What the cost of capital measures
The weighted average cost of capital (WACC) is the average return a company must earn on its investments to satisfy all its investors, both lenders and shareholders. It is the minimum acceptable return for a project of average risk, which is why it is used as the discount rate when valuing cash flows.
WACC = (E / V) x Re + (D / V) x Rd x (1 - T)
where E is the market value of equity, D the market value of debt, V = E + D, Re the cost of equity, Rd the pre-tax cost of debt and T the tax rate. Everything depends on getting each input right.
Step 1: the cost of equity
Equity holders bear risk, so they require a return above the risk-free rate. The capital asset pricing model (CAPM) gives it as:
Re = Rf + Beta x (market risk premium)
| Input | What it is | Where it comes from |
|---|---|---|
| Rf | Risk-free rate | Yield on long-term government bonds in the same currency as the cash flows |
| Beta | Sensitivity of the stock to market movements | Regression of stock returns on market returns, or peer firms |
| Market risk premium | Expected market return less Rf | Historical averages or survey estimates, commonly 4 to 7 percent |
Cost of equity (hypothetical)
Rf = 4 percent, beta = 1.2, market risk premium = 6 percent.
Re = 4 + 1.2 x 6 = 4 + 7.2 = 11.2 percent.
A beta above 1 means the stock is more volatile than the market, so equity investors demand more. Always check that Rf and the market premium are consistent with each other and with the currency of your cash flows.
Step 2: the after-tax cost of debt
Debt is cheaper than equity because lenders are paid first and, in most tax systems, interest is tax-deductible. Use the current yield to maturity on the firm's long-term debt, not the coupon on old bonds, since the cost of capital is forward-looking.
After-tax cost of debt = Rd x (1 - T). With Rd = 6 percent and T = 25 percent, the after-tax cost is 6 x 0.75 = 4.5 percent.
The deduction applies only if the firm earns enough taxable profit to use it. Mention this if the case describes a firm making losses.
Step 3: the weights
Use market values, not book values, because the cost of capital reflects what investors would pay today. Market value of equity is the share price times shares outstanding. Market value of debt is usually approximated by book value unless the debt trades at a significantly different price.
WACC (hypothetical)
E = $600 million, D = $400 million, so V = $1,000 million. Weights: E/V = 60 percent, D/V = 40 percent.
WACC = 0.60 x 11.2 + 0.40 x 4.5 = 6.72 + 1.80 = 8.52 percent.
Say which capital structure you use, the firm's current structure or a target, and why. Weights should reflect the structure the firm will use to finance the project, not necessarily the historical one.
Using peer betas: unlever and relever
When a firm or division is not publicly traded, or its financing is about to change, take betas from comparable firms. Observed (levered) betas include the effect of each firm's debt, so you must remove it to get the underlying business risk, then add back your own structure.
Unlevered beta = Levered beta / (1 + (1 - T) x D/E)
Unlever and relever (hypothetical, continuing the firm above)
The firm's levered beta is 1.2 at D/E = 400 / 600 = 0.667 and T = 25 percent.
Unlevered beta = 1.2 / (1 + 0.75 x 0.667) = 1.2 / 1.5 = 0.80.
If the firm moves to D/E = 1.0, the relevered beta = 0.80 x (1 + 0.75 x 1.0) = 0.80 x 1.75 = 1.40.
New cost of equity = 4 + 1.4 x 6 = 12.4 percent. Equity gets riskier as debt rises, which offsets part of the benefit of cheaper debt.
Be careful with the standard formula's assumption that debt is risk-free (debt beta of zero). For highly leveraged firms, mention that this simplification understates the risk borne by lenders.
