years, more than double the 8.0% operating income growth of the latest year and several times the growth of sales. If growth were 8.0%, five years of it at these settings gives an enterprise value of $2,091.3 billion, which is 35.1% below the market's.
What the gap can mean
There are three ways to close the gap between what the price needs and what the record shows, and a reader should say which one they are choosing.
A lower discount rate. Holding growth at the recent 8.0%, the discount rate that makes the numbers meet is 6.8%, well below the 8.9% used here. Since the 8.9% rests on an illustrative cost of equity of 9%, the question becomes whether a rate near 6.8% is fair for a business of Apple's stability, which the inputs of the CAPM lesson can be used to test.
More generous long-run assumptions. A higher long-run growth rate or a higher return on new investment makes the business worth more after year 5, and so needs less growth before it. At 7% and 4% growth for ever, five years of 4.4% growth is enough.
A longer period of strong growth. Five years was chosen for tidiness. Ten years of slower growth, say, can reach the same value as five years of faster growth. The calculator cannot show that, and a fuller analysis would.
None of this is advice about Apple's shares, and the reverse method does not produce one. What it does is turn an argument about whether a price is too high into an argument about the assumptions, which can be checked against results quarter by quarter.
What a reverse DCF cannot tell you
- It depends on the fixed inputs. Change the discount rate, the horizon or the terminal assumptions and the implied growth changes with them.
- It summarises, and may not match anyone's view. Different investors hold different expectations. The implied growth is a figure that fits the price, not a forecast anyone has made.
- It uses a single growth rate. A real path may start fast and slow, or the reverse, and the summary figure hides the shape.
- The price is a moving target. The market value used here is from March 2025, and a price moves every day.
- It is not a verdict. A price that implies unusual growth may still be right, and one that implies little may still be wrong.
What Microsoft's market value implies
A reverse discounted cash flow runs the valuation backwards: instead of forecasting growth and finding a value, it takes the market value and finds the growth that would be needed to justify it. The lesson uses Apple. The same method can be applied to Microsoft, with the figures approximate and dated: a market value of $3,100,000 million, the figure stated on the cover of its annual report for shares held by outsiders at 31 December 2024, an enterprise value of $3,048,586 million once its net cash is taken off, and the after-tax operating profit of $105,869 million. The assumptions are the lab's: a cost of capital of 8.9%, terminal growth of 3% and a return on new investment of 20%. The only thing that varies in the table is the share of profit reinvested over the first five years.
| Share of operating profit reinvested in years 1 to 5 | Growth each year for five years that the market value implies |
|---|---|
| 10.0% | 18.8% |
| 20.0% | 19.4% |
| 33.8% | 20.2% |
The market value implies after-tax operating profit growing by about 18.8% to 20.2% a year for five years, depending on how much is reinvested. Microsoft's actual reinvestment rate in its latest year was 33.8%, which gives 20.2%. For comparison, its revenue grew 14.9% and its operating profit 17.4% in that year. The market value is therefore consistent with growth that is about as fast as last year's, sustained for five years, and then settling to 3%. Apple's calculator, at its default settings, lands in a similar place.
Reading the result across companies
A reverse DCF does not say that a price is right or wrong. It gives a number to test against your own view: is five years of growth near 20% plausible for a business of this size? The answer depends on competition, the size of the market and the company's ability to keep reinvesting at high returns. If the implied growth looks achievable, the price is not demanding; if it looks beyond anything the company has done, the price assumes more than the record supports.
Three cautions apply in the international setting. The cost of capital must belong to the currency of the cash flows. The market value must be taken on a date close to the accounts, which these approximations are not. And the net cash and share count must follow the company's own accounting, including any non-controlling interests, equity-accounted holdings or treasury shares, which appear on IFRS balance sheets such as Toyota's. With those checks, the same reverse calculation can be applied to a company anywhere.
Common mistakes
Treating the implied growth as the market's forecast
It is the growth that fits the price under the assumptions chosen. Another set of assumptions gives another answer.
Ignoring the discount rate
A change of a point or two in the rate shifts the implied growth more than most debates about growth itself.
