If I wanted something from the shop and didn’t have enough money, I could borrow 50 cents from my brother. Perhaps I would promise to pay him back tomorrow. Perhaps, because siblings are rarely known for their charitable lending policies, I would have to throw in a sweet too.
Fifty cents back tomorrow, plus one sweet.
It wasn’t called interest. Neither of us knew what interest was. But somehow, the arrangement made perfect sense. The 50 cents belonged to him. I wanted to use it. And if I wanted him to give up his money today and trust me to return it tomorrow, I had to give him some reason to say yes.
Years later, we give this relationship much more sophisticated names. We call the 50 cents debt. We call the sweet interest. We calculate percentages, tax effects and repayment schedules. But underneath all of that, the bargain hasn’t changed very much. Someone else has money. We want to use it. And using their money costs us something.
I think this is why the cost of debt is relatively easy to understand. The cost announces itself. If a company borrows €100 at 5%, we can see what the lender wants in return. We know the interest rate. We know that the €100 itself eventually has to be repaid.
Debt sends an invoice.
The more interesting question begins when someone gives us money and seemingly asks for none of those things.
Suppose my brother doesn’t lend me the 50 cents this time. Instead, he gives it to me. There is no promise that I will repay him tomorrow. No sweet every week. No fixed payment at all.
That sounds rather wonderful. Perhaps I have finally discovered free money.
Except, of course, I haven’t. Because my brother hasn’t suddenly become generous. He has simply made a different kind of bargain. Instead of lending me the money, he wants a piece of whatever I am going to do with it. And now something strange happens. The obvious cost disappears. But the money hasn’t become free.
So, where is the cost?
This was the part that confused me for quite a while when I first came across the idea of a cost of equity.
Debt made sense. Somebody gave us €100, told us what they wanted for letting us use it, and expected their €100 back at the end. Equity didn’t look like that. If you put €100 into my company, I don’t promise to pay you €5 every year. I don’t promise to return the €100 on a particular date. If the company has a terrible year, you might receive nothing at all.
So where exactly is the cost?
I think the mistake is that we are still looking for the sweet. We are looking for something the company is contractually required to hand over, because that is what cost looked like when we were talking about debt.
But think about what happened to your €100 the moment you gave it to me. You could have put it somewhere else. You could have earned a return somewhere safer. You could have invested in another company. You could simply have kept it. Whatever else you might have done with that €100 is no longer available to you because you chose to put it here. And you haven’t only given something up. You have taken a risk.
The lender has a contractual claim to interest and repayment. If the company fails, lenders generally stand ahead of shareholders. You, as the shareholder, are waiting for whatever remains. Suddenly, the lack of an invoice starts to look rather less like free money.
If I want you to give up the alternatives available to you, put your money into my company and accept more uncertainty in return, you are probably going to want something from me too. Now we have found the cost. We just can’t see the number yet.
The absence of an invoice doesn’t mean the absence of a cost.
And perhaps this is what makes the cost of equity more interesting than the cost of debt. Nobody has written the answer down for us. We have to work out what return might make giving up those other opportunities, and accepting that risk, worthwhile.
One way of estimating that return is to look at dividends. If a company has a fairly stable history of paying them, we can work backwards from its share price, dividend and expected growth to get some idea of what shareholders require.
It is a useful approach, but there is something about it that still leaves me slightly unsatisfied. Because if I am trying to understand why a shareholder expects a return in the first place, the answer cannot simply be that they expect dividends to grow.
So let’s go back to the €100.
You could put it somewhere relatively safe and earn 4%. Or you could put it into my company, where I can’t promise what you will receive, I can’t promise when you will receive it, and if everything goes badly, the lenders will be paid before you.
If I offered you the same 4% for both, why would you choose me? You probably wouldn’t.
And I think this gets us closer to what we are actually trying to measure. It isn’t just that shareholders want a return because they gave us money. They want a return that makes sense for what we are asking them to risk. The more uncertain that position becomes, the more they are likely to want in return.
