Cost of Capital

Slides

Expert-Level Understanding

Now let’s connect it to bigger ideas:

• Why YTM matters:

Companies refinance, issue new bonds, or roll over loans. If you want to know what debt truly costs them going forward, it’s the market rate (YTM), not some old coupon rate from years ago.

• Why after-tax matters:

Because debt reduces taxable income, governments are essentially subsidizing borrowing. That’s why WACC always uses after-tax debt cost.

• Why market weights matter:

WACC is about the opportunity cost of capital today. Market values tell you what investors are willing to pay for debt and equity now. Book values are historical and may misrepresent reality.

• Debt vs. Equity costs:
• Debt is usually cheaper (lower return required) because lenders get paid first and are safer.
• Equity is riskier and thus has a higher cost.
• The company’s overall cost of capital is the blend — WACC.
• Strategic Insight:
• If debt markets price your company’s bonds at a high spread (say 8% over Treasuries), it’s a signal of perceived risk.
• As a CFO, you can use this information to gauge market confidence in your creditworthiness.

Notes

• Capital is scarce, so we’re making a tradeoff and must ensure that tradeoff is worth our while. It’s an accountability measure

• The ‘weights’ are the % of debt and equity
• Debt provides a shield, effectively reducing the cost of our debt by the % of the tax rate. So we pay the effective rate of whatever 1 - T is

🌱 Plain English Explanation

1. Cost of Debt (rD):
• This is essentially the interest rate the company pays on its debt today.
• But we don’t just look at the coupon (the fixed % on the bond when it was issued).
• Instead, we look at the current yield to maturity (YTM) — what it would cost the company right now if it wanted to borrow.
2. Current IRR vs. Historical Coupon:
• The coupon is what the company promised to pay when it first issued the bond.
• But bonds trade every day in the market, so investors now demand a certain yield (YTM) based on risk and interest rates.
• That’s why we use the current IRR (today’s required return), not the stale coupon.
3. Spread over Treasuries:
• Think of it this way: U.S. Treasury bonds are “risk-free.”
• Investors in your company’s debt want more return because you’re riskier than the U.S. government.
• The extra return they demand is called a spread (e.g., 3% over 10-year Treasuries).
4. Weights in WACC:
• When you blend debt and equity in WACC, you use the market value proportions (what the company’s debt and equity are worth in the market today), not book values on the balance sheet.
5. T = marginal cash tax rate:
• Interest on debt is tax-deductible.
• So, the effective cost of debt is reduced by the tax shield: rD x (1-T)
• Example: if debt costs 6% and taxes are 25%, effective after-tax cost of debt = 4.5%.

📊 Example

Suppose your company has:

• Bonds trading at a YTM of 7%.
• Treasury yields at 3% → spread = 4%.
• Tax rate = 25%.

After-tax cost of debt = 7% × (1 – 0.25) = 5.25%.

That 5.25% is what you plug into your WACC formula.

✅ Bottom line you could say to a professor or board:

“The cost of debt we use in WACC isn’t the old coupon rate — it’s the current market yield to maturity on our bonds, because that reflects what it costs us to borrow today. We adjust that for the tax shield (since interest is deductible) and weight it by the market value of debt versus equity. That gives us the true effective cost of debt capital in our blended WACC.”

Risk & Return


• Only compensated for the systematic risk - that which can’t be diversified away
• This is the market's logic: The market will not compensate you for taking on a risk that you could have easily eliminated for free. This type of company-specific, diversifiable risk is often called idiosyncratic risk.
• You only get rewarded—with a higher expected return, or a risk premium—for taking on risk that cannot be diversified away. This is called systematic risk or market risk. What is this? It's the risk that affects all companies. Think of a major economic recession, a global pandemic, or a significant change in interest rates. In a deep recession, people might buy a little less ice cream and a little less hot chocolate. This is a risk that impacts the entire system. You can't escape it simply by owning different assets. Because sophisticated investors cannot eliminate this risk, they demand to be compensated for bearing it. This compensation is the risk premium—the extra return you expect to earn from investing in the stock market over and above a "risk-free" investment like a government bond. So, the big takeaway is this: You are paid to take on risks you can't get rid of (systematic), but you are not paid to take on risks you could have easily shed (idiosyncratic). Your job as an investor is to eliminate the uncompensated, diversifiable risk so you're left with only the market risk that, hopefully, pays you a premium.

• ri and rm, if beta is positive then if the market moves then the security moves in the same direciton. If Beta is 0 then it has no affect on the stock, if beta is negative, then it moves opposite ot the market

• The CAPM teaches how to calculate the risk premium.
• The risk free rate explains the compensation we say we need for the time value of money
• The risk premium is what we must be compensated for to tolerate the risk we’re undertaking.
• So what’s the risk premium?
• First, Beta, which is the securities sensitivity to market risk. How sensistive
• Price per unit of risk we want to be compensated for, well diversified portfolio - the risk free rate. Since we’ve already added the risk free rate, we need to subtract that from
• We should be only compensated for the additional risk we’re taking so that’s why we take rm - rf.

