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Chapter 2 of 6 · 12 min

WACC: the discount rate

The blended return lenders and shareholders demand, and why it is the rate for unlevered cash flow.

By the end of this chapter you can
  • Calculate the cost of equity with CAPM
  • Blend equity and after-tax debt into WACC at market-value weights
  • Back out the beta that a stated WACC implies
  • Explain why more debt does not lower WACC forever
1

The intuition

Picture a house bought with a 60% mortgage and 40% of your own savings. The bank wants 6% a year on its share. You want 12% on yours, because you take the bigger risk: if the house loses value, your savings take the hit first. The return the house has to earn to keep both of you happy is the weighted average: 60% × 6% + 40% × 12% = 8.4%.

The key idea

WACC is the price of the money tied up in the business. A dollar of future cash flow is only worth paying for today if it earns at least that return, which is why unlevered cash flow is discounted at WACC.

2

Why it works

Unlevered free cash flow belongs to everyone who funds the business, so the rate you discount it at has to be the return everyone together requires. That is a weighted average of what each group demands.

  • Equity costs more than debt. Shareholders are paid last and absorb every surprise, so they demand a higher return.
  • Debt is cheaper again after tax. Interest is tax-deductible, so a 6% loan at a 25% tax rate really costs 4.5%. This is where the interest tax saving you left out of free cash flow shows up.
  • The cost of equity comes from CAPM: the risk-free rate plus beta times the equity risk premium. Beta measures how much the stock swings with the market; the premium is the extra return investors want for holding shares rather than government bonds.
  • Weights use market values. Investors want a return on what their stake is worth today, not on what the accountants recorded when the shares were issued.
A worked blend
Equity, at market value$600M at 10.0%
Debt$400M at 6.0% pre-tax
After-tax cost of debt6.0% × (1 − 25%) = 4.5%
Weights60% equity · 40% debt
= WACC60% × 10.0% + 40% × 4.5% = 7.8%
3

The formulas

Cost of equity = rf + β × ERP

Start from the risk-free return and add the market's premium, scaled by how much this stock moves with the market.

After-tax cost of debt = rd × (1 − t)

The interest rate, less the tax the interest saves.

E weight = equity ÷ (equity + debt)

Each group's share of the capital, at market value. The debt weight is the rest.

WACC = wE × cost of equity + wD × after-tax cost of debt

The blended return the whole capital structure demands.

Implied β = ((WACC − wD × rd × (1 − t)) ÷ wE − rf) ÷ ERP

Run it backwards: remove debt's share, scale up to the cost of equity, then undo CAPM.

4

Worked example

A first-round classic. Build it in the order you would say it out loud: cost of equity, cost of debt, weights, blend.

Drawing the numbers…
5

See it move

Same company. Change the capital structure and the inputs, and the recipe recomputes the blend.

Drawing the numbers…
Try this
  • Raise the debt with equity unchanged. The debt slice grows and WACC slides toward the after-tax cost of debt.
  • Raise beta. The cost of equity rises, but WACC rises by less: the change is scaled down by the equity weight.
  • Raise the pre-tax cost of debt by a full point. WACC rises by less than a point — only by the debt weight × (1 − tax rate).
  • Notice what these sliders hold still: the cost of equity does not react when you add debt. In a real company it would. The traps below explain why that matters.
6

Run it backwards

Same company, reversed: you are given WACC and every input except beta. What beta is that WACC assuming?

Drawing the numbers…

Take the blend apart in the order you built it. Remove debt's contribution, divide by the equity weight to get the cost of equity, then undo CAPM: subtract the risk-free rate and divide by the equity risk premium.

This is how you test a WACC someone hands you. If the implied beta comes out at 2.5 for a sleepy utility, something upstream is wrong.

7

Traps

Using book values for the weights.
Use market capitalization for equity. Book equity can be a small fraction of market value, or even negative after years of buybacks.
Using the pre-tax cost of debt.
Multiply by (1 − t). The tax saving on interest is the reason unlevered cash flow ignores interest, so it has to appear here instead.
Taking the cost of debt from the coupon on old bonds.
Use what the company would pay to borrow today: the current yield on its debt, or the rate on similar new issues.
Saying more debt always lowers WACC.
Only if the cost of equity stays put, and it will not. More debt makes the equity riskier, so beta and the cost of equity rise, and eventually lenders charge more too. WACC falls at first and then rises: it is U-shaped.
Using the market return in CAPM instead of the premium.
CAPM is rf + β × (market return − rf). If you are given the market return, subtract the risk-free rate first.
8

Say it in the interview

The interviewer asks

“How do you calculate WACC?”

Say yours out loud first, then compare.
9

Check yourself

4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.

Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.

0 of 4
Drawing your questions…
Remember
  • Cost of equity = rf + β × ERP.
  • Debt enters after tax: rd × (1 − t).
  • Weights at market value, never book.
  • WACC is U-shaped in leverage, not falling forever.