Which sounds simple enough, until we try to put a number on risk.
Imagine two companies. Both are clearly less certain than leaving your money somewhere relatively safe. But when the wider market weakens, one company tends to move fairly calmly while the other falls much harder. When the market recovers, the second tends to react more strongly on the way back up too.
It feels strange to look at both of them and simply say, Well, they’re risky. That tells us almost nothing.
If putting your €100 into one of them exposes you much more strongly to what is happening in the wider market, surely that should matter when we ask what return would make the investment worthwhile. What we need, then, is some way of describing that relationship.
How sensitive is this particular investment to what is happening in the market around it?
Finance gives that relationship a number.
Beta.
But even here, I think we need to be careful about what we mean when we say risk.
A beta of 1 gives us a useful reference point: the investment carries systematic risk broadly in line with the market. A beta above 1 suggests greater sensitivity to market movements; below 1, less.
Imagine you put your entire €100 into one company and its factory burns down. That is unquestionably a risk. If that were your only investment, it could be disastrous.
But you didn’t have to put everything into one company. You could have spread your money across twenty different businesses. The factory still burns down, and that company still suffers, but the other nineteen investments don’t necessarily burn with it.
Now imagine something different. The economy falls into recession. Consumers cut spending. Companies delay investment. Financing becomes harder. Share prices across the market fall.
Owning twenty companies doesn’t remove you from the economy those twenty companies are operating in. And that difference matters.
There are risks we can reduce by spreading our investments around, and there are risks that remain even after we have done that. If investors can reasonably diversify away the first kind, it doesn’t make much sense to offer them a higher expected return simply because they chose not to.
It is the second kind — the wider market risk that remains — that we are interested in here. Finance calls it systematic risk.
And suddenly we have most of what we need. We know what you could earn relatively safely. We know you should expect something extra for stepping away from that safety and accepting the risk of the market. And beta gives us some idea of how much of that market risk this particular investment exposes you to.
Put those pieces together and we arrive at the Capital Asset Pricing Model, or CAPM.
Suppose the relatively safe return is 4%, while the market is expected to return 10%. The difference is 6%. That 6% is what investors expect, in this simplified example, for leaving the relatively safe investment and accepting the systematic risk of the market.
Now suppose our company’s beta is 1.2. Its exposure is higher than the market reference point, so we adjust that 6% by 1.2. That gives us 7.2%. Add back the 4% we started with and we arrive at 11.2%.
That is our estimated cost of equity.
Not because shareholders sent us an invoice demanding exactly 11.2%. They didn’t. We built the number from the position we were asking them to stand in.
Four per cent was available relatively safely. The market offered an additional return for taking market risk. Our investment exposed them to more systematic risk than the market reference point. So 11.2% becomes our estimate of what might make putting their money here worthwhile.
For me, that is much easier to understand than meeting CAPM for the first time as a formula.
And perhaps 11.2% is a perfectly reasonable answer — as long as the company keeps asking its shareholders to take roughly the kind of risk they signed up for.
But companies don’t always do that.
What happens when the business changes?
Imagine a company that has spent years operating supermarkets. Its beta reflects years of the market watching that business: how it performs when consumers spend more or less, what happens when the economy strengthens or weakens, and how its share price tends to respond when the wider market moves.
Then one day, the company decides it wants to build luxury hotels. It already has a beta. It would be wonderfully convenient to use it. But something about that should bother us.
The fact that a supermarket company owns a hotel doesn’t make a hotel behave like a supermarket. Customers behave differently. Costs behave differently. Demand may respond differently to a recession. The things that make the business vulnerable are different.
So if beta is supposed to tell us something about the systematic risk investors are being asked to carry, using the supermarket’s beta for the hotel begins to feel wrong.
The company’s history can tell us what it is like to own a supermarket business. We are trying to find out what it is like to own a hotel business.
Perhaps, then, we should look at a company that already does exactly that.
