Unit 13 · Lesson 3 Corporate finance

Last lesson you guessed 10%. Now find the real number.

The story so far In Lesson 13.2 you judged the van with a 10% discount rate. But where should that number come from? Your shop's money comes from two places: a $40,000 bank loan at 8%, and $60,000 of owners' money, yours and your investor's. Neither one is free. The bank wants its interest, and the owners want a return big enough to be worth the risk. Blend the two, and you get the shop's real hurdle: the cost of capital.

What

The cost of capital is the average yearly return a company must pay its lenders and owners for using their money.

Why

It's the hurdle every project has to clear. A project that earns less than it destroys value, even if it makes a profit.

How

Find what debt costs after taxes, find what owners expect, then average the two by how much of each the company uses.

Who

Corporate treasurers manage the mix of debt and equity. Equity research analysts and investment bankers estimate it to value companies. CFOs set it as the hurdle rate.

What you're looking at: where the shop's money comes from and the bar it sets. On the left, 40% debt that costs 6% after taxes and 60% equity that costs 15%. On the right, the blended hurdle of 11.4%, and the van's 15.2% return flying over it.

01 See it

Every dollar has a price.

In Lesson 13.1 you learned the two kinds of money. Now you put a price on each, and blend them into one number.

Cost of debt, after taxes

The cost of debt starts with the interest rate. But interest is an expense on the income statement (Lesson 12.1), so it lowers taxes. That makes debt cheaper than its rate. To keep the math simple, this lesson uses a flat 25% tax rate.

After-tax cost of debt = interest rate × (1 − tax rate)

In this example

The bank loan: 8% × (1 − 0.25) = 8% × 0.75 = 6%. Every $100 of interest saves $25 of tax.

Cost of equity

The cost of equity is the return owners expect. Nobody sends a bill for it, but if owners don't earn it, they sell their shares or stop investing. It's always higher than the cost of debt, because owners get paid last: lenders get their interest first, even in a bad year (Lesson 13.1).

In this example

Your owners: Expect 15% a year. The bank only asks 8%, because it gets paid first.

The CAPM: where 15% comes from

Wall Street estimates the cost of equity with the CAPM, the capital asset pricing model. It starts from the risk-free rate, what U.S. government bonds pay. Then it adds extra return for risk: the market risk premium, times the company's beta, which measures how much it swings compared with the market.

Cost of equity = risk-free rate + beta × market risk premium

In this example

Risk-free rate: 4% from government bonds.
Beta: 2. A small, young shop swings about twice as much as the market.
Market risk premium: 5.5%.
Cost of equity: 4% + 2 × 5.5% = 4% + 11% = 15%.

Weights

A company's mix of debt and equity is its capital structure. Each kind of money counts by its share of the total.

Debt weight = debtdebt + equity

In this example

Debt: $40,000$100,000 = 40%
Equity: $60,000$100,000 = 60%

WACC: the blend

Multiply each cost by its weight and add them up. That's the weighted average cost of capital, or WACC, the company's cost of capital.

WACC = debt weight × after-tax cost of debt + equity weight × cost of equity

In this example

Debt part: 0.40 × 6% = 2.4%
Equity part: 0.60 × 15% = 9%
WACC: 2.4% + 9% = 11.4%

WACC is the hurdle

WACC is the discount rate to use for projects as risky as the business itself. A project is worth doing when its IRR beats the WACC, which is the same as having an NPV above zero at the WACC.

In this example

The van: IRR 15.2% beats 11.4%. At 11.4%, its NPV is about $977, less than the $1,372 you found at 10%, but still above zero. Buy it.
The parts booth: IRR about 13.6% also beats 11.4%. NPV about $300.

Share of the shop paid for with debt 40%

What you're looking at: the shop's money split into debt (blue, 6% after taxes) and equity (green, 15%). Move the slider to change the mix and watch the WACC, then see whether the van (IRR 15.2%) and the booth (IRR 13.6%) still clear it. Simplified: it keeps both costs fixed, which real lenders and owners don't (see the worked example).

02 Hear it

Two minutes. Just listen.

Tap any line to jump to it.

03 Play it

Clear the hurdle.

Eight questions about what money costs. Each one gives you the numbers. One try each.

Question 1 of 8

Right0 of 0

What you're looking at: made-up companies and projects. Each lists the numbers, then asks one question.

04 Break it down

The logic, step by step.

Finding any company's cost of capital takes four steps.

Step 1: Cost of debt, after taxes

Interest rate × (1 − tax rate)

In this example

The loan: 8% × 0.75 = 6%.

Step 2: Cost of equity

Risk-free rate + beta × market risk premium

In this example

The owners: 4% + 2 × 5.5% = 15%.

Step 3: Weights

Weight = each sourcetotal money

In this example

The mix: $40,000$100,000 = 40% debt, $60,000$100,000 = 60% equity.

