1. Bonds 101 (the basics)

A bond is just an IOU:

• You give me $100 today.
• I promise to pay you periodic coupons (like interest) along the way.
• At the end (maturity), I pay you back the face value ($100).

Key parts:

• Face Value (Par): Usually $1,000 or $100 per bond.
• Coupon Rate: The annual interest % paid on face value. (e.g., 5% coupon = $50 per year on a $1,000 bond).
• Maturity: When the bond “expires” and you get your $1,000 back.
• Price: What the bond sells for in the market today (can be above or below par).

“A bond’s YTM is the IRR that equates today’s price to the stream of promised coupons and repayment at par. It’s like the return the issuer promises you if they pay in full. But that’s not necessarily what you’ll earn. Because issuers sometimes default or markets change, your actual expected return is usually lower. That’s why analysts talk about spreads and risk-adjusted returns — the gap between the ‘promised’ YTM and the realistic expected payoff.”

• Bonds = IOUs with coupons and principal.
• YTM = IRR of promised cash flows at today’s price.
• Promised vs. Expected: YTM assumes 100% repayment; expected return adjusts for default/reinvestment risk.
• In practice, CFOs and analysts use YTM because it reflects market pricing of risk, even though it’s not literally the realized return.

YTM

Teaching Metaphor

Imagine lending your friend $100:

• He promises to pay you $5 each year and $100 at the end.
• If he’s rock-solid trustworthy (like the U.S. Treasury), your promised return ≈ expected return.
• If he’s shaky, he might default — you’re promised $105 but might only get $60 back in total.
• YTM still calculates return as if he pays you everything, but you as the lender know there’s a chance reality falls short.

So: YTM is the “promised yield,” expected return adjusts for “real-life risk.”

3. Why YTM is a Promised Return, not an Expected Return

This is the crux of your note.

• Promised return: YTM assumes you receive every coupon and principal in full, on time — “100 cents on the dollar.”
• Expected return: Reality might differ.
• The issuer could default (pay less than promised).
• You might have to reinvest coupons at different rates.
• You might sell before maturity at a different price.

👉 So YTM is like a best-case, contractual IRR. It does not adjust for credit risk or reinvestment risk.

How Professionals Deal with That

Since YTM isn’t the true expected return, here’s how markets handle the gap:

1. Credit Spreads:
• Investors demand higher YTM for riskier bonds.
• Example: Treasuries at 3%, risky corporate at 7% → 4% “spread” compensates for default risk.
2. Default-Adjusted Yield (Expected Return):
• Analysts adjust promised payments by the probability of default and recovery rate.
• Example: If there’s a 10% chance the issuer defaults and pays back only 50% of par, expected cash flows are lower, so expected return < YTM.
3. Market Practice:
• CFOs and WACC models usually just use YTM as the cost of debt, since it reflects market pricing of risk today.
• In other words: the bond’s YTM already “bakes in” what the market thinks about default risk.

1. IRR Refresher (Internal Rate of Return)

👉 Definition:

The IRR is the discount rate that makes the net present value (NPV) of an investment = 0.

In plain speak:

• You invest money today.
• You get cash flows in the future.
• IRR is the break-even “interest rate” that equates what you pay in with what you get out.

Common contexts where IRR shows up:

1. Corporate projects (CapEx):
• If you spend $1m on a factory, IRR is the annualized return on the cash inflows.
• If IRR > WACC → value creating.
2. Private equity & venture capital:
• IRR measures annualized returns on a fund or deal.
• They like IRR because it accounts for timing of exits and distributions.
3. Bonds (YTM):
• The IRR of a bond’s promised coupons and final repayment at par, given today’s price.

👉 Think of IRR as the “DNA of return” — any stream of cash flows can be distilled into a single break-even rate of return.

2. Bond Example: YTM vs Expected Return

Bond Details

• Face value: $100
• Coupon: 10% = $10 per year
• Maturity: 1 year (to keep it simple)
• Current price: $95

5. Compare

• YTM (promised IRR): 14.4%
• Expected return: 6.3%

That’s a huge gap — because YTM assumes you will get all promised coupons + principal, but when default risk is realistic, the expected payoff is much lower.

6. Teaching Angle

You could say:

“A bond’s YTM is like a glossy brochure: it shows you the return if everything goes perfectly. But once you factor in the probability of default and the actual recovery you’d get in a bad state, the expected return is often far lower. That’s why credit spreads exist — they compensate for that risk. In our 3-year example, the promised yield is 14.4%, but the expected return is only 6.3%. The difference is the price of risk.”

