Discounted cash flow valuation: from forecasts to a value per share
A discounted cash flow valuation turns a forecast into a price in four steps: forecast the cash, discount it, add what the business holds and subtract what it owes. This lesson runs the whole chain for Apple with a calculator, shows how the answer moves with each input, and ties growth to the investment needed to deliver it.
- Level
- Beginner
- Reading time
- About 28 minutes
- Know this first
- Forecasting and terminal value
By the end you will be able to:
- turn forecast free cash flows and a terminal value into an enterprise value
- bridge from enterprise value to equity value and a value per share
- link growth to reinvestment and the return on new investment
- read a sensitivity table and say which inputs move the answer most
From a forecast to a price
A discounted cash flow valuation, usually shortened to DCF, answers one question: what is a stream of future cash worth today? The earlier lessons in this module supplied the parts. Free cash flow to the firm says how much cash a business frees. The forecast and terminal value turn it into a stream that runs for ever. The weighted average cost of capital supplies the rate at which that stream is discounted. This lesson joins them, adds the last two steps that turn the value of a business into the value of a share, and runs the whole chain for Apple.
A DCF does not produce a fact. It produces a value that follows from a set of assumptions, and its worth lies in showing which assumptions matter. So the lesson also shows how the answer moves, and ties growth, which a forecast simply states, to the investment needed to deliver it.
The four steps
The enterprise value is the value of the business to lenders and owners together, so it ignores how the business is financed. To reach the value of the owners' share alone, add what the business holds that is not part of its operations, mainly cash and marketable securities, because they belong to the owners too, and take off what is owed to lenders. What is left is the equity value. Dividing it by the number of shares gives the value of one share.
Growth has to be paid for
A forecast that simply says cash flow will grow 8% a year hides a question: what does the business have to spend to grow that fast? Growth needs new investment, in plants, stock and people, and the cash for it comes out of what would otherwise be free cash flow. The link between them is one of the most useful ideas in valuation:
A business that reinvests 40% of its after-tax profit and earns 15% on new investment grows 6% a year. If it earns only 8% on new investment, the same reinvestment gives 3.2% growth. In the other direction, to grow 6% while earning 8% on new investment it must reinvest 75% of profit and pay out a quarter. The calculator below uses this structure. In the five forecast years you choose growth and the share of profit reinvested, and the ledger shows the return on new investment they imply. After year 5 you choose long-run growth and the return on new investment, and the reinvestment rate follows as growth divided by that return.
The return on new investment has a special role. If new investment earns exactly the cost of capital, growth adds nothing to value: the business spends a dollar to get a dollar's worth. Growth creates value only when new investment earns more than the cost of capital. A terminal growth rate with a low return on new investment adds little, and one with an enormous return, held for ever, adds a lot that competitors would be expected to compete away.
Apple's starting point
The calculator is set up for Apple, using figures from the previous lessons. The starting profit is NOPAT of $112.28 billion for fiscal 2025. Over fiscal 2024 and 2025 together Apple reinvested 9.9% of its NOPAT, so the starting reinvestment rate is 10%. The discount rate of 8.9% is the market-weighted cost of capital from the lesson on the weighted average cost of capital, 8.85%, rounded; that lesson used a cost of equity of 9% as an illustration, and the rate here inherits that. Net cash is $33.76 billion: cash and marketable securities of $132,420 million less debt of $98,657 million. Shares are the 14.776 billion outstanding at 17 October 2025.
Run the valuation
Set growth in after-tax operating profit for the five forecast years, long-run growth after that, the discount rate, the share of profit reinvested in the forecast years, and the return that new investment earns after year 5. The left page builds the enterprise value. The right page bridges to the value of a share and compares it with the market value of about $3,253 billion. Cash arrives at the end of each year. Figures are rounded to one decimal, so a column can differ from its total by 0.1.
