Bond Pricing & Yields

This page consolidates the bond math and pricing logic from Ch15 into one focused exam-prep reference. The structural details of bonds (callable / serial / convertible, secured / debenture, registered / bearer) are in LongTermFinancing. This page is just about how bond prices and yields move and how to read a quote.

graph TD
    BR["Bond Rate vs Market Rate"]
    BR -->|"Bond rate &gt; market rate"| PR["Premium Bond<br/>Sells ABOVE face value"]
    BR -->|"Bond rate = market rate"| PAR["Par Bond<br/>Sells AT face value"]
    BR -->|"Bond rate &lt; market rate"| DI["Discount Bond<br/>Sells BELOW face value"]

    IR["Interest Rates Rise<br/>(market)"] -->|"Existing bonds less attractive"| BP1["Bond Prices FALL"]
    IR2["Interest Rates Fall<br/>(market)"] -->|"Existing bonds more attractive"| BP2["Bond Prices RISE"]

How It Appears Per Course

ADMN 201

LO4 covers long-term financing through bonds. This page extracts the price/yield mechanics that the textbook treats as a numerical sub-topic — the kind of question that asks “if rates go up, what happens to the price of an existing bond?”

The Inverse Relationship: Rates vs. Prices

The most important rule in Ch15 bond material:

When market interest rates rise, existing bond prices fall. When market interest rates fall, existing bond prices rise.

Why this works (the intuition):

You hold a bond paying 4% interest.
The market rate suddenly rises to 6%.
New bonds being issued pay 6%. Why would anyone buy your 4% bond at face value?
They wouldn’t — so to sell, you must drop your price below face value (a discount).
The discount makes your bond’s effective yield match the new 6% market rate.

This is why bond prices move daily even when nothing about the issuing company changed.

Exam trap: This was a 🟦 resolved error in the study plan (2026-04-25 — “Bond pricing direction: rates ↑ → price ↓”). Drill until automatic.

Premium vs. Discount Bonds

A bond’s market price depends on three things:

Its stated (coupon) interest rate
The going (market) rate of interest on similar-quality bonds
Its redemption / maturity date

Situation	Sells At	Reason
Stated rate > market rate	Premium (above face value)	Bond pays more than alternatives — investors compete for it
Stated rate = market rate	Par (at face value)	Bond is exactly competitive
Stated rate < market rate	Discount (below face value)	Bond pays less than alternatives — must drop price to sell

The premium/discount size depends on how far in the future the maturity date is. A long-dated bond is more sensitive to rate moves than a short-dated one.

Reading a Bond Quote

Bond prices are quoted as a % of face value (NOT in dollars). Face value is typically $1,000 — but the quote ignores the dollar sign and the 1,000.

Quote	What it means
100	At par — $1, 000 f a ce v a l u ese ll s f or$ 1,000
85	$850 (85$ 1,000) — discount bond
101.92	$1, 019.20 (101.92$ 1,000) — premium bond
155.25	$1, 552.50 (155.25$ 1,000) — deep premium

Coupon (interest) rates are also quoted as % of par:

“6½s” pays 6.5% of par per year ( $65/ ye a ro na$ 1,000 face value)
Interest is typically paid semi-annually at half the stated rate ($32.50 every 6 months)

Bond Yield Calculation

Bond Yield = Annual Interest Paid ÷ Current Market Price

This is the real return you earn — not the coupon rate, which is fixed against face value.

Worked Example

You bought a $1, 000 p a r - v a l u e b o n d in 2010 f or * *$ 650**. Stated rate 6%; matures 2030.

Annual interest received: $1, 000 \times 6$ 60/year**
Yield based on actual investment: $60 \div$ 650 = 9.2%
At maturity in 2030, you also receive the full $1, 000 f a ce v a l u e — t ha t^{'} s an e x t r a$ 350 capital gain on top of the yield.
Your effective total return is therefore even higher than 9.2%.

Key insight: Bond yield is what matters, not coupon rate. A 6% coupon on a discounted bond gives you a higher yield than 6%; a 6% coupon on a premium bond gives you less.

Bond Ratings

Default risk = the chance that the issuer will miss a promised payment. Rating agencies grade bonds:

Rating Agency	High Grade	Investment Grade	Speculative	Junk
Moody’s	Aaa, Aa	A, Baa	Ba, B	Caa, C
Standard & Poor’s	AAA, AA	A, BBB	BB, B	CCC, D

Higher rating → lower default risk → lower interest rate the issuer must offer
Lower rating → higher default risk → issuer must pay higher interest to attract investors (“junk bonds”)
Example: Moody’s downgraded Enbridge after its $37B Spectra Energy acquisition due to integration/execution risk — debt got more expensive

How a Premium/Discount Resolves at Maturity

This is the often-missed exam point: regardless of what you paid, you receive face value at maturity.

Scenario	Payment at maturity	Capital gain/loss
Bought premium ($1,100)	$1,000	Loss of $100
Bought at par ($1,000)	$1,000	$0
Bought at discount ($800)	$1,000	Gain of $200

So a premium bond’s higher coupon is partially eaten by the capital loss at maturity. The yield calculation (above) accounts for this — which is why yield is the right comparison metric.

Cross-Course Connections

LongTermFinancing — full bond structure: callable / serial / convertible, secured / debenture, registered / bearer
SecuritiesMarkets — the secondary market where existing bonds trade
InvestmentVehicles — bond ETFs and bond mutual funds package these instruments for retail
DiversificationAndROI — bonds are the lower-risk leg of asset allocation
BankOfCanada — Bank of Canada rate decisions move the “market rate” that determines bond prices

Deeper Reference (ACC 926 — archived)

PresentValueMeasurement — the PV/FV mechanics behind why bond prices move with rates (effective interest method)
PresentValue-LongTermFinancing — connection: NPV intuition ↔ PV/FV/annuity formulas

Key Points for Exam/Study

Rates ↑ → Bond Prices ↓ (and vice versa) — the single most important rule
Premium: stated rate > market rate; sells above face value
Discount: stated rate < market rate; sells below face value
Par: stated rate = market rate; sells at face value
Bond quote of 85 = $850 o na$ 1,000 bond; quote of 101.92 = $1,019.20
“6½s” = pays 6.5% of par annually; usually paid semi-annually
Yield = Annual Interest ÷ Current Market Price (not the coupon rate)
Bought at $650, 6$ 1,000 face → 9.2% yield (plus eventual $350 capital gain at maturity)
Moody’s: Aaa > Aa > A > Baa > Ba > B > Caa > C
S&P: AAA > AA > A > BBB > BB > B > CCC > D
Junk bonds = low rating → must pay high interest to attract investors

Open Questions

How does a callable bond’s price react differently to falling rates than a non-callable bond?
Why do long-dated bonds move more than short-dated bonds for the same rate change?

Josh's StudyWiki

Explorer

BondPricingAndYields