The Market Risk Premium Definition

The slide notes:

• “The market risk premium is the compensation investors require for the ‘average’ risk.”
• It’s literally: expected market return – risk-free rate.
• This sets the baseline premium for equity risk. Beta then scales it up or down depending on your company’s sensitivity to the market.

“CAPM says: investors want a risk-free return plus extra pay for risk. The extra depends on two things: the average market risk premium and how risky your stock is relative to the market (beta). Multiply them and you get the risk premium for your stock. Add it to the risk-free rate and you have the cost of equity — the minimum return investors demand to hold your shares.”

5. Example in Numbers

Suppose we regress 5 years of monthly returns of Tesla against S&P 500. We get:

• Alpha = 0.5% (Tesla tends to earn a small return even when market is flat).
• Beta = 1.8 (Tesla is very sensitive; if market goes up 1%, Tesla goes up 1.8%).
• R² = 0.40 (40% of Tesla’s returns are explained by the market, rest is firm-specific).

So: Tesla’s cost of equity would be calculated with β = 1.8 in CAPM.

✅ How you could explain in class or boardroom:

“Beta is estimated by running a regression of our stock’s returns against the market index. The slope of that line tells us how much our stock typically moves when the market moves. A beta above 1 means our equity is riskier than average, below 1 means it’s more defensive. We then use that beta in CAPM to estimate the cost of equity, which feeds into WACC.”

Summary:

• Start with the risk-free rate → “table stakes,” the baseline of what any investor can get from Treasuries.
• Add a risk premium → the extra compensation for taking on systematic (market) risk.
• Scale that premium by beta → to reflect how sensitive your stock is to market swings.

Let me fine-tune and extend what you said, so you can explain it with total rigor and confidence.

2. Risk premium = β × (Market Risk Premium)

• Market Risk Premium (rm – rf):
• The average extra return investors demand for holding the whole stock market instead of risk-free bonds.
• Example: If S&P 500 expected return = 9%, Treasuries = 4%, then market risk premium = 5%.
• Beta (β):
• A measure of how risky your stock is compared to the market.
• β = 1: your stock moves in line with the market.
• β > 1: your stock is riskier than the market (more volatile).
• β < 1: safer than the market (e.g., utilities).

👉 Together: β × (market risk premium) = the extra return required for the specific riskiness of your stock.

The Intuition Behind Beta

• Beta = “How sensitive is my stock’s return to movements in the market?”
• If the market goes up 1%, does my stock typically go up 0.5% (low beta), 1% (average beta), or 1.5% (high beta)?
• Mathematically, it’s the slope of the line when you plot stock returns vs market returns.

How It’s Done in Practice

1. Collect Data
• Choose a time horizon (2–5 years of monthly returns is common; sometimes daily if you want higher frequency).
• Compute percentage returns for your stock and for the market index (e.g., S&P 500).
2. Run the Regression
• In Excel, you can use LINEST() or Data Analysis → Regression.
• In R/Python, you’d run a simple linear regression.
• The coefficient on market return is your beta.
3. Interpret
• β = 1.0 → stock moves in line with market.
• β = 1.5 → 50% more volatile than market (amplifies swings).
• β = 0.5 → only half as sensitive (defensive stock).
• β < 0 → moves opposite the market (rare, think gold mining or hedges).

1. Risk-Free Rate (rf)

✔️ You nailed this: “don’t even talk to me unless you beat Treasuries.”

• Think 10-year Treasury yield.
• Everyone agrees this is the baseline return with (essentially) zero default risk.

2. Market Risk Premium (rm – rf)

✔️ You’re right that we subtract the risk-free rate from the market return. Why?

• Because the stock market’s total return (rm) already includes the risk-free rate.
• What we care about is the excess return of the market above Treasuries.
• This is the “price of risk” for the average stock.

Example:

• S&P 500 expected return = 9%
• Treasury = 4%
• Market risk premium = 5%

“CAPM says the return investors demand is: risk-free rate plus extra compensation for risk. The extra comes from the market’s risk premium, scaled by beta. Beta measures how much the stock amplifies or dampens market movements — it’s the stock’s sensitivity to systematic risk. If beta is 1, you get market-like risk. If it’s 2, the stock doubles the market’s swings. If it’s 0, the stock is insulated from the market. CAPM turns those relationships into a required rate of return, which becomes the cost of equity in WACC.”

Putting It All Together

• DCF = the full method: forecast expected cash flows → discount by cost of capital → sum them up.
• NPV = the decision rule from DCF: is the present value of inflows greater than the investment outlay?
• Expected cash flow = your best probability-weighted forecast of future cash.
• Cost of capital = the discount rate, reflecting investors’ required returns for bearing systematic risk.

