Bond Terminology and Definitions

A bond's market value drops to $920 after a yield spike, but its book value sits at $1,085 on the original yield. Confusing them leads to catastrophic accounting errors.

Face value $F$ is the nominal amount. It determines coupons. Redemption value $C$ is paid at maturity. When $C=F$, the bond is at par. Unless stated otherwise, assume $C=F$.

$$\text{Coupon}=Fr$$

Here $r$ is the rate per coupon period. Annual 6% semi-annual means $r=3\%$ per period. Coupons are always based on $F$, not $C$.

The yield to maturity $i$ equates the bond's price to the PV of its cash flows. It is the rate per coupon period.

HIGH-FREQUENCY: This is the cornerstone of all FM bond calculations.

$$P=Fr\cdot a_{\overline{n|i}}+C\cdot v^n$$

The price decomposes into the PV of coupons (annuity) plus PV of the redemption (bullet).

Common mistakes

• Confusing $F$ and $C$. Coupons = $Fr$, not $Cr$. If $F=1000$, $C=1050$, $r=4\%$: coupon = $40, not $42. Trap: $42.
• Using annual rate for per-period. 6% semi-annual bond: $i=3\%$, not 6%. Using 6% gives $a_{\overline{20|0.06}}=11.47$ instead of 14.88. Price is drastically wrong.
• Getting premium/discount backwards. High coupon relative to yield = premium. "High coupon = discount" is backwards.

Bottom line

• Basic price: $P=Fr\cdot a_{\overline{n|i}}+C\cdot v^n$. Coupon annuity plus bullet redemption.
• Premium/discount: $P=C+(Fr-Ci)\cdot a_{\overline{n|i}}$. Premium when $Fr>Ci$, discount when $Fr<Ci$.
• Book value uses the original purchase yield with $n-t$ remaining periods. Market value uses the current market yield.
• Premium write-down: $(Fr-Ci)\cdot v^{n-t+1}$. Book value decreases toward $C$; write-up has the opposite sign.

Exam shortcut

Before any calculation, write $F$, $C$, $r$, $i$, $n$. Confirm each rate is per period. Check if $C=F$. "redeemable at 105" means $C=1050$. "Basic = Annuity + Bullet." "R > Y = P" (coupon Rate > Yield means Premium. "Premium falls, Discount rises") both converge to $C$.

The full lesson (about 2,524 words, 17 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• 4a

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