Lesson A1.5 · 5 of 5 · Valuation
Valuation scenarios: expected value and reverse DCF, step by step
Valuation scenarios replace a single figure with three stories about the future, each with its own assumptions and probability. Expected value is the probability-weighted average of the values. Sensitivity analysis shows which assumption matters most, and a reverse DCF starts from the price and tells you what growth the market is assuming.
Terms in this lesson
- DCF
- Today's value of all the cash a company will produce in the future.
- Fair value
- What a stock should be worth, based on the business behind it.
- WACC
- What the money the company runs on costs it, on average.
Bear, base and bull cases, with probabilities
In the margin of safety lesson you combined the ends of each range to see how wide the answer could be. A scenario goes further: it is a consistent story about the business in which the assumptions move together. In a recession, growth slows and the return investors demand for risk rises at the same time.
| Scenario | Growth, years 1-5 | Rate | Long-term growth | Value per share |
|---|---|---|---|---|
| Bear (25%) | 0% | 11% | 1% | £16.72 |
| Base (50%) | 5% | 10% | 2.5% | £30.47 |
| Bull (25%) | 10% | 9% | 3% | £50.27 |
Illustrative example: a company with base-year FCFF of £100m, net debt of £300m and 40m shares. Each value is a full DCF, as in the chapter’s first lesson. Our calculations.
Definition
How is expected value calculated?
Multiply each value by its probability and add them up.
0.25 × 16.72 + 0.5 × 30.47 + 0.25 × 50.27 = £31.98. The probabilities are assumptions too: state them and test them. Expected value lands above the base case because the bull case is further from it (+£19.80) than the bear case (-£13.75). Note the bear case alongside it: it tells you how much you could lose if it comes true.
The illustrative company in the table.
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Create a free accountSensitivity analysis: which assumption matters most
Sensitivity analysis changes one assumption at a time and holds the rest still. It shows you where to spend your time: on the assumption that moves value most. In the Apple model (as at 31 December 2025, base value $123.56), each assumption is moved up and down.
| Assumption changed | Down | Up |
|---|---|---|
| Growth in years 1-5: 4% / 8% (from 6%) | $113.82 (-7.9%) | $134.01 (+8.5%) |
| Long-term growth: 2% / 4% (from 3%) | $111.36 (-9.9%) | $139.99 (+13.3%) |
| WACC: 10.75% / 8.75% (from 9.75%) | $107.87 (-12.7%) | $144.71 (+17.1%) |
Each row changes only its own assumption; the rest stay as in the base model. Our calculations.
Reverse DCF: what growth the share price builds in
Definition
What does a reverse DCF do?
It starts from today’s price and finds the assumption that justifies it.
You keep the model and every assumption but one, usually growth. Then you solve for the value of that one which makes value per share equal the price. The question is no longer “what is it worth?” but “what would someone have to believe to pay this price?”. You then compare the answer with the company’s history and with what is plausible for its business.
All three start from the Apple model, with the closing price on 31 December 2025 and long-term growth of 3%; the first two keep the 9.75% WACC. Put another way, in this model the price at the time implied cash flow growth above 15% a year for a decade, or far less risk than CAPM suggests, or some mix of the two. Apple’s revenue grew 6.4% in financial year 2025. Whether growth like that is plausible is your call: a reverse DCF simply puts the assumption in plain sight.
A full example: Apple scenarios with probabilities
| Apple, 31 December 2025 | Growth, years 1-5 | WACC | Long-term growth | Value |
|---|---|---|---|---|
| Bear (25%) | 3% | 10.75% | 2% | $87.73 |
| Base (50%) | 6% | 9.75% | 3% | $123.56 |
| Bull (25%) | 10% | 8.75% | 3.5% | $183.82 |
| Expected value | $129.67 |
The assumptions and probabilities are our choices, for the exercise. Base-year FCFF of $102.0bn, net debt and the diluted share count are those from the DCF lesson. Closing price on 31 December 2025: $271.86.
Real case
Apple: our scenarios against the price
When all your scenarios land far from the price, the useful question is what the market sees that you do not, or what you see that the market does not. The analysis page shows Apple’s growth and margins over several years, so you can judge your assumptions yourself.
Lessons are educational. They are not a recommendation to buy or sell. Investing involves risk and you can lose money. Sources: the Apple DCF model from the DCF lesson (Apple, Form 10-K for the financial year ended 27 September 2025: operating income, tax, depreciation and amortisation, capex, working capital, net sales $416,161m and $391,035m; Form 10-Q for the quarter ended 27 December 2025: borrowings, cash, shares); the WACC from the cost of capital lesson (US Treasury and Aswath Damodaran, January 2026 data); closing price on 31 December 2025: Yahoo Finance. The sterling company is illustrative; the scenarios, probabilities and calculations are ours.