✅ One-liner you could use in class:

“DCF is the framework. NPV is the decision rule. Expected cash flow is the numerator, cost of capital is the denominator. If the present value of expected cash flows discounted by the cost of capital exceeds what we pay in, we take the project — it means we’re creating value.”

Step 1: The Core Principle

• Business risk = volatility in the firm’s operating cash flows (driven by industry, competition, technology, demand swings, etc.).
• This risk exists no matter how you finance the firm.
• Capital structure doesn’t change business risk — it only changes how that risk is shared between debt holders and equity holders.

🌱 Step 2: No Debt (All-Equity Firm)

• If the firm has no debt, all risk falls on equity holders.
• Example: EBIT swings between $50m and $150m depending on the economy. With no debt, shareholders absorb the entire swing.

👉 Equity beta = business risk only.

🌱 Step 3: Add Debt (Leverage)

• Suppose the firm borrows money and now has fixed interest payments.
• Debt holders get their interest no matter what, as long as the firm stays solvent. They face little risk (senior in claims, often collateralized).
• Equity holders are now “residual claimants.” They only get what’s left after debt is paid.

👉 This makes their returns more volatile.

• In good years → equity return is amplified (because they use debt to juice returns).
• In bad years → equity gets crushed, because debt still must be paid.

This is why we say equity holders now bear business risk + financial risk.

🌱 Step 4: The Intuition in Simple Words

• Leverage = using debt = magnifies outcomes.
• It doesn’t make the company’s operations riskier; it makes the equity holder’s position riskier.
• The same business volatility is now spread over a smaller equity base, so equity’s volatility (and required return) goes up.

Increase the risk of equity b/c we now have less equity, the less of it comes second in the shoot, debotrs paid first. And the less amount we have is more concentrated…

Plain Speak Version

1. Debt is cheaper than equity.
• Lenders (bondholders) demand lower returns than shareholders.
• Why? Because lenders get paid first and have collateral, so they take less risk.
2. Debt has a tax shield.
• Interest payments reduce taxable income.
• That means you pay less in taxes, which makes debt effectively even cheaper.
3. If you use more debt, you need less equity.
• Equity is more expensive, so shifting toward debt seems like it should lower your WACC.
4. BUT the cost of equity goes up.
• More debt makes equity riskier (because lenders get priority, shareholders are “last in line”).
• Shareholders demand a higher return to compensate.
5. So what happens to WACC?
• Without taxes: WACC stays the same as you increase leverage.
• With taxes: WACC may go down at first (because of the tax shield benefit of debt).

📈 The More Insightful, Advanced Version

• Modigliani–Miller (M&M) Theorem (no taxes):
• In a perfect world (no taxes, no bankruptcy costs), WACC doesn’t change with leverage.
• Why? The lower cost of debt is exactly offset by the higher cost of equity.
• So capital structure wouldn’t matter.
• Introduce Taxes:
• Because interest is tax-deductible, debt creates value through the tax shield.
• This means WACC actually falls as you add debt — but only up to a point.
• Introduce Bankruptcy Costs / Financial Distress:
• If you keep piling on debt, lenders and equity holders both perceive more risk of default.
• Debt gets more expensive (higher yields).
• Equity gets more expensive (higher beta, higher CAPM cost of equity).
• The tax shield benefit is eaten up by distress costs.
• This is why firms don’t finance with 100% debt — there’s an optimal capital structure where WACC is minimized.

🧠 Key Insights for a CFO

1. Debt can lower WACC — but not endlessly.
• Small/moderate debt adds value through tax shields.
• Too much debt → higher risk premiums, higher costs of both debt and equity.
2. Equity holders get squeezed.
• As leverage rises, equity holders are more exposed to volatility.
• Their beta rises, so their CAPM cost of equity shoots up.
3. Trade-off Theory of Capital Structure:
• The “sweet spot” is where the tax shield from debt just outweighs the cost of financial distress.
4. Signals to the market:
• Increasing leverage can be read two ways:
• Positive signal (“management confident in stable cash flows”).
• Negative signal (“firm desperate for cheap cash, riskier capital structure”).
• Interpretation depends on context and industry norms.

✅ Plain Explanation You Could Give in Class:

“At first, adding debt lowers WACC because debt is cheaper than equity and it brings a tax shield. But as you add more debt, equity becomes riskier, and its cost rises. Ignoring taxes, the two effects offset and WACC doesn’t change. With taxes, WACC falls initially, but in reality, too much debt eventually drives up the cost of both debt and equity, so WACC bottoms out and then rises again. That’s why companies aim for an optimal capital structure, balancing the tax benefit of debt against the costs of financial distress.”