Unit 15 · Lesson 1 Valuing a company

Someone wants to buy your business. What is it really worth?

The story so far Your two bike shops and the repair van (Lessons 13.1 to 13.3) now make steady money. A big bike chain calls and offers $500,000 for the whole business. That's more money than you've ever seen. But is it a good price? The business should bring in $40,000 of free cash next year, growing $5,000 a year, and it will keep running long after that. This lesson turns that future cash into one number for today.

What

A DCF, or discounted cash flow, values a company as the present value of all the cash it will make in the future.

Why

It's how buyers, investors and bankers decide what to pay for a company or a share of stock. It's also the most common valuation question in finance interviews.

How

Forecast the free cash for a few years, add a value for everything after, and bring it all back to today at the cost of capital.

Who

Investment bankers build DCFs to price deals. Equity research analysts use them to rate stocks buy or sell. Private equity associates use them to decide what to bid.

What you're looking at: the idea of a DCF. Each coin is a year of free cash from your business. Coins further in the future count for less today, so they're drawn smaller. The green coin stands for every year after year 5. Add them all up at today's value and you get what the business is worth: $660,945.

01 See it

A company is a stream of cash.

In Lesson 14.3, a bond was worth the present value of its payments. A company works the same way. The only differences: you have to forecast its cash yourself, and it never stops paying.

Step one: free cash flow

Profit isn't cash (Lesson 12.3). What a buyer cares about is free cash flow: cash from running the business, minus what you spend on equipment and buildings, called capital spending (capex). It's the cash that's truly free to pay the lenders and owners.

Free cash flow = cash from operations − capital spending

In this example

Next year: Cash from operations $55,000 − new tools and a van repair $15,000 = $40,000 of free cash flow.

Step two: forecast a few years

Nobody can see far ahead, so analysts forecast free cash flow year by year for a short stretch, usually 5 to 10 years. That stretch is the forecast period.

In this example

5-year forecast: Growing $5,000 a year: $40,000, $45,000, $50,000, $55,000, $60,000.

Step three: bring each year back to today

Discount each year's cash, just like the van in Lesson 13.2. The discount rate for a whole company is its cost of capital, the WACC from Lesson 13.3, because that's what its lenders and owners expect to earn.

Value today = cash in year 1(1 + rate) + cash in year 2(1 + rate)² + …

In this example

At a 10% discount rate: $40,0001.1 + $45,0001.1² + $50,0001.1³ + $55,0001.1⁴ + $60,0001.1⁵
Each one today: $36,364 + $37,190 + $37,566 + $37,566 + $37,255 = about $185,940.

Step four: everything after year 5

Your shops won't close after year 5. The value of all the years after the forecast is the terminal value. The usual way to find it assumes the cash grows at a small, steady rate forever, the long-term growth rate.

Terminal value = next year's free cash flowdiscount rate − growth rate

Keep that growth rate small, about 2% to 3%. No company can grow faster than the whole economy forever, or it would someday be bigger than the economy. And it must stay below the discount rate, or the formula breaks.

In this example

Growth after year 5: 2%: Year 6 cash: $60,000 × 1.02 = $61,200.
Terminal value: $61,20010% − 2% = $61,2000.08 = $765,000, valued as of year 5.
Brought back to today: $765,0001.1⁵ = $475,005.

Step five: add it up

The 5 forecast years plus the terminal value give the enterprise value: what the whole business is worth.

In this example

Enterprise value: $185,940 + $475,005 = $660,945. The chain's $500,000 offer is $160,945 too low.
How much comes from after year 5: $475,005$660,945 = about 72%. Most of the value is in years you can't see.

From the business to the owners

Lenders get paid before owners. To find what belongs to the owners, the equity value, subtract debt and add back cash the business holds. For a public company, divide by the number of shares to get the value per share.

Equity value = enterprise value − debt + cash

Value per share = equity valuenumber of shares

In this example

Your share: $660,945 − the $40,000 bank loan + $20,000 in the bank = $640,945.
If the business had 100,000 shares: $640,945100,000 = about $6.41 a share.

The catch: small guesses, big swings

A DCF is only as good as its guesses. Because the terminal value is so big, a small change in the discount rate moves the answer a lot. So analysts always run a sensitivity analysis: the same DCF at several rates. Slide the rate and watch the offer.

In this example

10% → 12%: Enterprise value falls from $660,945 to about $523,441, still above the offer. At 13% it falls to about $473,562, below it.

Discount rate (cost of capital) 10%

What you're looking at: what your business is worth today at discount rates from 8% to 14%, with 2% long-term growth. Blue is the 5 forecast years; green is everything after year 5. The dashed line is the chain's $500,000 offer.

02 Hear it

Two minutes. Just listen.

Tap any line to jump to it.

03 Play it

Valuation desk.

Eight questions a first-year analyst gets asked. Each one gives you the numbers. One try each.

Question 1 of 8

Right0 of 0

What you're looking at: made-up companies. Each lists the numbers, then asks one question.

04 Break it down

The logic, step by step.

Every DCF follows the same five steps.

Step 1: Forecast free cash flow

Cash from operations − capital spending, for each forecast year

In this example

Years 1 to 5: $40,000, $45,000, $50,000, $55,000, $60,000.

