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.

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

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 $a_{\overline{20\vert 0.06}} = 11.47$ 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: $P = Fr \cdot a_{\overline{n\vert i}} + C \cdot v^n$. Coupon annuity plus bullet redemption.
• Premium/discount: $P = C + (Fr - Ci) \cdot a_{\overline{n\vert i}}$. 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 3,182 words, 21 min read) adds 4 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• 4a

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