Imagine there is another listed company that has spent years operating luxury hotels. The market has been watching it all this time. We can see how its shares have responded to movements in the wider market. Its beta gives us something we didn’t have before: evidence about the kind of systematic business risk we are actually trying to understand.
It is tempting to take that beta and stop there. Except there is another difference between the two companies.
Suppose the hotel company has borrowed heavily, while our supermarket company has very little debt. Now its shareholders aren’t only experiencing the risk of operating hotels. They are experiencing that risk while standing behind a large amount of debt.
Those interest payments don’t disappear because the hotel has had a bad year. The lenders are still waiting to be paid before shareholders receive whatever remains.
So the beta we found contains two things tangled together: the risk of being in the hotel business, and the additional financial risk created by the way this particular hotel company chose to finance itself.
We wanted the first one. The second belongs to them. Which means, somehow, we need to separate the two.
We strip away the effect of their debt from the beta. Finance calls this ungearing, and what we are left with is the asset beta: a cleaner estimate of the systematic risk attached to the underlying business itself, before the effect of that company’s financial gearing.
Now we have what we went looking for: the risk of operating hotels.
But our imaginary hotel won’t exist without financing either. We removed the other company’s debt because it belonged to them. Our company has its own financing structure, and our shareholders will experience the hotel project inside that structure.
So after taking their financing out, we put ours in. Their financing comes out. Our financing goes in. That is regearing.
And what we end up with is an equity beta that reflects the hotel business we actually want to enter, together with the financial risk our own shareholders would carry while we do it.
We can take that beta back to CAPM and ask the same question again: what return would make this risk worth taking?
Perhaps the answer is 11%. After all of that, there is something quite satisfying about finally arriving at the number. We started with shareholders whose money appeared not to cost us anything at all, and somehow managed to make that invisible cost visible.
Except the company didn’t get all of its money from shareholders. Some of it came from the people whose cost was obvious from the beginning: the lenders.
And now we have two numbers sitting in front of us.
What does all of this money cost us together?
Suppose the company’s long-term financing has a total market value of €1 million. €700,000 is equity and €300,000 is debt.
The shareholders require 11%. The debt costs 6%.
What, then, does the company’s money cost?
It can’t simply be 11%, because that pretends the debt doesn’t exist. It can’t be 6%, because that pretends the shareholders don’t exist. And simply averaging the two to get 8.5% doesn’t feel right either. That would quietly assume that half our financing came from each.
It didn’t.
For every €1 million of capital, €700,000 belongs to the equity side of the calculation. Surely its cost should have a larger influence on the answer than the cost attached to the €300,000 of debt.
So perhaps the answer is not to choose between 11% and 6% at all. Perhaps we need both: what does each source of money cost us, and how much of our money came from that source?
There is one more small wrinkle. Interest on debt normally reduces taxable profit, which means the effective cost of debt to the company is actually lower than the interest rate alone suggests.
Once we account for all of that, we finally have one number that tries to describe what the entire pool of capital costs us: the debt, the equity, their different costs and their different proportions.
The Weighted Average Cost of Capital.
WACC.
For something with such an intimidating name, I find the question underneath it surprisingly ordinary. Our money came from different people. Those people gave up different things, accepted different risks and therefore require different returns.
What does all of that money cost us together?
Suppose the answer is roughly 9%. At first, that might feel like the end of the calculation. I think it is actually where the number starts becoming useful. Because if the people providing our capital collectively require around 9% for the opportunity and risk they have accepted, then simply taking their money and making some money with it isn’t necessarily enough.
We have to make enough. Otherwise, why are we using their capital here rather than somewhere else?
That is why the cost of capital becomes a hurdle. It gives us a benchmark for asking whether an investment is generating enough return to justify the money being put into it. And even then, we have to be careful with the 9%. If the company is considering another project with roughly the same kind of business risk and expects to finance itself in roughly the same way, using its existing WACC may make sense.
