---
title: "What is a DCF? What a corner shop is worth"
description: "One fictional convenience store, valued step by step with a discounted cash flow: three growth assumptions take it from $1,000K to $3,582K."
date: 2026-10-08
updated: 2026-10-09
tags: [dcf, valuation, basics]
author: "Allen Yan"
image: https://sweetvaluelab.com/blog/img/63ef2b0c22d01a2f.png
lang: en
canonical: https://sweetvaluelab.com/blog/what-is-a-dcf
---

A DCF, a discounted cash flow valuation, values a business by taking the cash it can hand out in the future, converting each year's cash into today's money, and adding it up. It is how Warren Buffett defines intrinsic value in Berkshire Hathaway's Owner's Manual: the discounted value of the cash that can be taken out of a business during its remaining life. He adds that the definition is simple and the calculation is not.

This post works one through from the start. The business is a fictional neighbourhood convenience store, and every amount is in thousands of dollars ($K). It is the same store, with the same numbers, as a talk given on 2026-10-10; the slides (in Chinese) are [here](https://sweetvaluelab.com/slides/zh/dcf-valuation-101).

## Step 1: The discount rate, or what $100 next year is worth today

The discount rate r is the annual rate used to turn money in the future into money today.

The basic reference point is the risk-free rate, usually the yield on the 10-year US Treasury. On 2026-10-07 it was 5.28%: lend to the US government, with next to no risk of default, and you collect 5.28% a year.

- $100 put into Treasuries today becomes 100 × 1.0528 = $105.28 in a year.
- Going the other way, $100 that arrives a year from now is worth 100 ÷ 1.0528 = $94.98 today.

The same $100 is worth about $5 less for arriving a year later. That is discounting. A year forward you multiply by (1 + r), a year back you divide by (1 + r): discounting is compounding run backwards.

A stock or a small business is not as safe as a Treasury. Its cash flow can shrink or disappear, so you ask for more than the Treasury pays:

```
r = risk-free rate + risk premium
```

The riskier the business, the bigger the premium. For the store we take 5% (Treasuries) plus 5% (the premium for a small shop), so r = 10%, and that is the rate used throughout. In practice the premium comes from CAPM and WACC, which this post leaves out.

## Step 2: Free cash flow, the cash a DCF discounts

There are several candidates for "the company's future cash". A DCF uses the last one:

| Candidate | The problem |
|---|---|
| Dividends | How much to pay out is the company's choice, and many pay nothing; Amazon has never paid a regular dividend |
| Net income | An accounting profit, which does not match the cash coming in |
| Operating cash flow (CFO) | Cash, but before the spending needed to keep the business running |
| **Free cash flow (FCF)** | The cash left after capital spending, free to pay dividends, buy back shares, repay debt or keep |

Net income is the one that trips people up, so two examples from the store. Replace the fridges for $100K this year and the cash leaves this year, while the income statement depreciates them over five years at $20K a year. Afternoon snacks for the office block next door, billed monthly, count as profit the month they are delivered, and the cash arrives the following quarter. Operating cash flow starts from net income and turns those back into cash:

```
CFO = net income + depreciation and amortisation ± change in working capital
FCF = CFO − CapEx
```

CapEx is capital spending: a new fridge counts, and so does a new till. Textbooks distinguish FCFF from FCFE; this post uses the simpler CFO − CapEx and deals with cash and debt separately in Step 8.

## Step 3: A neighbourhood convenience store, and what it is worth

Roughly, the store's year looks like this:

| Line | $K a year |
|---|---|
| Revenue | 2,000 |
| − Cost of goods | 1,340 |
| − Rent, wages, utilities | 500 |
| − Tax | 40 |
| = Operating cash flow | 120 |
| − Capital spending (fridges, tills) | 20 |
| **= Free cash flow** | **100** |

A 33% gross margin, 25% operating costs and a 5% free cash flow margin are about right for a convenience store. Treating the after-tax figure as operating cash flow is a simplification; strictly, depreciation is added back and working capital adjusted.

Start with the simplest assumption: the store makes $100K of free cash flow every year, with no growth, and the discount rate is 10%. What is it worth?

## Step 4: Present value, bringing each year's cash back to today

Year 1's $100K, brought back to today, is divided by 1.1 once: 100 ÷ 1.1 = $90.9K. Year 2's waits two years and is divided twice: 100 ÷ 1.1² = $82.6K. As a formula:

```
PV(FCFₜ) = FCFₜ ÷ (1 + r)ᵗ
```

PV is present value. FCFₜ is the free cash flow in year t, and (1 + r)ᵗ is (1 + r) to the power t.