Discounted at 8.9%, the business is worth $1,841.9 billion, and with $33.8 billion of net cash the shares are worth $1,875.7 billion, or $126.94 each. That is 42.3% below the market value of about $3,253 billion.
Six experiments. First, the starting settings give an enterprise value of $1,841.9 billion, an equity value of $1,875.7 billion and $126.94 a share, 42.3% below the market value. 75.4% of the enterprise value comes from after year 5. Second, set the return on new investment after year 5 to 9%, close to the cost of capital: the value per share falls to $106.67, because the growth now costs as much as it earns. Third, raise it to 50%: $136.89, since each dollar of growth now comes cheap. Fourth, move the discount rate to 7%, which gives $185.95, and to 11%, which gives $94.30. Fifth, set growth in years 1 to 5 to 0%, giving $102.58, then to 12%, giving $169.26. Look at the last line of the right-hand page as you do: at 12% growth and 10% reinvested, new investment would have to earn 120% a year, a sign that the combination is not credible. Sixth, return growth to 5% and set the reinvested share to 30%. The value per share falls to $120.12, because the same growth now takes much more of each year's profit.
Apple at the starting settings
The table sets out the whole chain in billions of dollars. Enterprise value is the sum of the two present values, $453.5 billion for years 1 to 5 and $1,388.4 billion for everything after. Cash and marketable securities of $132,420 million are added and debt, commercial paper plus term debt, of $98,657 million is taken off, leaving the equity value. Dividing by the 14.776 billion shares gives the value of a share.
| Apple, billions of US dollars | Default settings |
|---|---|
| Present value of years 1 to 5 | 453.5 |
| Present value of the terminal value | 1,388.4 |
| Enterprise value | 1,841.9 |
| Add: cash and marketable securities | 132.4 |
| Less: commercial paper and term debt | (98.7) |
| Equity value | 1,875.7 |
| Shares outstanding, billions | 14.776 |
| Value per share, $ | 126.94 |
| Market value of shares held outside the company, 28 March 2025 | 3,253.4 |
| Market value per share, $ (that value divided by shares at 17 October 2025) | 220.18 |
The comparison with the market is the last two lines. The market value of the shares held outside the company on 28 March 2025 was $3,253,431 million, or about $220 a share on the 10-K cover share count. Two cautions apply to that comparison. The market value is from March 2025, six months before the fiscal year end, and the shares outstanding are from October 2025, so the per-share figure is approximate. And the starting inputs are an illustration of method, not a forecast.
How far the answer moves
No single DCF value deserves much trust, so careful work always shows a range. The first table holds growth in the five forecast years at 5% and changes the two assumptions behind the terminal value. The second holds long-run growth at 3% and changes growth in years 1 to 5 against the discount rate. Cells are values per share in dollars.
| Discount rate | Long-run growth 2% | Long-run growth 3% | Long-run growth 4% |
|---|---|---|---|
| 7% | 162 | 186 | 226 |
| 8% | 135 | 149 | 171 |
| 8.9% | 117 | 127 | 140 |
| 10% | 101 | 107 | 116 |
| 11% | 90 | 94 | 100 |
| Growth in years 1 to 5 | Discount rate 8.0% | Discount rate 8.9% | Discount rate 10.0% |
|---|---|---|---|
| 0% | 120 | 103 | 87 |
| 3% | 137 | 117 | 99 |
| 5% | 149 | 127 | 107 |
| 8% | 170 | 144 | 121 |
| 12% | 200 | 169 | 142 |
The ranges are wide. In the first table a two-point change in the rate moves the value far more than a one-point change in long-run growth, and the two compound. In the second, moving the rate from 8.0% to 10.0% at 5% growth takes the value from $149 to $107, and it takes growth in the first five years rising from 0% to 8% a year, from $103 to $144, to add as much at an 8.9% rate. Only one cell in either table, a 7% rate with 4% growth for ever, at $226, reaches the market's roughly $220 a share. Reading what a price assumes in this way is the subject of the final lesson.