Comparing implied growth with the wrong record
Profit growth flattered by a falling tax rate, or sales growth that ignores margins, is the wrong yardstick. Use the measure the model uses, after-tax operating profit, and check one-off items.
Stopping at the answer
The point of the method is the comparison with the record and with the alternatives, not the number.
Using it to claim a price is wrong
It can show that a price needs a great deal to go right. Whether it will is a separate judgement.
Try it yourself
1. A business is worth $1,000 million. Its free cash flow next year is expected to be $50 million and the discount rate is 9%. What growth for ever does the price imply?
Show the working
Value = cash flow ÷ (r − g), so g = r − cash flow ÷ value = 9% − 50 ÷ 1,000 = 4%.
2. Same business, but $50 million is this year's cash flow, which will grow at g next year. What growth does the price imply?
Show the working
1,000 = 50 × (1 + g) ÷ (0.09 − g). Rearranged, g = (1,000 × 0.09 − 50) ÷ (1,000 + 50) = 3.81%.
3. Why does a lower discount rate reduce the growth a price implies?
Show the working
A lower rate raises the present value of any growth path, so less growth is needed to reach the same price.
4. A price implies 15% growth for five years but the business has grown 6% a year. Name three ways the gap might be explained.
Show the working
The market may use a lower discount rate than the model. It may assume higher long-run growth or returns after the forecast. Or it may expect a longer period of above-average growth than five years. Each is a claim that can be examined.
Where this is used
- An investor tests what a share price assumes before deciding whether the assumptions are reasonable.
- A board checks what its own share price implies about expected growth, as one input to decisions on buybacks or acquisitions.
- A reviewer of an analyst's report asks what growth the target price needs.
- A lender or buyer in a deal tests what a negotiated price assumes.
Key terms
- Reverse DCF
- A discounted cash flow solved backwards: the price is given and an input, usually growth, is solved for.
- Implied growth
- The growth that makes discounted cash flows equal the market value.
- Market-implied expectations
- What a price assumes about future cash flows.
- Goal seek
- Trial-and-error solving for the input that gives a chosen output.
- Implied discount rate
- The rate at which a stated forecast is worth the market price.
- Hold constant
- To keep an input fixed while another is solved for.
Questions people ask
Does a reverse DCF tell me whether to buy a share?
No. It shows what a price assumes. Whether the assumptions are likely is a judgement the method leaves to the reader, and nothing in this module is investment advice.
Why hold the discount rate fixed instead of solving for it?
Either is allowed. Solving for growth is common because growth can be compared with a record. Solving for the rate shows how low the market's rate would have to be if growth is held to the record, as the lesson did.
Why five years?
It is a convention. A longer horizon at lower growth can give the same value, so the implied rate should not be read as a forecast for exactly five years.
What if the implied growth is negative?
Then the price assumes the business will shrink, or that the discount rate and long-run assumptions are harsher than the model's. It is also a useful result: it says the price expects little.
Sources and review
- Apple Inc., Form 8-K, Exhibit 99.1: fourth quarter and full-year fiscal 2025 results, filed with the US Securities and Exchange Commission. Source of the income statement, balance sheet and cash flow statement figures.
- Apple Inc., Form 10-K for the fiscal year ended 27 September 2025. Source of the market value of shares held by non-affiliates at 28 March 2025.
- New Constructs, What is a reverse DCF model?, for the idea of working backwards from prices to the cash flow expectations they contain.
- Microsoft Corporation, Form 8-K, Exhibit 99.1: fourth quarter and fiscal year 2025 results, filed with the US Securities and Exchange Commission. Source of Microsoft's statements.
- Microsoft Corporation, Form 10-K for the fiscal year ended 30 June 2025. Source of the market value of shares held by non-affiliates at 31 December 2024 (stated as $3.1 trillion) and of the shares outstanding at 24 July 2025 (7,433,166,379).
How the numbers were checked: Apple's sales, operating income and tax rates were rebuilt from the filed statements. The implied growth shown by the calculator was put back through a separate forward valuation for more than a thousand combinations of inputs and reproduced the target value to eight decimal places each time, and the discount rate that fits a given growth figure was checked the same way. Every cell in the table was recomputed in plain code.