FIN435 Chapter 7 — Bond Valuation Study Guide + Practice

How to use this study guide

Review the Concepts & Theory Checklist.
Do the True/False section without notes.
Do the 3 calculation problems using the formula sheet (Excel or calculator).

What to compute	Formula / Excel
Cash flows per period	PMT = (Coupon rate × Face value) / 2
# of periods	NPER = Years × 2
Yield to maturity (nominal APR)	YTM = RATE(NPER, PMT, -Price, 1000) × 2
Current yield	Current yield = Annual coupon / Price = (Coupon rate × Face value) / Price
Capital gain yield (1-year)	Capital gain yield = YTM − current yield
Relationship	YTM = Current yield + Capital gain yield

Coupon rate vs. yield: coupon rate is based on face value; yields are based on market price.
Current yield = annual coupon ÷ price (ignores capital gain/loss).
YTM is the discount rate that sets price equal to PV of all promised cash flows (coupon income + price pull-to-par).
Capital gain yield (for a holding period) is the percentage price change over that period.
YTM ≈ total return = Current yield + Capital gain yield (intuitive decomposition).
If YTM is unchanged, discount bonds tend to have positive capital gain yield (price drifts up toward par), while premium bonds tend to have negative capital gain yield (price drifts down toward par).
Discount bond: Price < par → YTM > coupon rate. Premium bond: Price > par → YTM < coupon rate.

Bond prices move inversely with yields. If market yields rise, existing fixed-rate bond prices fall.
Sensitivity to yield changes increases with longer maturity and lower coupon (higher duration).
Quick ranking (all else equal): long maturity & low coupon (or zero-coupon) = most sensitive; short maturity = least sensitive.
Price response is curved (convex): for large yield moves, duration alone is an approximation.

Macaulay duration is the weighted-average time to receive cash flows (in years).
Modified duration converts Macaulay duration into an interest-rate sensitivity measure.
First-order approximation: %ΔPrice ≈ −(Modified Duration) × Δy (Δy in decimals, e.g., 0.01).
Higher duration: bigger price gains when yields fall, but bigger losses when yields rise.

Callable bonds give the issuer the right to repay early, usually when rates fall.
Call risk: upside is capped (price may stop rising as much when yields fall).
When rates fall, callable bonds often exhibit shorter effective duration (the call option becomes more likely).
Reinvestment risk: if you receive principal back early, you may have to reinvest at lower rates.

Treasuries are the benchmark “low default risk” curve; corporate yields usually include a credit spread over Treasuries.
Bond ratings (AAA…BB…etc.) summarize default risk; downgrades typically raise required yield and lower price.
High-yield (“junk”) bonds are more exposed to default risk and spread changes (especially in recessions).

Treasuries: very high liquidity, very low credit risk; main risk is interest-rate risk (duration) and inflation.
Investment-grade corporates: add credit risk + liquidity risk; spreads vary with the business cycle.
High-yield (junk): higher spreads/yields but higher default and downgrade risk; behaves more like “credit” than pure rates.
Municipals: often federal tax-advantaged; compare using tax-equivalent yield; credit and liquidity can vary widely.
TIPS: principal adjusts with inflation (CPI); protects purchasing power, but still has real-rate (duration) risk.
Tip: even with inflation protection, a long-maturity TIPS can be very rate-sensitive (to real yields).