Cost of capital: the rate a project clears

Money in a business came from somewhere, and whoever supplied it had somewhere else to put it. The cost of capital is the return those suppliers could have earned elsewhere for taking the same risk. That is the bar the business has to clear before it has done anything for them at all.

So it is an opportunity cost, not an invoice. Interest on a loan does arrive as a payment, which is why the debt side feels like a bill. The equity side never does. Nobody sends a company a demand for the 10 percent its shareholders require. That figure is the return they gave up by leaving money here rather than in the next best thing of matching risk, and it is no less real for being invisible.

The clearest case is a company with no borrowing at all, funding everything out of profit it kept. Nothing leaves the bank account, so on a cash view its capital looks free. It is not. Retained profit belongs to the shareholders, who could have had it and put it to work themselves, so keeping it is only justified if the company beats what they would have earned. This is opportunity cost pointed at funding.

Two things follow. A project can be profitable in the accounting sense and still be a mistake: earning 5 percent on capital that costs 8 percent shrinks the firm while the income statement shows a profit. And the number is forward-looking. It is what money would cost to raise now, not the rate on a loan signed years ago at a rate nobody can get today.

A company usually raises money from more than one source, and the sources do not charge the same amount. The cost of capital for the firm as a whole is the average of those costs, weighted by how much of the funding each source supplies. That average is the weighted average cost of capital, or WACC.

$$r_{\text{WACC}} = \frac{E}{V} \times R_e + \frac{D}{V} \times R_d \times (1 - t)$$

$E$ is the market value of the equity, $D$ the market value of the debt, and $V = E + D$ the two added together. $R_e$ is the return shareholders require, $R_d$ the rate lenders charge before tax, and $t$ the marginal tax rate on the profit the interest shelters.

The first worked example runs it on $7,000,000 of equity at 10 percent and $3,000,000 of debt at 6 percent, taxed at 25 percent:

Because the weights add to 1, the answer always lands between the two costs and slides towards whichever source is growing. The WACC calculator runs that arithmetic on any mix.

Use market values, not balance sheet values: the question is what the capital in place is worth now. Neither cost is printed on a statement. The cost of debt is what the firm would pay to borrow today. The cost of equity is an estimate, usually the risk-free rate plus beta times the equity risk premium, and careful estimates of it sit a point or two apart, so read the output as a range.

Put the two claims side by side and the price difference stops looking odd.

Shareholders absorb the swing in a company's results, in both directions. Lenders mostly do not, because their claim is fixed and ranks ahead. Anything carrying more risk has to offer more return to attract money, so the residual claim prices higher than the fixed one.

Be careful with the word premium here. The equity risk premium is measured against the risk-free rate, not against what this particular company pays its own lenders, and the two gaps are not the same size. Lenders charge a premium of their own for the chance of not being repaid, so as a borrower weakens and its debt starts pricing that chance, the distance between its two costs of funding closes. For a sound borrower the two usually sit a few percentage points apart. For one the market doubts, they converge.

The conclusion people jump to is that a firm should borrow as much as it can and enjoy the cheaper source. The arithmetic says so only while both input costs hold still, and they do not. Every extra dollar of debt puts another fixed claim ahead of the shareholders, so what is left over swings harder and the cost of equity rises with financial leverage. Lenders watching their cover thin out charge more too, and add covenants on top.

The cheaper source is cheaper because it is safer for the person supplying it, and what makes it safer for them is what makes it riskier for the company: a payment that must be made on a date, in a year that may be bad. Firms in one industry do cluster around similar funding mixes rather than borrowing to the limit, which is what that trade-off predicts. Take it as consistent with the trade-off rather than as proof of it: firms in an industry also share asset types, cash flow patterns and tax positions, and they watch what their peers do.

Where a tax system treats interest as a cost of doing business, a company that pays interest pays less tax, so borrowing costs the interest less the tax saved. At a 25 percent marginal rate, a 6 percent loan costs the company 4.5 percent. Dividends and buybacks come out of profit already taxed, so there is nothing to deduct against them. That asymmetry is why the debt term carries $(1 - t)$ and the equity term does not.