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Get an instant quoteUsing WACC correctly
WACC is the right discount rate for projects with the same risk as the company's existing business, financed in the company's usual way. Using it blindly can mislead.
| Situation | Problem with using company WACC | Better approach |
|---|---|---|
| Project is riskier than the firm | Accepts too many risky projects | Use a higher, project-specific rate based on comparable firms |
| Project is safer than the firm | Rejects good safe projects | Use a lower rate |
| Overseas project | Country and currency risk ignored | Adjust rates for currency and country risk, or model cash flows in local currency with a local rate |
| Project with special financing | WACC assumes standard structure | Consider adjusted present value (APV) |
Show the effect of the rate in your answer. A project with a $10 million outlay and a perpetual annual cash flow of $0.9 million has a value of 0.9 / 0.0852 = $10.56 million at an 8.52 percent rate and a net present value of $0.56 million. At 9.5 percent it is worth 0.9 / 0.095 = $9.47 million, a negative NPV of $0.53 million. A one-point change in the rate reverses the decision, which is why the cost of capital deserves care. See our guide to valuation and discounted cash flow for the next step.
A full worked problem: a project-specific discount rate
Suppose a firm in a different business considers a division in a new industry. The firm's own beta is not relevant, so you use comparable companies.
Peer betas to a project WACC (hypothetical)
Tax rate 25 percent. Risk-free rate 4 percent. Market risk premium 6 percent. Peers: Company A has a levered beta of 1.1 and D/E of 0.50; Company B has 1.3 and D/E of 1.00.
Unlever: A = 1.1 / (1 + 0.75 x 0.50) = 1.1 / 1.375 = 0.800. B = 1.3 / (1 + 0.75 x 1.00) = 1.3 / 1.75 = 0.743. Average = 0.771.
Relever at the division's target D/E of 0.25 (debt is 20 percent of value): 0.771 x (1 + 0.75 x 0.25) = 0.771 x 1.1875 = 0.916.
Cost of equity = 4 + 0.916 x 6 = 9.50 percent. Pre-tax cost of debt 5.5 percent, so after tax = 5.5 x 0.75 = 4.125 percent.
WACC = 0.80 x 9.50 + 0.20 x 4.125 = 7.60 + 0.825 = 8.42 percent.
The division's own rate is lower than the parent's 8.52 percent in the earlier example, because the peers are less risky. Using the parent's rate would overstate the hurdle for this division, and for a riskier division it would understate it.
How sensitive is WACC to the market premium?
The market risk premium is an estimate, and it moves the answer more than most students expect. Using the division above, with beta 0.916:
| Market risk premium | Cost of equity | WACC |
|---|---|---|
| 5 percent | 4 + 0.916 x 5 = 8.58 percent | 0.8 x 8.58 + 0.825 = 7.69 percent |
| 6 percent | 9.50 percent | 8.42 percent |
| 7 percent | 4 + 0.916 x 7 = 10.41 percent | 0.8 x 10.41 + 0.825 = 9.16 percent |
A one-point change in the premium moves WACC by about 0.7 points, enough to flip many project decisions. In your write-up, report a range, say which premium you used and why, and show the decision at both ends. A conclusion that holds across the range is much stronger than one that depends on a single input.
Writing the WACC section of an assignment
- State each input with its source Risk-free rate (which bond), beta (which peers and window), premium (which estimate).
- Show the table of inputs One row per input, so a marker can check it quickly.
- Explain choices in one sentence each Why target weights, why peer betas, why market values.
- Round at the end Keep three or four decimals in the steps to avoid compounding rounding errors.
- Link to the decision Say what NPV or value results at your rate and at a higher and a lower one.
Common mistakes
- Using book values for weights Use market values of equity, and market or fair value for debt where possible.
- Forgetting the tax shield Multiply the cost of debt by (1 minus tax rate) in WACC.
- Using coupon rate as cost of debt Use the current yield to maturity.
- Mismatched inputs Match the currency and maturity of the risk-free rate to the cash flows.
- Using WACC for any project Adjust for projects with different risk or financing.
- Unlabeled assumptions State your market premium and where it comes from.
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