Understand bonds - coupon, maturity, face value

2.1.2 · Stock-Market › Equity & Fixed Income

Teen pillars

Bond ki ACTUAL VALUE scratch se nikalna

Step 1 — Cashflows list karo. Face value $F$, annual coupon rate $c$, aur $n$ saal baaki maturity wala bond yeh deta hai:

• Coupon $C=c\cdot F$ saal $1,2,\dots ,n$ ke end mein.
• Face value $F$ saal $n$ mein.

Step 2 — Har ek ko discount karo. Saal $t$ mein mila ek dollar aaj $\frac{1}{(1+r{)}^t}$ worth karta hai. Yeh step kyu? Kyunki aaj ka \1t$saalonmein$$(1+r)^t$ ban jaata hai, toh ulta karne ke liye divide karte hain.

Step 3 — Sab jodo:

$P=\underset{\text{coupons}}{\underbrace{\sum _{t=1}^n\frac{C}{(1+r{)}^t}}}+\underset{\text{face value}}{\underbrace{\frac{F}{(1+r{)}^n}}}$

Step 4 — Coupon sum collapse karo. Yeh ek geometric series hai jiska first term $\frac{C}{1+r}$ aur ratio $\frac{1}{1+r}$ hai. $x=\frac{1}{1+r}$ ke saath ${\sum }_{t=1}^n{x}^t=x\frac{1-x^n}{1-x}$ use karte hue:

$\boxed{P=C\left[\frac{1-(1+r{)}^{-n}}{r}\right]+\frac{F}{(1+r{)}^n}}$

Worked examples

Common mistakes (steel-manned)

Active recall

Connections

• Yield to Maturity (YTM) — woh actual return jo price ko coupons se jodata hai.
• Interest Rates and Bond Prices — ulta see-saw relationship.
• Present Value & Discounting — bond pricing ka engine.
• Duration & Interest Rate Risk — price rate moves ke liye kitni sensitive hai.
• Equity vs Debt — bonds (lending) vs stocks (ownership).
• Zero-Coupon Bonds — special case jahan $C=0$.

Concept Map