The store is worth the sum of every year's present value:

```
Value = Σ PV(FCFₜ)
      = Σ FCFₜ ÷ (1 + r)ᵗ
```

That is the whole DCF formula; every step after this one is a way of computing that sum. What is left to decide is which year the sum stops at.

## Step 5: Perpetuity, $1,000K for a store that never grows

Suppose the store stays open forever and makes $100K every year, unchanged. The answer is:

```
Value = FCF ÷ r = 100 ÷ 10% = $1,000K
```

![Thirty equal grey bars, the blue bars inside them falling from 90.9 to 5.7](https://sweetvaluelab.com/blog/img/08210d76d3ce8aa6.svg "Illustration, r = 10%. The store takes in $100K every year, but each year's cash is worth less today: $90.9K for year 1, $38.6K for year 10, $5.7K for year 30. The blue bars add up to $614K over ten years, $943K over thirty, and approach $1,000K forever.")

Why exactly FCF ÷ r? Write out every year, call the total V for Value, and divide both sides by (1 + r):

```
V             = FCF/(1+r) + FCF/(1+r)² + FCF/(1+r)³ + …
V ÷ (1+r)     =             FCF/(1+r)² + FCF/(1+r)³ + …
```

The second line is the first with every term moved back one place, minus its first term. Subtract, and everything after the first term cancels:

```
V − V ÷ (1+r) = FCF/(1+r)
V × (1+r) − V = FCF
V × r         = FCF
V             = FCF ÷ r
```

The second line multiplies both sides by (1 + r). The check is easy: $1,000K earning 10% produces exactly $100K a year.

## Step 6: The Gordon growth model, $1,471K at 3% a year

$100K every single year is too tidy. Customers trickle in and prices rise now and then, so the cash usually grows. Say it grows g = 3% a year:

- Year 1's FCF grows to 100 × 1.03 = $103K, worth 103 ÷ 1.1 = $93.6K today.
- Year 2's FCF grows to 100 × 1.03² = $106.1K, worth 106.1 ÷ 1.1² = $87.7K today.

Year t's present value has a numerator growing at g and a denominator discounting at r:

```
PV(FCFₜ) = FCF × (1 + g)ᵗ ÷ (1 + r)ᵗ
```

Here FCF is this year's $100K, already in hand and not counted. As in Step 4, the value is the sum of all the present values, and it simplifies to a short expression:

```
Value = Σ PV(FCFₜ)
      = Σ FCF × (1 + g)ᵗ ÷ (1 + r)ᵗ
      = FCF × (1 + g) ÷ (r − g)
```

That is the Gordon growth model. With the numbers in:

```
Value = 100 × 1.03 ÷ (10% − 3%) = $1,471K
```

That is 47% more than the $1,000K with no growth. The numerator carries one (1 + g) because the first cash to discount is next year's 103; this year's 100 is already in the till.

![Thirty rising grey bars, the blue bars inside them falling from 93.6 to 13.9](https://sweetvaluelab.com/blog/img/8c44d37c06f86bbd.svg "Illustration, r = 10%, g = 3%. The cash coming in rises from $103K in year 1 to $242.7K in year 30, while its value today falls from $93.6K to $13.9K. The blue bars add up to $1,267K over thirty years and approach $1,471K forever.")

The proof is Step 5's trick again. From one year to the next, the numerator gains a (1 + g) and the denominator a (1 + r), so multiplying both sides by (1 + g)/(1 + r) moves every term back one place:

```
V                   = FCF(1+g)/(1+r) + FCF(1+g)²/(1+r)² + …
V × (1+g)/(1+r)     =                  FCF(1+g)²/(1+r)² + …
```

Subtract to leave the first term, then multiply both sides by (1 + r):

```
V − V × (1+g)/(1+r) = FCF(1+g)/(1+r)
V × (r − g)/(1+r)   = FCF(1+g)/(1+r)
V × (r − g)         = FCF × (1+g)
V                   = FCF × (1+g) ÷ (r − g)
```

The second line uses 1 − (1+g)/(1+r) = (r − g)/(1+r). With g = 0 the result falls back to Step 5's FCF ÷ r.

The denominator is r − g, which puts a hard limit on g. The same store, changing only g:

| g | r − g | Value ($K) |
|---|---|---|
| 0% | 10% | 1,000 |
| 3% | 7% | 1,471 |
| 8% | 2% | 5,400 |
| 9% | 1% | 10,900 |
| ≥ 10% | ≤ 0 | meaningless |

g has to stay below r. The subtraction above relies on each term being smaller than the last, which means (1+g)/(1+r) below 1. Once g catches r the terms stop shrinking, the sum is infinite, and the formula returns infinity or a negative number. The closer g gets to r, the harder the result runs away: from 3% to 8%, the value multiplies by 3.7.

