# Discounted Cash Flow (DCF)

Using cash flows is the best way to value a business.

There’s little consensus on the right way to value a share — except that it’s part art, part science.

Compare it with valuing a piece of artwork such as Andy Warhol’s “200 One Dollar Bills” silkscreen, which recently sold for a staggering $43.8 million (£28.5 million). How would you justify that price when the *materials* probably cost 200 one-dollar bills?

To start, you could attribute much of the value to the Warhol name. Then you’d probably consider the meaning to the buyer, the piece’s importance relative to other works, and what someone else might pay for it down the road.

Some rely on “relative” valuation, comparing multiples such as price-to-earnings with the same metrics for competitors, but Fools should prefer to focus on the company’s underlying fundamentals — like cash flow and earnings — rather than where the share may trade relative to competitors.

**The value of future cash**

More often than ever, earnings per share is manipulated by one-time charges, non-IFRS accounting, and subjective management teams that do all they can to make earnings look better.

But cash is *fact*.

By estimating how much cash a company will make available to shareholders after it invests in new assets and satisfies other obligations (i.e., to lenders and pensions), we can begin to determine how much that future cash is worth today — and can then estimate the intrinsic value of a share. This is known as discounted cash flow, or DCF, analysis.

To illustrate, say your friend Steve offered you £1,000 today or the promise of £1,000 five years from now. You’d be foolish (lower case “f”) not to take the £1,000 today, because you can put that money to work earning interest — and assuming inflation follows history, £1,000 will buy more goods today than it will in five years.

But what if Steve asks how much you’ll pay him *today* for his promise of £1,000 five years from now (just as you pay for the promise of a company’s future cash flows)?

This is a tougher question. You need to factor in expected inflation over the next five years in addition to a decent rate of return relative to Steve’s trustworthiness (for this exercise, we’ll consider his word his bond). Let’s say the “discount” rate that we believe fairly compensates us for expected inflation and for the risk of lending to Steve is 6%.

The equation to determine how much you’d lend Steve today would be:

Future value / (1 + discount rate)^{number of years}

or £1,000 / (1.06)^{5} = £747.26

So, the amount we should pay today for Steve’s £1,000 in five years is £747.26.

Taking it a step further, if Steve said he’d pay us £1,000 in year five and another £1,000 in years six and seven, now how much would we pay today?

Time ofcash flow |
Amount ofcash flow |
Formula |
Present Value |
---|---|---|---|

Year 5 | £1,000 | (£1,000 / (1.06)^{5} |
£747.26 |

Year 6 | £1,000 | (£1,000 / (1.06)^{6} |
£704.96 |

Year 7 | £1,000 | (£1,000 / (1.06)^{7} |
£665.06 |

Sum | £2,117.28 |

Put simply, you would give Steve £2,117.28 today for the promise of three £1,000 payments delivered in years 5 through 7.

This second example is closer to discounted cash flow valuation: We estimate future cash flows, discount that cash at a rate that adequately reflects its risk, and come to a fair value for the cash today.

**Two kinds of free cash**

Unfortunately, there’s no “Steve” in the share market telling us exactly how much he’ll give us down the road. So, how do we determine which cash flows to measure?

When valuing a company, we target the cash flows left over — the “free” cash — after the company has invested in projects to further grow the business (i.e., capital expenditures and acquisitions). In other words, this is the cash that *could* be paid out to investors and is thus cash we can use to measure value. There are two major types of free cash: free cash to firm and free cash to equity.

**Free cash flow to firm (FCFF)** is what’s left over before the company has paid interest to debt holders and after corporate reinvestment needs.

**How to calculate FCFF**: Start with after-tax operating income, add back non-cash depreciation expenses, and subtract capital expenditures and changes in working capital (current assets minus current liabilities).**What’s the discount rate**? Because you’re factoring both the cost of debt and equity for the firm, you discount FCFF at the company’s weighted average cost of capital, a mix of its cost of debt and equity.**Done. Then what?**Back out all non-equity commitments (debt obligations, operating leases) and add back cash to arrive at the equity value — the number we care about as equity investors. Divide that amount by the number of shares outstanding to get the fair value per share.

**Free cash flow to equity (FCFE)** is cash left over after all non-equity obligations have been met.

**How to calculate FCFE**: Start with net income, add back non-cash depreciation expenses, and subtract capital expenditures and changes in non-working capital. Any new debt proceeds received by the company could theoretically be paid out to equity holders as a dividend, so that should also be added to the calculation.**What’s the discount rate?**FCFE is discounted at the company’s cost of equity, traditionally measured by the capital asset pricing model, or CAPM, which factors in a risk-free rate (for valuations done in Sterling, this is the 10-year gilt rate), the investment’s beta (to measure relative risk to the market), and the equity risk premium (compensates investors for extra risk with shares over bonds).**Done. Then what?**Divide the equity value by number of shares outstanding to get the fair value per share.

Valuation models using either free cash flow to firm or equity should arrive at the same conclusion, but depending on the type of company being analysed, one model can be “better” than the other.

For instance, companies with fluctuating levels of debt make projecting future equity cash flows difficult, so it’s more prudent to value the entire firm using free cash flow to firm and back out all non-equity obligations. On the other hand, for companies with no debt or stable debt ratios, free cash flow to equity valuations can be much clearer.

**Play with numbers**

Prudent Fools test various scenarios for each company’s projected free cash flows to determine a range of potential values. Valuing a company to the penny, as many City analysts do, is an exercise in futility because it assumes you’ve perfectly modeled the future. Don’t be so confident to think that you know a company’s exact standing five years from now or more.

The ultimate objective to valuing a share is to make sure you’re paying at least a fair price for your investment — one that should generate attractive returns — and obtaining a suitable margin of safety. Overpaying for a share is one of the most common causes of permanent loss of capital.

**The bottom line**

Just as each art appraiser has a slightly different method of valuing art, each investor will have a different formula for valuing shares — but DCF analysis is one solid way to value the underlying *business*, which in turn helps us make smarter long-term investments.

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