Professor Jessie

Chapter 7: Valuing Bonds

FIN 3400 — Finance for Non-Financial Managers · MDC Kendall · Fall 2026
Module 2 — Exam: Nov 1 (200 pts)
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The Bond Market: Bigger Than You Think

When most people hear "financial markets," they immediately think of the stock market. But here's a surprise: the bond market is actually larger than the stock market. At the end of 2023, outstanding U.S. bonds totaled over $54 trillion, while all U.S. common stock was worth roughly $38 trillion. Daily bond trading exceeds $910 billion.

Why Bonds Matter

Bonds are the backbone of corporate and government finance. When a company needs to build a factory, or when a city needs to construct a school, they don't issue stock — they borrow. Bonds are how that borrowing happens at scale. Some bonds are among the safest investments in the world; others are risky, high-yield instruments that can rival stocks for volatility.

Discussion starter: If you had $10,000 to invest for 10 years, would you buy a government bond paying 4% or a stock portfolio that might return 10% but could also lose 30%? Your answer reveals your risk tolerance — and this chapter gives you the tools to quantify that tradeoff.

Anatomy of a Bond

A bond is simply a publicly traded loan. When you buy a bond, you're lending money to the issuer — a corporation, the federal government, or a municipality. In return, the issuer promises to pay you regular interest and eventually return your principal.

The Indenture: The Bond's Contract

Every bond comes with an indenture agreement — a legal document spelling out exactly what the issuer owes and what happens if they can't pay. Think of it as the terms and conditions of a loan, but legally binding and publicly filed.

Key Bond Features

CharacteristicWhat It MeansTypical Values
Par valueThe principal amount the issuer promises to repay at maturity$1,000
Time to maturityYears remaining until the principal is returned1 to 30 years
Coupon rateAnnual interest rate as a percentage of par value, usually paid semiannually2% to 10%
Call provisionIssuer's right to repay early, typically if rates have fallenOften callable after 10 years
Bond priceMarket price quoted as a percentage of par value80% to 120% of par
Key insight: The coupon rate is fixed when the bond is issued and never changes. But the bond's price changes every day as market interest rates move. This fixed-coupon, floating-price dynamic is the heart of bond valuation.

Who Issues Bonds?

Different entities issue bonds for different reasons, and each type carries its own risk profile:

U.S. Treasury Bonds

Issued by the federal government to finance national operations. These are considered among the safest investments in the world — backed by the full faith and credit of the U.S. government. Because the risk is near zero, the yields are also the lowest.

Corporate Bonds

Companies issue bonds to fund inventory, equipment, R&D, and expansion. The risk depends entirely on the company's financial health — Apple's bonds are far safer than a struggling retailer's. Corporate yields are always higher than Treasury yields of the same maturity, and the gap (called the spread) widens with risk.

Municipal Bonds

States, cities, and counties issue "munis" to fund public projects — schools, roads, water systems. Their key advantage: interest is typically tax-free at the federal level, making them attractive to investors in high tax brackets.

Specialized Bond Securities

Reading Bond Quotes

Bond prices are quoted as a percentage of par value. A bond quoted at 103 is trading at $1,030 (103% of $1,000 par). A bond at 97 costs $970.

Premium vs. Discount

Premium Bond

  • Price > 100% of par
  • Happens when coupon rate > market rate
  • Investors pay extra for the above-market coupon

Discount Bond

  • Price < 100% of par
  • Happens when coupon rate < market rate
  • Investors demand a lower price to compensate

What You'll See in a Quote

FieldMeaning
Coupon rateAnnual interest rate paid to bondholders
MaturityDate the principal is repaid
BidPrice at which you can sell
AskPrice at which you can buy
Change (CHG)Price change over the trading day
Ask YieldAnnual return if bought at ask price and held to maturity
Real example: Miami-Dade County issued a municipal bond with a 4.00% coupon, maturing October 2051, trading at 99.500 with a yield of 4.03%. Notice the bond trades at a slight discount — the yield is slightly above the coupon rate.

Valuing Bonds with Present Value

Bond valuation is a direct application of the time value of money. A bond's price equals the present value of all its future cash flows, discounted at the prevailing market interest rate.

What Are the Cash Flows?

Every bond provides two types of cash flow:

The Bond Pricing Formula

P = C × [1 − (1 + i)^−n] / i + F / (1 + i)^n

Where P = bond price, C = coupon payment, i = market discount rate per period, n = number of periods, and F = face value.

Example: 20-Year Bond at 7% Coupon

Consider a 20-year bond with a 7% annual coupon (paid semiannually, so $35 every 6 months) and a par value of $1,000. If the market demands a 6% annual yield (3% per semiannual period):

Because the 7% coupon exceeds the 6% market rate, this bond trades at a premium — investors pay more than par to capture the above-market coupon.

Zero-Coupon Bonds: Deep Discounts

Not all bonds pay interest. A zero-coupon bond makes no periodic payments — instead, it's sold at a deep discount and pays the full par value at maturity. Your return comes entirely from the price appreciation.