## Step 7: A two-stage DCF, fast first and slow later

Steps 5 and 6 both assume g never changes. Real businesses are messier. Say the owner plans to open more branches, reaching four shops over ten years, so the cash grows fast; once the branches are open, the business can only grow with the town. One g cannot describe that, so split the future in two, each with its own g:

| Stage | Years | g | How it is valued |
|---|---|---|---|
| Forecast | 1–10 | 15% (new branches) | Visible enough to value year by year, discounting each and adding them up |
| Terminal | after year 10 | 3% (with the town) | Too far to see, so valued in one go with Step 6's formula: the terminal value (TV) |

```
Value = Σₜ₌₁..₁₀ FCFₜ ÷ (1 + r)ᵗ + TV₁₀ ÷ (1 + r)¹⁰
```

A forecast g of 15% is above r, and that is fine: ten years add up to a finite number. Step 6's "g below r" governs the part that goes on forever, which is why growth has to come down after year 10. You can use three stages or four; each one adds a growth rate to guess, and two is the usual compromise.

### The first ten years, one row each

Every row is the same three steps:

```
FCFₜ     = FCFₜ₋₁ × (1 + g)
DFₜ      = 1 ÷ (1 + r)ᵗ
PV(FCFₜ) = FCFₜ × DFₜ
```

DFₜ is the discount factor, what $1 in year t is worth today. Year 1: 100 × 1.15 = 115.0, 1 ÷ 1.1 = 0.9091, 115.0 × 0.9091 = 104.5. All ten years, in $K:

| Year t | g | FCFₜ | DFₜ | PV(FCFₜ) | Cumulative PV |
|---|---|---|---|---|---|
| 0 (this year) | | 100.0 | | | |
| 1 | 15% | 115.0 | 0.9091 | 104.5 | 104.5 |
| 2 | 15% | 132.3 | 0.8264 | 109.3 | 213.8 |
| 3 | 15% | 152.1 | 0.7513 | 114.3 | 328.1 |
| 4 | 15% | 174.9 | 0.6830 | 119.5 | 447.6 |
| 5 | 15% | 201.1 | 0.6209 | 124.9 | 572.5 |
| 6 | 15% | 231.3 | 0.5645 | 130.6 | 703.0 |
| 7 | 15% | 266.0 | 0.5132 | 136.5 | 839.5 |
| 8 | 15% | 305.9 | 0.4665 | 142.7 | 982.2 |
| 9 | 15% | 351.8 | 0.4241 | 149.2 | 1,131.4 |
| 10 | 15% | 404.6 | 0.3855 | 156.0 | 1,287.4 |

FCF grows from 100 to 404.6, four times over, and the present value rises too, from 104.5 to 156.0. Growth of 15% outruns a 10% discount, the opposite of Steps 5 and 6, where present values fell every year. The ten years add up to $1,287K.

### After year 10: the terminal value

After year 10 there are no more rows; Step 6's formula does it in one go. Standing at the end of year 10, "this year's FCF" in the formula is year 10's 404.6:

```
TV₁₀   = FCF₁₀ × (1 + g) ÷ (r − g)
       = 404.6 × 1.03 ÷ (10% − 3%) = 416.7 ÷ 0.07 ≈ 5,953
PV(TV) = TV₁₀ × DF₁₀ = 5,953 × 0.3855 ≈ 2,295
```

5,953 is the value as seen from the end of year 10, so it still has to be multiplied by year 10's discount factor to bring it back to today. Forgetting that, and adding 5,953 straight in, is the most common mistake. The two stages together:

```
Enterprise Value = 1,287 + 2,295 = $3,582K
```

Stretching the picture to thirty years shows what the terminal value is:

![Thirty grey bars rising fast for ten years; the blue bars rise from 104.5 to 156.0, then fall to 41.9](https://sweetvaluelab.com/blog/img/d69d99726c01fa53.svg "Illustration, r = 10%, g = 15% for ten years and 3% after. For ten years both bars rise; after year 10 the cash keeps rising, to $730.7K in year 30, while its value today falls from $156.0K to $41.9K. The terminal value of 2,295 is every blue bar from year 11 on; thirty years reach only 1,679, and the other 616 lie beyond year 30.")