What to make of a gap with the market
The starting settings put Apple's value well below its market value. That is a statement about the settings, and there are several honest ways to read it. The discount rate comes from an illustrative cost of equity, and a lower true cost of capital would raise the value a lot. Growth of 5% for five years is modest next to some of the history: Apple's net sales grew 4.2% a year over fiscal 2023 to 2025, but its operating income grew 8.0% in fiscal 2025 alone, and the business is shifting toward higher-margin services. The reinvestment rate is an average of two noisy years. And buyers may expect a very long period of high returns, which a five-year forecast cannot capture. None of these is a reason to expect the market to be wrong or right. Each is a reason to look at the inputs before looking at the output.
What a DCF cannot tell you
- It is only as good as its inputs. The rate, long-run growth and margins are judgements, and the output moves a lot with each.
- Precision is false comfort. A value to the cent from a model with these inputs describes the arithmetic, not the business.
- Employee share awards are left out of the share count. Treating share-based pay as a cost in the cash flows, as the first lesson did, covers awards to come. Awards already granted and unvested are claims on the equity that this calculator ignores.
- Leases and other obligations need a rule. Apple's lease liabilities are not in the debt figure here, consistent with lease payments being treated as running costs.
- The balance sheet date matters. Cash and debt at a different date from the cash flows can distort the bridge.
From enterprise value to equity value in three balance sheets
A discounted cash flow gives the value of the whole operating business, the enterprise value. To reach a value for shareholders it has to be bridged to equity, adding what the company owns that is not in the operating cash flows and subtracting what is owed to others. The items depend on the balance sheet. The table lists the main bridge items for Apple, Microsoft and Toyota.
| Latest balance sheet, millions | Apple | Microsoft | Toyota |
|---|---|---|---|
| Cash and investments | $132,420 | $94,565 | ¥8,982,404 |
| Borrowings | $98,657 | $43,151 | ¥38,792,879 |
| Net cash (net debt) | $33,763 | $51,414 | ¥(29,810,475) |
| Non-controlling interests | none reported | none reported | ¥954,088 |
| Equity-method investments | not shown separately | $15,405 | ¥5,798,051 |
| Financial services receivables | none | none | ¥33,625,035 |
Apple and Microsoft are simple: both hold more cash and investments than borrowings, so the bridge adds a net cash balance of $51,414 million at Microsoft and a smaller one at Apple, and neither reports a non-controlling interest. Toyota has several extra items. Borrowings far exceed cash, but they fund a finance arm whose receivables of ¥33,625,035 million would be valued as part of that business. Non-controlling interests of ¥954,088 million belong to outside shareholders in subsidiaries whose cash flows are fully included, so their share has to be taken off. Equity-method investments of ¥5,798,051 million (6.2% of total assets) are companies whose profit is not in operating cash flow, so they are added at an estimate of their own value.
Which share count
The last step divides equity value by the number of shares, and there are several to choose from. Microsoft's income statement uses 7,465 million diluted shares for the year, which includes shares that could be issued under employee awards, while the cover of its annual report gives 7,433.2 million shares outstanding at 24 July 2025. The two differ because one is an average for the year including dilution, and the other is a count on a date after repurchases. Toyota holds ¥4,415,943 million of its own shares as treasury stock, and those shares must not be counted as outstanding. The most careful choice is the latest count of shares outstanding plus the dilution from awards that are likely to be exercised.
Accounting differences that reach the model
A valuation model uses reported numbers, so the accounting standard shows through. Research and development is expensed at US GAAP companies such as Microsoft and Apple, which lowers reported operating profit and the capital base; under IFRS some development costs are capitalised. Impairment losses can be reversed under IFRS but not US GAAP. Neither difference changes the cash a business generates, so a model built on cash flows is less affected than one built on profit, and this is one of the arguments for valuing cash flows. But the reinvestment rate and the return on capital in the terminal value are both calculated from accounting numbers and are sensitive to these rules.