Example: 20-Year Zero at 6% Yield

What's the price of a $1,000 par zero-coupon bond maturing in 20 years, priced to yield 6%? Using semiannual compounding (standard for U.S. bonds):

P = $1,000 / (1.03)^40 = $306.56

You pay $306.56 today and receive $1,000 in 20 years. That $693.44 difference is your accumulated interest — effectively a 6% annual return compounded semiannually.

Why semiannual? U.S. bonds conventionally use semiannual compounding, even zeros. This means the annual yield is divided by 2, and the number of years is multiplied by 2 to get the number of periods. Don't forget this on exams!

Bond Prices and Interest Rate Risk

Here's the most important relationship in bond investing: market interest rates and bond prices move in opposite directions. When rates rise, existing bond prices fall. When rates fall, existing bond prices rise.

Why?

A bond's coupon is fixed at issuance. If new bonds are being issued at higher rates, your old bond with its lower coupon looks less attractive — so its price must drop to offer the same yield as new bonds. The reverse happens when rates fall.

Bond price vs. market interest rate for a 10-year, 5% coupon bond

Two Types of Risk

Interest Rate Risk

  • Risk of capital loss if rates rise
  • Longer maturity = greater risk
  • Lower coupon = greater risk

Reinvestment Rate Risk

  • Risk that coupon payments must be reinvested at lower rates
  • Higher coupon = greater risk
  • Shorter maturity = greater risk
Think about it: These two risks pull in opposite directions. Long-term bonds have high interest rate risk but low reinvestment risk. Short-term bonds have low interest rate risk but high reinvestment risk. There's no free lunch — every bond exposes you to one or both.

Understanding Bond Yields

"Yield" isn't a single number — bonds have several yield measures, each telling you something different:

Current Yield

The simplest measure: annual coupon payment divided by current price.

Current Yield = Annual Coupon / Bond Price

Easy to compute, but it only captures the income portion — it ignores the capital gain or loss you'll experience as the bond price moves toward par at maturity.

Yield to Maturity (YTM)

The most meaningful yield measure. YTM is the total annualized return you'll earn if you buy at today's price and hold until maturity. It includes both coupon income and the price appreciation/depreciation to par. Computing YTM requires finding the internal rate of return of the bond's cash flows — essentially trial and error or a financial calculator.

Yield to Call

If a bond is callable, the issuer might repay it early. Yield to call measures the return if the bond is called at the earliest call date rather than held to maturity. When rates fall, issuers often call bonds to refinance cheaper — so yield to call can be more relevant than YTM for callable bonds.

Taxable Equivalent Yield

Municipal bonds pay tax-free interest. To compare a muni yield to a taxable bond yield, adjust for taxes:

Taxable Equivalent Yield = Muni Yield / (1 − Tax Rate)

A 4% muni yield for an investor in the 24% bracket equals a 5.26% taxable yield (4% / 0.76). Suddenly that "low" muni yield looks much more competitive.

Bond Ratings and Credit Risk

Credit risk — the chance the issuer won't make payments — is the primary driver of yield differences between bonds. Rating agencies grade bonds by credit quality:

The Big Three Rating Agencies

Investment Grade Bonds

RatingQuality LevelWhat It Means
AAAHighest qualityExtremely strong capacity to meet commitments
AAHigh qualityVery strong capacity to meet commitments
AUpper medium gradeStrong, but somewhat susceptible to economic downturns
BBBMedium gradeAdequate protection, but vulnerable to adverse conditions

Below Investment Grade ("Junk" Bonds)

RatingLevelWhat It Means
BBSomewhat speculativeMajor ongoing uncertainties
BSpeculativeAdverse conditions likely to impair capacity
CCCHighly speculativeCurrently vulnerable to nonpayment
DDefaultPayments are in default or jeopardized
Key relationship: Lower ratings → higher credit risk → higher yields. The gap between Treasury yields and corporate bond yields (the spread) widens during recessions as downgrades increase, and narrows during expansions. This spread is a key economic indicator.

Types of Corporate Bonds

Beyond credit ratings, bonds differ in their collateral and priority:

Secured vs. Unsecured

Seniority

In bankruptcy, senior bonds have priority claims over junior bonds. Senior bondholders get paid first from whatever assets remain. This priority structure means senior bonds carry lower yields — less risk, less reward.

Bond Market Structure

Unlike stocks, which trade primarily on exchanges, bonds trade in a decentralized, over-the-counter (OTC) market. Most trades happen between bond dealers and large institutions — mutual funds, pension funds, and insurance companies. The NYSE operates the largest centralized U.S. bond market, but it's small compared to the OTC market.

Key Takeaways

Next up: Chapter 8 — Valuing Stocks. We'll shift from bonds (where cash flows are known) to stocks (where cash flows are uncertain) and learn why equity valuation is both harder and more fascinating than bond valuation.

Further Learning Resources

Explore these to deepen your understanding of this chapter's topics:

▶ YouTube Valuation of Bonds and Yield to Maturity ▶ YouTube Yield to Maturity Explained in 5 Minutes ▶ YouTube YTM — Approximate YTM and Bond Pricing 📖 Investopedia Bonds — Definition, Types, and How They Work 💬 Reddit r/bonds — Fixed income discussions