✅ Key learning: YTM = promised IRR. Expected return = probability-adjusted IRR. The divergence grows with time horizon and default risk — which is why long-dated, risky bonds can show sky-high YTMs that aren’t realistic as expected returns.

Step 3: Compare

• YTM (promised IRR): 15.8%
• Expected Return (risk-adjusted): 8.4%

The difference is the credit risk premium: YTM “overstates” the likely payoff if there’s a chance of default.

3. Teaching Metaphor

You could say:

“YTM is like the speedometer reading if you drove nonstop at the promised speed — 60 mph. Expected return is your real-world average speed after you factor in traffic, breakdowns, and detours. They start from the same trip, but one is perfect-world, the other is reality.”

✅ Key takeaway:

• IRR is the break-even interest rate that makes NPV zero.
• YTM is the IRR of a bond’s promised cash flows.
• But if defaults are possible, your expected return is lower than YTM.

3. Step 2: Expected Return (with Default Risk)

Let’s assume:

• Probability of default each year = 10% (independent each year).
• Recovery if default = $40 (40% of par), received immediately when default happens.
• If no default, you get full coupons + principal.

Expected cash flows (simplified method):

We compute “expected payoff” each year weighted by survival/default probability.

• Year 1:
• Survival prob = 90% → payoff = $10
• Default prob = 10% → payoff = $40
• Expected = (0.9 × 10) + (0.1 × 40) = 9 + 4 = 13
• Year 2 (only if survived Year 1):
• Survival to Year 2 = 0.9 × 0.9 = 81%
• Pay $10 if survive; $40 if default.
• Expected = (0.81 × 10) + (0.09 × 40) = 8.1 + 3.6 = 11.7
• Year 3:
• Survival to Year 3 = 0.9³ = 72.9%
• Pay $110 if survive; $40 if default in Year 3.
• Expected = (0.729 × 110) + (0.081 × 40) = 80.2 + 3.2 = 83.4

Total expected payoff stream:

• Year 1: 13
• Year 2: 11.7
• Year 3: 83.4

Total = 108.1

Total expected payoff stream:

• Year 1: 13
• Year 2: 11.7
• Year 3: 83.4

Total = 108.1

4. Expected Return Calculation

• You pay $90 today.
• Expected payoff over 3 years = 108.1.
• The IRR on these expected cash flows ≈ 6.3% annually.

5. Compare

• YTM (promised IRR): 14.4%
• Expected return: 6.3%

That’s a huge gap — because YTM assumes you will get all promised coupons + principal, but when default risk is realistic, the expected payoff is much lower.

1. Bonds: The Foundation

• A bond is simply debt in tradable form: you lend money today, receive coupons (interest) along the way, and principal at maturity.
• Its value = the present value of future promised cash flows.

2. Yield to Maturity (YTM)

• Definition: the internal rate of return (IRR) that equates today’s bond price to the PV of all promised coupons + principal.
• Formula:

1. Interpretation: YTM is the “break-even promised return” if the bond pays 100 cents on the dollar.

3. Promised vs. Expected Returns

2. Promised (YTM): assumes the borrower never defaults and you receive every coupon and principal repayment.
3. Expected: adjusts promised cash flows for probability of default and recovery rates.
4. In risky bonds, YTM can be much higher than expected return.
• Example: 3-year 10% coupon bond, price $90 → YTM = 14.4%.
• With 10% annual default risk → expected return = 6.3%.
5. Market prices already embed default risk → that’s why junk bonds trade at steep YTMs.

6. Strategic Insight for a CFO

• If YTM < WACC (equity cost): adding some debt lowers overall cost of capital.
• If YTM is rising: markets see you as riskier → cost of debt climbs.
• If your bonds trade at wide spreads over Treasuries: a signal of higher perceived default risk.
• For valuation: CFOs and analysts use YTM (promised return) because it reflects the market consensus expected return once default risk is priced into the bond price.

✅ How you’d explain it in class or to your board:

“A bond’s yield to maturity is the IRR on its promised cash flows. It assumes full repayment, so it’s technically a promised return, not an expected return. In practice, the market price already reflects default risk, so the YTM we observe in the market is the right measure of our cost of debt. In WACC, we take that YTM, adjust it for the tax shield, and weight it with market values of debt and equity. That’s why the cost of debt in our capital structure analysis comes directly from the yields on our bonds, not the coupon rates we issued years ago.”

Would you like me to now draw the full bridge — a one-page diagram that connects:

Bonds → YTM (IRR) → Promised vs Expected → rD(1–T) in WACC → ROIC/WACC spread → valuation? That would serve as your “cheat sheet map.”