How WACC is calculated

WACC is the weighted average cost of capital. It is the blended return a company has to earn on the money funding it: what shareholders require, mixed with what lenders charge once any tax relief on interest is counted, in proportion to the market share of each claim.

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

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

The first worked example fills that in. Equity of $6,000,000 at 9 percent, debt of $4,000,000 at 5 percent, tax at 25 percent:

Because the weights add to 1, WACC lands between the cost of equity and the after-tax cost of debt. On these figures that range is 9 percent down to 3.75 percent, and 6.9 percent sits 40 percent of the way down it, which is exactly the debt weight. Rebuilt from cash amounts: nine percent of $6,000,000 is $540{,}000$, 3.75 percent of $4,000,000 is $150{,}000$, and $690{,}000$ on $10{,}000{,}000$ of capital is 6.9 percent.

The WACC calculator above returns WACC, each weight, and the after-tax cost of debt. What comes out is a nominal rate, so it belongs against cash flows that already contain inflation. It is the discount rate in a net present value for a project of the firm's ordinary risk, and the bar an internal rate of return has to clear. The cost of capital is the same object seen as an opportunity cost. This page is the formula that produces the rate.

The two fractions $\frac{E}{V}$ and $\frac{D}{V}$ are the weights. They are how the capital in place is valued now, because WACC is the return required on that capital from here forward, not a record of how the firm last raised money.

Equity at market value is the share count times the share price. Debt at market value is what the bonds would sell for. Where the debt is not traded, book value is a fair stand-in, because a loan whose rate is close to today's rate is worth close to what is owed. Book equity is not a stand-in for market equity. Profitable firms usually trade above the equity the accounts carry, so replacing market equity with book equity shrinks the equity weight, inflates the debt weight, and pulls WACC down toward the cheap source.

Take the first worked example and swap only the equity figure, from $6,000,000 at market to $4,000,000 at book, against the same $4,000,000 of debt:

The book-weighted sum is $0.50 \times 9 + 0.50 \times 3.75 = 6.375$. Just over half a percentage point looks small until it is applied to every year of a forecast. A hurdle that is too low accepts the marginal projects, which are the ones where half a point decides the answer. Reading debt off the balance sheet is often fine. Carrying that habit across to equity is not.

Two-source weights are the usual case. Where preferred stock is material the formula grows a third term, $\frac{P}{V} \times R_p$, with $V$ widened to $E + P + D$ and no $(1 - t)$ against the preferred cost, because preferred dividends are paid from taxed profit like ordinary ones. A company with no debt has an equity weight of 1, and its WACC is its cost of equity.

Which mix to put in, current or target, is a forward-looking choice. If the firm will hold something close to the mix it has now, current market weights match. If it refinances toward a stated mix, the target weights match. Either way the costs are the costs of raising that mix today.

Interest counts as a cost of doing business wherever the tax code says it does, so a company that pays interest usually pays less tax. That is why the debt term is multiplied by $(1 - t)$ and the equity term is not. Dividends and buybacks come out of profit that has already been taxed, so there is nothing to deduct against them.

At a 25 percent tax rate, each unit of interest costs the company 0.75 once the deduction is counted, which turns a 5 percent cost of debt into 3.75 percent:

$$R_d \times (1 - t) = 5 \times (1 - 0.25) = 3.75$$

What the relief is worth to WACC is the debt weight times the cost of debt times the tax rate. On the first worked example that is $0.40 \times 5 \times 0.25 = 0.5$ percentage points. The second worked example measures the same gap from the other end, by setting the tax rate to 0: WACC rises from 6.9 percent to 7.4 percent, and the after-tax cost of debt returns to the full 5 percent the lender charges.

Three conditions sit behind that 0.5 point, 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 let the unused deduction be carried forward.
• 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 set their own caps, deny relief on some structures, or give equity a matching allowance so the bias toward debt disappears. The $t$ in the formula is the rate that actually applies to this company in this tax system, not a rate copied from another country.
• The rate has to be the marginal one. The figure that matters is the rate on the profit the interest actually shelters, over the life of the cash flows being discounted, not the effective rate from last year's accounts.

Where interest is not deductible, or there is no profit to shelter, set the tax rate to 0. The debt term then costs its full amount. The relief lowers the company's cost without lowering the lender's return: the tax authority pays the difference. It makes debt cheaper to the borrower, not free.

The weights can be read off a market. The two costs cannot. Neither $R_e$ nor $R_d$ is printed on the income statement, and using a figure that is printed there is the usual way to get WACC wrong in the inputs rather than in the weights.

The cost of debt is what the company would pay to borrow today, for a term and seniority close to the debt already in $D$. That is a current yield, not the coupon on borrowing it did years ago. A bond still paying a 5 percent coupon is not a 5 percent cost of debt if the same company would now pay more than 5 percent to issue again. For traded bonds the current yield is observable. For bank debt it is the rate on a new loan of similar size and covenants. Either way it already contains compensation for the chance of not being repaid.

