Valuation: what is a whole company worth?

Two analysts sit in the same room, look at the same company, and read the same numbers. One says it’s worth £100 million. The other says £250 million. Neither has made an error. They’ve simply made slightly different guesses about the future — and that’s all a valuation ever is. The headline “company valued at £2 billion” sounds like a measured fact, weighed on a scale. It isn’t. It’s an argument, dressed up as a number.

A company is worth its future cash

Start from a plain idea. Why would anyone pay anything for a whole company? Not for the building, not for the brand on the door. They pay for one thing: the cash the business will hand them in the years ahead. A company is worth the money it will throw off in the future — all of it, added up.

But there’s a catch, and it’s the same one from the cost-of-capital item earlier in this course. Cash later is worth less than cash now. A pound in your hand today can be put to work; a pound promised in ten years is just a promise, and you’d take less than a pound today to skip the wait. So you can’t simply add up future cash. You have to bring each future pound back to what it’s worth today — you discount it.

The rate you discount by is the return investors demand to put their money in this business — the discount rate. That’s exactly the cost of capital from before. Risky company, high demanded return, heavy discount. Safe company, lower return, lighter discount.

The forever formula

Here’s the cleanest version of the whole idea. Suppose a company produces a steady stream of cash every year, and that stream grows at a constant rate forever. There’s a tidy result for what that stream is worth today:

Value = annual cash ÷ (discount rate − growth rate)

Two letters do all the work. r is the discount rate, the return investors demand. g is the growth rate, how fast the cash builds each year. Value equals this year’s cash divided by the gap between them, (r − g).

It looks too simple to be useful. It is the backbone of how whole companies get valued.

Walk the numbers

Take a company throwing off £10 million of free cash a year — the cash left after it has paid for everything it needs to keep running.

Suppose investors demand 10% (r = 0.10) and the cash never grows (g = 0). Value = £10m ÷ (0.10 − 0) = £10m ÷ 0.10 = £100 million. Read that as: a flat £10m forever, discounted at 10%, is worth £100m today.

Now let the cash grow a modest 3% a year. Value = £10m ÷ (0.10 − 0.03) = £10m ÷ 0.07 = £143 million. Same cash this year. A small, believable growth assumption. The value jumped £43 million.

Push demanded return up to 12% while keeping 3% growth: £10m ÷ (0.12 − 0.03) = £10m ÷ 0.09 = £111 million. A two-percentage-point change in the return investors want knocked £32 million off.

Tiny guesses, huge swings

Here’s the part to feel in your stomach. Keep the cash fixed at £10m and the demanded return at 10%. Move growth from 3% to 6% — three percentage points, the difference between “grows nicely” and “grows really nicely.”

Value = £10m ÷ (0.10 − 0.06) = £10m ÷ 0.04 = £250 million.

From £143 million to £250 million. The company nearly doubled in value, and not one pound of actual cash changed. All that moved was a guess about the future, by three points. That is why two honest people value the same business at wildly different numbers. The answer isn’t hiding in the company. It’s hiding in the gap (r − g) — and when that gap is small, dividing by it makes the value enormous and twitchy. A whisper in the assumptions becomes a roar in the answer.

There’s a hard rule baked in: r must be bigger than g. If a company grew faster than the return you demand, forever, the formula spits out infinity — and nothing on earth grows faster than its discount rate forever. When you see g creeping up toward r, that’s the warning light: the model is leaving reality.

The shortcut, and what it hides

There’s a faster way valuers reach for: compare the company to similar ones. If comparable businesses sell for, say, ten times their annual cash, slap that multiple on yours. (The markets course taught the price-to-earnings ratio this way, asking “is this share cheap?” — an investor sizing up a stock. This is the deal-maker’s cousin: what is the whole business worth to someone buying all of it.) The multiple shortcut is quick and useful as a sanity check. But it’s borrowing someone else’s answer. Every one of those comparable prices was itself built on somebody’s guesses about r and g. The cash-based view is the foundation under the shortcut.

On the whole

A valuation is a forecast resting on two guesses. The future cash, and the gap between the return you demand and the rate it grows. Get those slightly wrong — and you will, because they’re the future — and the answer moves by tens of percent. The number that arrives looking so precise, “£2.4 billion,” to the hundred-million, is a confidence the maths doesn’t actually have.

This is worth carrying past company news. Whenever a single figure stands in for the worth of a complicated, living thing — a business, a deal, a forecast of any kind — there are assumptions underneath it, doing the heavy lifting and staying out of sight. The figure is only as solid as its softest guess. Hold such numbers loosely. The precision is real on the page and borrowed from the future.