But imagine taking that supermarket WACC and quietly using it to judge the luxury hotel. We already know what would be wrong with that. The money may come from the same company. The risk it is being asked to carry does not. The cost of capital has to reflect what we are actually asking investors to fund. And once we have gone through all of this trouble to understand what debt costs, what equity costs and how the two come together, there is one question that becomes almost impossible not to ask.
Eleven per cent for equity. Six per cent for debt. Why are we using so much of the expensive one?
If debt is cheaper, why don’t we just borrow more?
It sounds almost too obvious. If one source of money costs 11% and another costs 6%, use more of the 6%. And initially, there is some truth in that instinct. Lenders generally carry less risk than shareholders because they have contractual claims and stand ahead of shareholders if things go badly. Interest also normally brings a tax benefit.
Debt really can be cheaper.
So if we replace some expensive equity with cheaper debt, our overall cost of capital should fall. Under the traditional view of capital structure, initially, it does. The problem is that the 6% and the 11% don’t sit quietly beside one another while we rearrange the proportions.
This was the part I think I had missed. I had been treating cheaper as though it were a permanent property of the debt.
Six is less than eleven. Therefore, more six must make the average cheaper. But every time we add more debt, we are also changing the position of the people standing behind it. Debt arrives with promises. Interest this year. Interest next year. Interest when business is good. Interest when business is terrible.
Imagine two otherwise identical companies. They sell the same products, have the same customers and make exactly the same operating profit. One has almost no debt. The other has borrowed heavily. Now give both of them a terrible year. The first company has a terrible year. The second company has a terrible year and still has a large interest bill waiting to be paid.
If you are a shareholder in that second company, whatever might eventually be left for you has become much less certain. Would you still be happy requiring exactly the same return as before?
Probably not.
The business itself may not have changed, but your position has. So you start asking for more. The cost of equity rises. And if the company keeps borrowing, eventually lenders may start looking at their own position differently too. Lending another €1 million to a company with almost no debt is not the same proposition as lending another €1 million to a company already carrying enormous interest commitments. At some point, they may want more as well.
This is where something that looked so obvious at the beginning becomes much more interesting.
Debt can genuinely be the cheaper money. But using more of the cheaper thing can eventually make everything around it more expensive.
Under the traditional view of capital structure, there is therefore a point where those forces balance. Before it, cheaper debt helps pull the overall cost of capital down. Beyond it, the additional financial risk begins pushing the returns demanded by investors back up.
Somewhere between the two is the lowest WACC. And if the return investors require is lower, the future cash the company expects to generate is worth more today, all else being equal. So under this view, the point where WACC is lowest is also the point where company value is highest.
Only now do we really need a name for the balance we have been looking for.
The optimal capital structure.
I don’t think it is particularly useful to imagine that somewhere inside every company there is one perfect debt-to-equity percentage waiting patiently to be discovered. What matters more to me is the thought underneath it.
We started with something that seemed almost embarrassingly obvious: six per cent is cheaper than 11%. And that statement never stopped being true. What changed was everything around it.
The more debt we added, the more risk we pushed towards the shareholders standing behind it. Eventually, even the lenders began to see us differently. The thing that was cheaper on its own started changing the cost of everything else.
Which brings me back to the 50 cents. As children, the bargain was wonderfully small. I needed money. My brother had money. I borrowed his 50 cents, and he wanted a sweet for letting me use it. I understood that bargain before I knew what debt was, because the cost was sitting right there in my hand. Perhaps equity only feels stranger because its cost doesn’t come wrapped in a sweet.
The shareholder gives us money without knowing exactly what they will receive, or when. What they ask from us instead depends on what else they could have done with that money, what risks we are asking them to carry and where they will be standing if things go wrong.
And a company rarely has only one brother lending it 50 cents. Its money comes from different places, from people making different bargains and carrying different risks.
WACC is our attempt to bring all of those bargains together and ask what, taken as a whole, this money really costs us.
Not because money always sends us an invoice. Sometimes it does. Sometimes the cost is a sweet.
And sometimes the cost only becomes visible once we understand what someone had to give up to hand us the money in the first place.