In year 30 the store makes 730, more than in year 10, and that is worth 42 today. The further away the money, the less it is worth, but it keeps coming every year, so together it still adds up to more than the first ten years.

## Step 8: Equity value, adding the cash and taking away the debt

The $3,582K from Step 7 is the enterprise value. The free cash flow a DCF discounts is counted before interest and belongs to everyone who put money in: the owner, and the bank that lent to the store. So it is the value of the whole business, whoever paid for it.

The owner's part is the equity value. Say the store has $50K of cash on hand and owes the bank $150K:

```
Equity Value = Enterprise Value + Cash − Debt
             = 3,582 + 50 − 150 = $3,482K
```

Think of buying a house. It is worth $1M, the mortgage still has $600K to run, and what you actually own is $400K; if the seller leaves $50K in a drawer, it is $450K. Buying the store, you likewise take over the cash in its till and what it owes the bank.

The cash is added separately because free cash flow starts next year, and the $50K already saved is in none of those years. Only debt that pays interest counts, such as bank loans and bonds; what the store owes its suppliers is working capital, already handled in Step 2. A listed company's shareholders are its "owners", and equity value divided by the number of shares is the value per share.

## Step 9: Terminal value, where the part we see least holds the most

Of the two-stage $3,582K, the terminal value brought back to today is $2,295K, or 64%; the ten years worked out row by row are 36%. For the store that never grows, in Step 5, everything after year 10 was 39% (1,000 − 614 = 386). The faster the growth, the more of the value sits far in the future.

And the terminal value rests almost entirely on one number, terminal growth. Keep the first ten years and change only the g after year 10:

![Nine bars with the same grey base; the blue part grows from 1,560 to 8,423](https://sweetvaluelab.com/blog/img/7948161bf7f4ab31.svg "The same store, 15% growth for ten years, r = 10%, changing only terminal growth. The ten years' 1,287 is the same in every bar; only the terminal value moves. From g of 0% to 8%, the total rises from $2,847K to $9,710K. From 2% to 3% the value rises 9%; from 7% to 8%, 42%.")

The further right, the more sensitive: from 2% to 3% the value rises 9%; from 7% to 8%, 42%. The discount rate is just as touchy: a one-point change in r moves the store's value by 15% to 20%.

So terminal growth should be conservative. It has to stay below r, and no business can grow faster than the whole economy forever: the US economy has grown about 2% a year in real terms over the long run, about 4% with inflation. The usual choice is 2% to 3%.

## The answer: one store, three answers

Back to Step 3's question: a store with $100K of free cash flow a year, r = 10%. What is it worth?

| Assumption | Method | Enterprise value | Equity value (+50 − 150) |
|---|---|---|---|
| No growth, ever | Perpetuity: FCF ÷ r | $1,000K | $900K |
| 3% growth, forever | Gordon: FCF × (1 + g) ÷ (r − g) | $1,471K | $1,371K |
| 15% for ten years, then 3% | Two-stage: Σ PV(FCFₜ) + PV(TV) | $3,582K | $3,482K |

The same store and the same r give anything from $1,000K to $3,582K, 3.6 times apart. All of the difference comes from what you assume about growth, which is what Buffett meant by a calculation that is not simple.

## After the arithmetic

**You fill in r and g yourself.** Anyone can apply the formula, but those two numbers cannot be copied off a statement; they depend on how well you know the business: how steady the customers are and how much it owes. For this store, moving terminal g from 2% to 3% adds 9% to the value.

**A DCF also runs backwards.** Take today's price as the answer, work out the growth it implies, and ask whether the company can deliver it. That is a reverse DCF, and [this post](https://sweetvaluelab.com/blog/how-to-read-a-reverse-dcf) explains how to read one.

**What comes out is a range.** More than 60% of the value comes from the terminal value, which rests on the decades we can see least. With terminal g between 2% and 4%, the store is worth $3,276K to $3,991K. Only a price well below that range leaves room for being wrong, which is what a margin of safety means.

## Run one yourself

The store is made up; the same method works on a real company:

- [DCF calculator: NVIDIA](https://sweetvaluelab.com/tools/dcf?t=nvda). The numbers come filled in from its latest annual report. Change an assumption and the value per share moves, along with the tables under it. Any US stock works.
- [Reverse DCF: NVIDIA](https://sweetvaluelab.com/tools/reverse-dcf/nvda). From today's share price, the growth the market is assuming.
- [The talk's slides, in Chinese](https://sweetvaluelab.com/slides/zh/dcf-valuation-101). This post as 26 slides, with the same store and the same numbers.

A DCF gives the value your assumptions imply. It is not a forecast and not investment advice.