Common mistakes
Forecasting growth without the investment behind it
High growth with a low reinvestment rate means new investment earns a return no competitor would allow to last.
Mixing the discount rate and the cash flow
Free cash flow to the firm is discounted at the cost of capital. Cash flow after interest goes with the cost of equity.
Forgetting the bridge
The discounted cash flows give the value of the business. Cash is added and debt subtracted before dividing by shares.
Taking one answer as the answer
A DCF is a range. Show how the value moves with the rate and growth.
Comparing a value per share with a price from a different date
The share price, share count and balance sheet should be from the same date, or the gap is partly timing.
Try it yourself
1. A business has an enterprise value of $5,000 million, cash of $400 million and debt of $900 million, and 200 million shares. What is the value per share?
Show the working
Equity = 5,000 + 400 − 900 = $4,500 million. Per share = 4,500 ÷ 200 = $22.50.
2. A business reinvests 30% of its after-tax profit and earns 20% on new investment. At what rate does it grow?
Show the working
Growth = 30% × 20% = 6% a year.
3. A business expects to grow 4% a year for ever and new investment earns 16%. What share of its after-tax profit must it reinvest?
Show the working
Reinvestment rate = growth ÷ return = 4% ÷ 16% = 25%. Free cash flow is 75% of NOPAT.
4. New investment earns exactly the cost of capital. Does faster growth raise the value?
Show the working
No. Each dollar invested for growth is worth a dollar. Faster growth only adds value when new investment earns more than the cost of capital.
Where this is used
- An analyst values a listed company and compares the result with its share price.
- A buyer values a target to decide how much to offer.
- A company values a division before a sale or a spin-off.
- An investor in a private company values its stake when there is no market price.
Key terms
- Discounted cash flow (DCF)
- A valuation that discounts forecast cash flows to a present value.
- Enterprise value
- The value of the whole business to lenders and owners together.
- Equity value
- Enterprise value plus cash and securities less debt: the value of the owners' stake.
- Net cash
- Cash and securities less debt.
- Reinvestment rate
- The share of after-tax operating profit put back into the business.
- Return on new investment
- The after-tax operating profit earned on each dollar of new investment.
- Sensitivity table
- A table showing how a result changes as two inputs vary.
Questions people ask
Why value the business first and the shares second?
Because the cash flows of the business belong to lenders and owners together. Valuing them first keeps the result independent of the debt, and the bridge then divides it between lenders and owners.
Is a DCF better than a multiple?
It makes every assumption visible, which a multiple does not. It is also easier to bend to a conclusion. Each is a check on the other.
Why does the discount rate matter so much?
Most of the value lies in distant cash flows, and a small change in the rate compounds over many years.
What if the result is far from the market price?
Look at the inputs first. The gap is the sum of every difference between the assumptions used and the ones the market holds, and the final lesson shows how to read it.
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 shares outstanding and the market value of shares held by non-affiliates.
- Corporate Finance Institute, Free cash flow to firm (FCFF), for free cash flow to the firm in a DCF.
- eFinancialModels, Gordon growth model and terminal value, which notes that the method ignores return on invested capital and points to the value driver model used here.
- 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 Apple's statements.
- 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).
- Toyota Motor Corporation, FY2025 Financial Summary (IFRS, unaudited, in millions of yen), furnished to the US Securities and Exchange Commission on Form 6-K. Source of Toyota's statements.
- PwC, IFRS and US GAAP: Similarities and differences, internally developed intangible assets, for research and development costs.
- Deloitte, Roadmap: IFRS and US GAAP comparison, 1.7 Impairment of nonfinancial assets, for the impairment tests and the reversal of losses.
How the numbers were checked: Apple's statements were tied out by code, and NOPAT, net cash and shares in the calculator were asserted equal to the filed figures. The calculator was tested against separate arithmetic for more than a thousand combinations of inputs, including the bridge from enterprise value to equity value to value per share, and every figure in the tables above was recomputed from the same function.