Step 2: Pick the discount rate

The company's cost of capital (WACC)

In this example

The bike shops: 10%.

Step 3: Find the terminal value

next year's free cash flowdiscount rate − growth rate

In this example

At 2% growth: $61,2000.08 = $765,000.

Step 4: Discount everything to today

Enterprise value = today's value of each year + today's value of the terminal value

In this example

Add it up: $185,940 + $475,005 = $660,945.

Step 5: Get to the owners' share

Equity value = enterprise value − debt + cash

In this example

Your share: $660,945 − $40,000 + $20,000 = $640,945.

Worked example: should you take the offer?

The chain offers $500,000 for the whole business. Here are the facts:

Your DCF at 10%: $660,945 for the whole business.
At 12%: about $523,441. At 13%: about $473,562.
Your loan: $40,000. Cash in the bank: $20,000.

Compare. At 10%, the business is worth $660,945 − $500,000 = $160,945 more than the offer.
Test your guesses. The offer only looks fair if the right discount rate is about 13%, meaning the business is far riskier than you think.
Walk away with? If you sell for $500,000, you repay the $40,000 loan and keep the $20,000 cash: $500,000 − $40,000 + $20,000 = $480,000 for you.
Check the growth. If the shops could grow faster than $5,000 a year, the value goes up. If a new chain store opens next door, it goes down.
The answer. Don't take $500,000. Counter near $650,000, and be ready to explain your forecast, your rate and your growth. A DCF doesn't give you the price; it gives you the reasons behind the price.

05 Nature link

Most of an iceberg is underwater.

Ice is a little lighter than seawater, so an iceberg floats with only about a tenth of it showing. Ships learned the hard way that the part you see is not the part that matters. In 1912, the Titanic struck an iceberg below the waterline.

What you're looking at: an illustration, not data. The small peak above the water is the 5 years you forecast. The big mass below is the terminal value, the years you can't see.

Why this sticks. In your DCF, about 72% of the value sits below the waterline, after year 5. Check that part hardest; it's where a valuation sinks.

06 Notes

The page you'd copy down.

DCF: a company is worth the present value of its future free cash flow.
Free cash flow = cash from operations − capital spending: $55,000 − $15,000 = $40,000.
Discount each forecast year at the cost of capital (WACC). Years 1 to 5 at 10%: about $185,940.
Terminal value = next year's cashrate − growth: $61,2000.08 = $765,000, worth $475,005 today. Growth stays small (2% to 3%) and below the rate.
Enterprise value = $185,940 + $475,005 = $660,945. About 72% comes from the terminal value.
Equity value = enterprise value − debt + cash = $640,945. Per share = equity valueshares.
Higher discount rate, lower value. Always run a sensitivity analysis.

Fill in the blanks

1. Cash from operations of $80,000 minus capital spending of $30,000 is dollars of free cash flow.

2. When the discount rate goes up, a DCF value goes .

3. The value of all the years after the forecast is the .

4. Equity value = enterprise value − debt + .

07 Together

Grab a friend or a study group.

Value a favorite spot

Pick a local coffee shop or food truck. Guess its free cash next year and a growth rate. Use a 12% rate. What would you pay for it?

Argue the rate

One person plays the buyer and argues for a high discount rate. The other plays the seller and argues for a low one. Who wins, and why?

Interview drill

Take turns answering "Walk me through a DCF" in under a minute. Use the five steps from this lesson.

08 On your own

Just you and your money.

These stay on this device. Nobody else sees them.

72% of the bike shops' value comes after year 5. Does that make you trust a DCF more or less? Why?

Think of a company you know. Which do you think it will make more of over the next 10 years: more cash or less? What would change your mind?

If someone offered to buy a business you built, what would matter to you besides the price?

09 Check

Exam-style questions.

Written the way a college exam would ask them. Each right answer on the first try is worth 10 xp.

On the job: you're an equity research analyst

You cover a company that makes kitchen appliances. Your boss wants a quick DCF. Here's the situation:

Free cash flow next year: $50 million, growing 3% a year forever.
Cost of capital: 9%.
Debt: $200 million. Cash: $50 million.
Shares: 25 million. Today's stock price: $22.

Your task: find the enterprise value, the equity value and the value per share. Is the stock cheap or expensive? What if the cost of capital is really 10%? What would you tell your boss?

See a model answer

Enterprise value: with steady growth from next year, the whole company is one terminal value: $50 million9% − 3% = $50 million0.06 = about $833.3 million.

Equity value: $833.3 million − $200 million + $50 million = $683.3 million. Per share: $683.3 million25 million = about $27.33.

At 10%: $50 million0.07 = about $714.3 million; equity $564.3 million; about $22.57 a share, barely above today's $22.

To your boss: at 9%, the stock looks about 24% cheap, so it could be a buy. But one point on the discount rate wipes out almost all of that, so the call depends on how risky we think the company is. I'd rate it a cautious buy and dig into the growth and risk before we publish.

10 Where it leads

Every price hides a forecast.

What you're looking at: a map of where this lesson fits in the course. Read it left to right: the lessons it builds on, this lesson in the middle, and the lesson that comes next.

Back · Unit 12How the three statements connect
Back · Unit 13Picking projects with NPV
Back · Unit 13The cost of capital
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