The cost of equity is an estimate of what shareholders require. The usual construction is the capital asset pricing model: a risk-free rate, plus beta times the equity risk premium. The risk-free piece is a nominal government yield. Beta measures how hard this equity moves with the market. The premium is the extra return expected for holding equities rather than the risk-free asset, and published estimates of it sit a point or two apart.

That range is multiplied by the equity weight. On a 60 percent equity mix, a one point disagreement about the premium moves WACC by 0.6 points, which is larger than the 0.5 point the tax deduction is worth on the first worked example. Two careful estimates a point apart would put this firm's WACC near 6.3 percent or near 7.5 percent rather than on 6.9 percent. A published WACC is better read as a range a point or so wide.

The coupon on existing debt, the dividend yield, and last year's earnings yield are the three substitutions that look like costs and are not. Change the 9 percent or the 5 percent and 6.9 percent moves with it at the relevant weight: one extra point on the cost of equity adds 0.6 points of WACC here, and one extra point on the cost of debt adds $0.40 \times (1 - 0.25) = 0.3$ points.

Debt costs less than equity in almost every mix you can write down. Lenders are paid before shareholders and can force the issue if they are not, so they carry less risk and ask for less return. The tax deduction then takes a further slice off what the company pays. 5 percent before tax is 3.75 percent after it, against 9 percent on the equity.

So tilting the mix toward debt lowers WACC, which is what the third worked example shows. The same costs, tax still at 25 percent, but the funding flipped to $4,000,000 of equity and $6,000,000 of debt: WACC falls from 6.9 percent to 5.85 percent.

That fall is what you get when both input costs are held still. Holding them still is the trick in the sum. Every extra unit borrowed puts a fixed claim ahead of the shareholders, so what is left of the profit swings harder. The cost of equity rises with financial leverage, and lenders watching their cover thin out want more as well. Both inputs climb while the weights move toward the cheaper one, and the two effects pull against each other.

The classic result, from Modigliani and Miller, is that with no taxes and no cost of financial distress the two cancel exactly. Start from the second worked example, where the tax rate is 0 and WACC is 7.4 percent. Call that 7.4 percent the return on the assets. At the original mix, debt over equity is $4{,}000{,}000 / 6{,}000{,}000 = 2/3$, and the cost of equity that keeps WACC at 7.4 percent is:

$$R_e = 7.4 + \frac{2}{3} \times (7.4 - 5) = 7.4 + 1.6 = 9$$

which is the 9 percent the example started with. After the buyback, debt over equity is $6{,}000{,}000 / 4{,}000{,}000 = 1.5$, and the same identity says the cost of equity has to rise to:

$$R_e = 7.4 + 1.5 \times (7.4 - 5) = 7.4 + 3.6 = 11$$

Blend that 11 percent with the unchanged 5 percent cost of debt at the new 40/60 weights: $0.40 \times 11 + 0.60 \times 5 = 7.4$. WACC has not moved. How the firm is funded has changed the two costs by just enough to leave the blended required return where it was.

Add the tax deduction and the cancellation is no longer exact, so WACC falls with the debt weight for a while: that is the 6.9 to 5.85 move with costs held fixed. Add the cost of distress, where a forced sale or a covenant breach starts to look possible, and the fall stops being free. Reprice the 40/60 mix at 11 percent on the equity and 6 percent on the debt, which is 4.5 percent after the same 25 percent tax, and WACC reads $0.40 \times 11 + 0.60 \times 4.5 = 7.1$, above the 6.9 percent it started from. Cheaper debt did not stay cheaper.

Judging where the mix stops helping is a risk and return question, and it cannot be settled by pointing at a WACC that held both costs fixed. The leverage ratio calculator shows how a given mix turns a fall in assets into a larger fall in equity.

The 6.9 percent is a discount rate, not a figure to report.

A project of this firm's ordinary risk, funded in roughly this mix, has to earn 6.9 percent on the capital tied up in it before it has added anything for anyone. Discount its expected cash flows at 6.9 percent: a positive present value means it clears the bar, zero means it exactly covers the capital, and negative means the money is worth more in the next best use. That is a net present value test, and WACC is the $r$ in

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

The same test solved for the rate instead of the value gives the internal rate of return. A project whose IRR is above WACC passes on that measure too, for a conventional series that goes negative once and then stays positive. The two measures do not agree on ranking, because a rate says nothing about how much money is at stake.

WACC already contains the cost of the debt, so the cash flows it discounts are cash flows to the whole firm, before interest: free cash flow. Take interest out of the cash flow and then discount at WACC, and the lenders have been charged twice. The other pairing is cash flow to equity, after interest, discounted at the cost of equity.

WACC built from nominal borrowing rates and a nominal risk-free yield is a nominal rate. It belongs against cash flows that already include future prices. A forecast written in today's prices needs a real rate. Mixing the two charges inflation twice.

WACC is the right hurdle for a project that looks like the rest of the business and will be funded like it. Using the firm's 6.9 percent on a venture well outside its ordinary work discounts risky cash flows at a safer rate and flatters them. The cost of capital guide works that mistake in full, including a project that passes at a firm-wide rate and fails at a rate matched to its own risk.