The second worked example measures it by switching the relief off: the same firm and the same costs read 8.8 percent instead of 8.35 percent. That 0.45 point gap is the debt weight times the borrowing rate times the tax rate, and it grows with all three.

Three conditions sit behind it, and any of them can take it away.

• There has to be taxable profit to shelter. A company making losses deducts nothing this year, though many tax systems carry the relief forward to a profitable year.
• The deduction has to be allowed. In the United States, interest on business borrowing is generally deductible against taxable income, subject to a cap tied to earnings that has been rewritten more than once. Other countries cap it differently, deny it on some structures, or give equity a matching allowance that removes the tilt towards debt. Check the rule for the company and the year rather than carrying one country's treatment into another.
• The rate has to be the marginal one: the rate on the profit the interest actually shelters, not the average that falls out of last year's accounts.

Note what the relief does not do. It lowers the borrower's cost without lowering the lender's return: the tax authority pays the difference. It makes debt cheaper, not free.

The cost of capital is not a figure to admire on a slide. It is the rate that goes into a discounting calculation, which is where it decides things.

$$\text{NPV} = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t}$$

With $r$ set to the cost of capital, a positive net present value means the project earns more than the capital funding it costs, zero means exactly enough, and negative means the money is worth more somewhere else. The third worked example runs a project costing $2,000,000 that returns $520,000 a year for five years. Discounted at 8.35 percent those five payments are worth $2,057,196.98, so the NPV is $57,196.98 and it passes, barely. The net present value calculator above runs any version of it.

The same calculation solved for the rate instead of the value gives the internal rate of return: the rate at which NPV hits zero. For that project it is 9.4349 percent, which clears an 8.35 percent bar by about a point. The two measures agree on accept or reject for a series like this one, which goes negative once and then stays positive. They do not agree on ranking, because a rate says nothing about how much money is at stake.

Two consistency rules keep the discounting honest.

• Match the cash flow to the rate. WACC already contains the cost of the debt, so it belongs against free cash flow to the whole firm. Subtract interest from the cash flow and discount at WACC as well, and the debt has been charged twice.
• Match inflation to inflation. Ordinary loans and conventional government bonds are quoted in nominal terms, so a WACC built from them is a nominal rate and belongs against forecasts that carry price rises in them. Discount a forecast written in today's prices at a nominal rate and inflation gets charged twice, which understates the project. The error grows the longer the forecast runs.

A firm-wide cost of capital is an average of the risks the firm already runs. Used on a project riskier than that average it sets the bar too low; used on a safer one it sets the bar too high.

The fourth worked example takes the project that just passed and judges it as what it is, an entry into a new market where businesses of that kind are funded at around 13 percent. The same five payments are now worth $1,828,960.26 against the same $2,000,000 outlay, so the project that passed a moment ago now falls well short. Nothing about the project changed. Only the bar did.

Not every proposal is misjudged by a single rate. The ones that are, are those whose return lands between the firm-wide rate and the rate their own risk deserves, which is exactly the band the project above sits in at 9.4349 percent. Anything comfortably above both bars passes either way, and anything below both fails either way.

The damage also compounds. Round after round, risky proposals that fail on their own merits get funded and safe ones that would have passed get turned away, so the firm can drift riskier while the published hurdle rate sits where it always was. The average it was built from stops being true, which makes the next round worse. That is the quiet subsidy: safe projects, judged too harshly, hand their funding to risky projects judged too kindly.

The usual fix is to build a rate for the project rather than the firm, taking it from companies whose main business is that kind of work and adjusting for the funding mix. It needs comparable companies to exist and to be readable, which for a genuinely new line of business they may not be, so what comes out is an estimate and it will be argued over. An argued-over rate near the right risk still beats a precise rate built for a different one.