4. The cost of capital, and why half a point changes everything

Level 2: The value drivers

The three drivers so far all hang off a fourth number, one that describes not the company but whoever finances it. This academy's Macro course already explained what discounting is and why long-duration assets suffer more when rates rise; we take that as read. What is left is the missing piece: where that rate comes from when you value a specific company, and why moving it by half a point does more damage than almost any piece of company news.

It is not what money costs, it is what you give up earning

The cost of capital is not an accounting expense. It is the return demanded by the people putting up the money, and that demand comes out of an alternative: if your project does not offer at least what another one of comparable risk offers, the capital goes there instead. It is an opportunity cost, and that is why it turns up on no invoice.

A company is financed with two kinds of money, and each demands its own. Debt demands a contractual rate, and since interest is usually deductible, its effective cost is somewhat lower than the nominal rate. Equity demands nothing in writing, but demands far more: the shareholder is paid last, absorbs the losses first, and therefore asks for a clearly higher return. The weighted average of the two, with the weights calculated at market value rather than book value, is the cost of capital of the business.

What it actually depends on

• The risk-free rate. The floor everything else is stacked on top of. When it rises, everything rises.
• The equity risk premium. What investors as a whole demand above that floor for bearing the uncertainty of equities.
• Business risk. How much the business depends on the economic cycle and how much operating leverage it carries. A business with very fixed costs amplifies any swing in sales.
• Financial leverage. More debt makes the mix cheaper at first and makes equity dearer afterwards, because the shareholder ends up behind more people in the queue.
• The currency. Discounting cash flows in euros with a rate designed for dollars is a silent and frequent error.

The sensitivity, with numbers

Take a company with 100 million of free cash flow next year and an assumed perpetual growth rate of 3%. With a cost of capital of 8%, the value is 100 over 0.05, that is, 2,000 million.

Lower the cost of capital by half a point, to 7.5%: the value goes to 100 over 0.045, some 2,222 million. It has risen by more than 11% off half a point. Raise it by half a point, to 8.5%, and the value falls to 1,818 million, 9% less. A move no analyst can defend to decimal precision shifts the value by a tenth in each direction.

And it gets worse when the cost of capital and the growth rate are close together. With a cost of 6% and growth of 3%, the value would be 100 over 0.03, that is 3,333 million. Half a point less takes it to 4,000, 20% more. The same half point, far more poison.

Why companies whose value sits in the distance suffer twice over

Check the effect on a single payment. A hundred million arriving five years from now is worth, today, at 8%, some 68 million. At 8.5%, some 66.5: a loss of 2.3%.

The same hundred million at twenty years is worth, today, at 8%, some 21.5 million. At 8.5%, some 19.6: a loss of 8.8%. Almost four times the damage from the same half point, because the exponent acts twenty times instead of five. That is the mechanism by which a company whose value is concentrated in the decade ahead collapses on rate moves that barely graze a mature company.

The uncomfortable lesson

If value is that sensitive to a number nobody knows precisely, the honest conclusion is not to refine the calculation to the third decimal place. It is the opposite, and it is what this whole course rests on: stop chasing fair value and ask what expectations are implied in the price, checking whether they are still plausible across a whole reasonable range of costs of capital. The mechanics of reverse-engineering those expectations is the next level.

Three errors worth not making along the way. Using the historical rate on old debt instead of the rate the company would pay today. Treating a sensitivity measure calculated from five years of data as though it were a physical constant. And the worst of the lot: adding or removing points from the cost of capital so that the valuation produces the number you wanted. Damodaran has spent decades pointing out that the analyst's fear is not a risk of the business, and that if a scenario worries you it belongs in the cash flows, not camouflaged in the denominator.

A real case: 2022, without touching a single cash flow

The yield on the ten-year US Treasury went from moving around 1.5% at the end of 2021 to above 3.8% at the end of 2022. The floor under the cost of capital of every company in the world was lifted by more than two points in twelve months.

Apply the module's arithmetic. A company with 100 million of cash flow and perpetual growth of 3%, valued with a cost of capital of 7%, was worth 2,500 million. With the same cash flow, the same growth and the same management team, but a cost of capital of 9.3%, it comes to be worth 100 over 0.063, some 1,587 million: 36% less without a single euro of forecast having been revised.

That is why in 2022 companies whose sales were still growing fell hard. The business did not change: the fourth driver did. This is education, not advice or a recommendation on any security.