Step 4: Blend, then use it as the hurdle

IRR above WACC → build it

In this example

WACC: 0.40 × 6% + 0.60 × 15% = 11.4%. The van's 15.2% clears it.

Worked example: is more debt always cheaper?

The slider makes it look like piling on debt keeps lowering WACC. Here's what really happens if the shop borrows until debt is 70% of its money:

The bank: sees a riskier borrower and charges 12% instead of 8%.
The owners: now get paid after a much bigger interest bill, so they want 20% instead of 15%.
Tax rate: still 25%.

After-tax cost of debt. 12% × 0.75 = 9%.
Debt part. 0.70 × 9% = 6.3%.
Equity part. 0.30 × 20% = 6%.
WACC. 6.3% + 6% = 12.3%, higher than the 11.4% you started with.
The answer. No. A little debt is cheap, but too much makes everyone demand more. Companies look for a middle mix where WACC is lowest.

05 Nature link

Crows only crack the big shells.

On the Pacific coast of Canada, crows eat sea snails called whelks. To crack one, a crow flies straight up about 5 meters and drops it on the rocks, again and again until it breaks. Every flight costs energy. Scientists found that crows pick only the largest whelks: small ones take just as many drops and hold too little food to pay for the flights.

What you're looking at: an illustration, not data. A crow carrying a whelk up to drop it on the rocks. On the left, the big whelks crows choose; on the right, the small ones they leave.

Why this sticks. Every flight has a cost, so a whelk has to return more food than the flights take. A project has to return more than the cost of the money behind it. Both are hurdles.

06 Notes

The page you'd copy down.

After-tax cost of debt = rate × (1 − tax rate). 8% × 0.75 = 6%.
Cost of equity (CAPM) = risk-free rate + beta × market risk premium. 4% + 2 × 5.5% = 15%.
Equity costs more than debt: owners are paid last and take more risk.
Weights: $40,000$100,000 = 40% debt, 60% equity.
WACC = 0.40 × 6% + 0.60 × 15% = 11.4%.
Hurdle: build when IRR beats WACC. Van 15.2% > 11.4%; NPV at 11.4% about $977.
Too much debt raises both costs: at 70% debt, WACC rose to 12.3%.

Fill in the blanks

1. A 10% loan with a 30% tax rate has an after-tax cost of percent.

2. A stock that swings twice as much as the market has a of 2.

3. The blend of a company's cost of debt and cost of equity is called its .

4. Owners are paid last, so the cost of is higher than the cost of debt.

07 Together

Grab a friend or a study group.

Look up a beta

Pick three companies you know, like a utility, a grocery chain and a tech company. Look up each one's beta on a finance site and guess why they differ.

Bank vs. owner

One person is the bank, one is an investor. The shop asks each for $10,000. Argue about what return each of you should ask for, and why.

Slider challenge

Using the slider above, find the debt share where the parts booth starts clearing the hurdle. Then explain why the real answer would be harder to find.

08 On your own

Just you and your money.

These stay on this device. Nobody else sees them.

What's your own "cost of capital"? If you have a credit card or loan, what rate does your debt cost you?

Paying off a 24% credit card is like earning 24% for sure. What does that say about investing while carrying that debt?

Would you rather work on the company side (setting the hurdle) or the investor side (demanding the return)? Why?

09 Check

Exam-style questions.

Written the way a college exam would ask them. Each right answer on the first try is worth 10 xp.

On the job: you're an equity research analyst

You're estimating the cost of capital for a grocery chain. Here's the situation:

Equity: $600 million (what all its shares are worth on the stock market).
Debt: $400 million, at 6% interest.
Tax rate: 21%, the U.S. federal rate for corporations.
Risk-free rate: 4%. Beta: 1.2. Market risk premium: 5%.
A new project: a delivery service with an expected IRR of 9%.

Your task: find the after-tax cost of debt, the cost of equity, the weights and the WACC. Should the chain launch the delivery service?

See a model answer

After-tax cost of debt: 6% × (1 − 0.21) = 6% × 0.79 = 4.74%.

Cost of equity: 4% + 1.2 × 5% = 4% + 6% = 10%.

Weights: $400 million$1,000 million = 40% debt, $600 million$1,000 million = 60% equity.

WACC: 0.40 × 4.74% + 0.60 × 10% = 1.896% + 6% = about 7.9%.

Decision: the delivery service's 9% IRR beats the 7.9% hurdle, so its NPV is above zero. Launch it, as long as it's about as risky as the rest of the business.

10 Where it leads

The hurdle behind every decision.

What you're looking at: a map of where this lesson fits in the course. Read it left to right: the lessons it builds on, this lesson in the middle, and the lesson that comes next.

Back · Unit 13Raising money
Back · Unit 13Picking projects with NPV
Back · Unit 5What a stock is
You are hereThe cost of capital
Next · Unit 14Risk and return

Next lesson: Risk and return →Course map