Reverse DCF

Why this matters

A forward DCF has a weakness that The Limits of DCF Models described: the answer is only as good as the forecast, and a forecaster who likes a company can always find assumptions that justify its price. Running the calculation in reverse removes that freedom. You don't forecast. You read off what the price already assumes, and then ask whether you'd bet on it.

The idea

A DCF has a handful of inputs: today's free cash flow, growth over the forecast period, long-run growth after that, and the discount rate. Give it all of them and it produces a value. Give it the value and all but one of them, and it produces the missing input.

Discounted Cash Flow, Step by Step did this once for STU Corp. Its base-case value was $44.69 a share against a price of $50. Holding the discount rate at 9.8% and long-run growth at 3%, the price is justified if free cash flow grows about 12.8% a year for five years instead of 10%.

There's no formula that gives the answer directly. You change the growth rate until the value matches the price, which a spreadsheet's goal-seek tool does in a moment, and which the sandbox in that lesson lets you do by hand.

Three ways to state the same expectation

A growth rate is one way to describe what the market expects. Two others are often easier to judge.

Solve for	Holding fixed	What the price implies
Growth rate	Five years of growth, 9.8% discount rate, 3% long-run growth	12.8% a year, where the base case assumed 10%
Duration	10% growth, same discount rate and long-run growth	About seven years of 10% growth, where the base case assumed five
Margin	Revenue growing 10% a year for five years	Free cash flow of about 12.5% of revenue by year 5, up from 11% today

Each row is the same $50 price seen from a different side. The market isn't assuming anything wild about STU Corp. It expects somewhat faster growth, or the same growth for a couple of years longer, or a business that keeps a little more of each sales dollar. An investor who thinks the base case is too cautious on any one of those has a reason to consider the shares. One who thinks 10% for five years is already generous doesn't.

Where it earns its keep

The method is most valuable when the price is high and most of the value lies far in the future. Take a company growing quickly and trading at a hundred times its free cash flow. The numbers are hypothetical.

	Amount
Free cash flow today	$20 million
Market value of the shares	$2,000 million
Discount rate	10%
Long-run growth after the forecast period	3%
Implied growth if it lasts 5 years	56% a year
Implied growth if it lasts 10 years	29% a year
Implied growth if it lasts 15 years	21% a year
Free cash flow in year 10, on the 10-year path	$258 million

For the price to make sense, Company G's free cash flow has to grow 29% a year for a decade and reach about thirteen times today's level. If it then grows 3% a year for ever, the buyer earns 10% a year, which is only the discount rate. Anything less than that path, and the return is lower.

A forward DCF of Company G would be an argument about its prospects. The reverse version makes the test concrete. It doesn't say the shares are overpriced. It says what has to happen for them not to be, and leaves you to judge the odds.

Judging the answer

Once the implied expectation is on the table, test it three ways.

• Against the company's own record. Has it grown this fast before, and for how long? STU Corp's revenue grew about 14% this year, so 12.8% growth in cash flow isn't a stretch. A company that has never grown faster than 8% would need a reason.
• Against the size of the opportunity. Turn the implied cash flow into revenue, and compare that revenue with the whole market the company sells into. An implied path that needs more than the entire market fails without further analysis.
• Against what has to go right. List the things that must be true: customers keep renewing, competitors don't close the gap, margins hold while the company spends to grow. The more conditions, and the less control the company has over them, the less likely the path.

The scenarios from Scenario Analysis: Bull, Base, and Bear Cases fit naturally here. If the price implies something close to your bull case, you're being asked to pay in advance for the best outcome.

Limits

• The inputs you fix still matter. Change the discount rate from 9.8% to 9% and the implied growth falls. A reverse DCF moves the judgment. It doesn't remove it. Run it with more than one discount rate.
• Many combinations fit one price. The market might expect moderate growth for a long time or fast growth for a short time. The calculation can't tell you which.
• The price can be wrong. The method tells you what the price assumes. It doesn't mean investors as a group have thought it through.
• It needs positive cash flow to start from. For companies that are losing money, the same idea is applied to revenue and future margins, which High-Growth and Negative-Earnings Companies covers.

Key takeaways

• A reverse DCF starts from the price and solves for the assumption that justifies it.
• The result can be stated as a growth rate, a number of years, or a margin. Use whichever is easiest to judge.
• It's most useful for expensive companies, where the price depends on growth lasting a long time.
• Test the implied path against the company's record, the size of its market, and what must go right.
• It shows what the price assumes. Deciding whether that's likely is still your job.

Check your understanding

A reverse DCF shows that a company's share price assumes 25% yearly growth in free cash flow for ten years. Its best five-year stretch so far was 12% a year. What's the reasonable conclusion?

1. The price needs far more than the company has ever achieved, so you'd want a strong reason to expect it.
2. The shares are certain to fall, because the market has made a mistake that will soon be corrected.
3. The company will grow at 25%, because the market's forecast is built into the share price.

You run a reverse DCF at a 10% discount rate and get implied growth of 15%. At an 8% discount rate, what happens to the implied growth?

1. It rises, since a lower discount rate makes future cash flows worth less today.
2. It stays at 15%, since the share price and the cash flows haven't changed.
3. It falls, since future cash is worth more today and less of it is needed.

What's next

Both directions of DCF treat a company as a single stream of cash. Some companies are really several businesses with different prospects. Sum-of-the-Parts Valuation values each one separately.