Chapter 10 — Bodie, Kane & Marcus
Monmouth University
Par value, coupon rate, maturity, types of bonds
PV formula, price-yield inverse relationship, interest rate risk
YTM, YTC, current yield, holding period return
Credit ratings, yield spreads, financial ratios
Core idea: Bond prices and yields move in opposite directions. Understanding this inverse relationship is the foundation of fixed-income analysis.
The building blocks of fixed income
The principal repaid at maturity, typically $1,000.
Annual interest rate. Payment = Coupon Rate × Par Value. Usually paid semiannually.
The date the bondholder receives the face value. Notes: 1–10 yrs. Bonds: 10–30 yrs.
Legal contract specifying all terms between issuer and bondholder.
Think of it as a loan: You lend $1,000 (par). The borrower pays you interest (coupon) twice a year, then returns your $1,000 at maturity.
Issuer can repurchase at a specified call price. Benefits issuer when rates fall.
Bondholder can exchange for a specified number of common stock shares.
Bondholder can sell back at par. Benefits holder when rates rise.
Coupon resets periodically to a market benchmark (e.g., SOFR + spread).
No coupon payments. Sold at deep discount; all return comes from price appreciation.
Higher coupon to compensate for risk of loss triggered by natural disasters.
Present value of future cash flows
Key insight: Bond price = PV of all future cash flows, discounted at the market's required yield (YTM).
YTM < Coupon: Price > Par → Premium
YTM = Coupon: Price = Par → At Par
YTM > Coupon: Price < Par → Discount
| Bond A | Bond B | |
|---|---|---|
| Maturity | 10 years | 10 years |
| Coupon (annual) | 5% | 5% |
| YTM | 3% | 5% |
| Par Value | $1,000 | $1,000 |
N=10, PMT=50, I/Y=3, FV=1000
PV = $1,170.60 → Premium bond
N=10, PMT=50, I/Y=5, FV=1000
PV = $1,000.00 → At par
Why? Bond A's 5% coupon is generous compared to the 3% market rate. Investors will pay a premium for those above-market cash flows.
An 8% semiannual coupon bond, $1,000 par, 30-year maturity, YTM = 8%.
N=60, I/Y=4, PMT=40, FV=1000
When YTM equals the coupon rate, what happens to the price?
1. PV = $1,000 (exactly par)
2. When YTM = coupon rate, the bond trades at par. The coupon exactly compensates for the required yield.
Measuring bond returns
The discount rate that makes PV of all cash flows = bond price. Most important measure.
Assumes bond held to maturity and coupons reinvested at YTM.
Like YTM, but uses call date instead of maturity and call price instead of par.
Relevant for premium bonds that are likely to be called.
Annual coupon / Price
Simple income measure. Ignores capital gains/losses.
Trap: For premium bonds, Current Yield > YTM (because you'll lose money at maturity when price falls to par). For discount bonds, the opposite.
Calculator inputs:
Current Yield = 80/1276.76 = 6.27%
Notice: YTM (6.0%) < Current Yield (6.27%) < Coupon Rate (8.0%). This is a premium bond — the YTM accounts for the capital loss at maturity when price falls from $1,276 to $1,000.
YTM:
YTC:
Current Yield = 80/1150 = 6.96%
Which yield matters? For premium bonds (price > par), the issuer has incentive to call — refinance at lower rates. So YTC is the more conservative (and realistic) yield estimate.
Average return if held to maturity and coupons reinvested at YTM rate.
Known at time of purchase.
Actual return over your holding period. Depends on selling price (which depends on yields at sale date).
If yields rise: Bond price falls → HPR < initial YTM
If yields fall: Bond price rises → HPR > initial YTM
As maturity approaches, all bonds converge to par value — regardless of whether they started as premium or discount.
Premium: Price declines gradually to $1,000
At Par: Price stays at $1,000
Discount: Price rises gradually to $1,000
This assumes constant market interest rates. In reality, rate changes cause price fluctuations around this path.
You bought a convertible bond for $1,093.76. It converts into 58 shares. Current stock price = $15.60.
At what stock price will you convert?
Conversion premium ($)?
20-year zero-coupon, par=$1,000, semiannual compounding, required return=12%.
What is the price?
Q1: Convert when stock price > 1093.76/58 = $18.86
Market conversion value = 58 × $15.60 = $904.80. Premium = $1,093.76 − $904.80 = $188.96
Q2: PV = 1000/(1.06)40 = 1000/10.286 = $97.22
What if the borrower can't pay?
| S&P | Moody's | Grade | Description |
|---|---|---|---|
| AAA | Aaa | Investment Grade | Highest quality, minimal risk |
| AA | Aa | High quality, very low risk | |
| A | A | Upper-medium quality | |
| BBB | Baa | Medium quality (lowest investment grade) | |
| BB | Ba | Speculative (Junk) | Speculative elements |
| B | B | Highly speculative | |
| CCC–D | Caa–C | Substantial risk to default/in default |
The BBB/Baa line matters: Many institutional investors (pension funds, insurance companies) can only hold investment-grade bonds. A downgrade from BBB to BB triggers forced selling — "fallen angels."
Compensates for:
Spreads widen in crises: During 2008, investment-grade spreads hit 600+ bps. Junk spreads exceeded 2,000 bps.
| Ratio Category | What It Measures | Safer Bonds Have... |
|---|---|---|
| Coverage ratios | Earnings relative to fixed costs (interest, lease payments) | Higher coverage |
| Leverage ratio | Debt relative to equity | Lower leverage |
| Liquidity ratios | Current assets vs. current liabilities | Higher liquidity |
| Profitability ratios | ROA, ROE, profit margins | Higher profitability |
| Cash flow-to-debt | Operating cash flow vs. total debt | Higher cash flow |
Think like a lender: Would you lend money to a company with declining earnings, high debt, and low cash? The same logic applies to bond investors.
8% semiannual bond, quoted at $990. 30 days since last coupon, 182-day period.
Accrued = (80/2) × (30/182) = 40 × 0.1648 = $6.59
Invoice Price = $990 + $6.59 = $996.59
Why? The seller held the bond for 30 days since the last coupon and earned interest during that time. The buyer must compensate them for it.
| Formula | Name |
|---|---|
| P = Σ C/(1+y)t + FV/(1+y)T | Bond Price |
| Current Yield = Annual Coupon / Price | Current Yield |
| HPR = (Pend + Coupon − Pbegin) / Pbegin | Holding Period Return |
| Invoice = Quoted + Accrued Interest | Invoice Price |
| Accrued = (C/2) × (days / period) | Accrued Interest |
| Zero Price = FV / (1+y/2)2T | Zero-Coupon Pricing |
You hold a 30-year bond with an 8% annual coupon, initially priced at par (YTM=8%). After 1 year, the yield falls and the price rises to $1,050.
Price change + coupon received
Total income / initial price
1. Capital gain = $1,050 − $1,000 = $50. Coupon = $80. Total = $130
2. HPR = $130 / $1,000 = 13.0% (much higher than initial YTM of 8% because yields fell!)