Bond Valuation: The Intuition First
Imagine you lend ₹1,000 to a friend. You both agree that every year, your friend will pay you ₹80 as interest (8% of ₹1,000). After 5 years, your friend returns your ₹1,000. That's a bond in its simplest form.
A bond is just a loan that can be traded. The person who buys the bond is lending money. The bond's face value (₹1,000) is the amount you get back at the end. The coupon rate (8%) determines the annual interest payment. The maturity (5 years) is when you get your principal back.
Now, here's the key question: What is this bond worth today?
If you could earn 10% interest elsewhere, would you pay ₹1,000 for a bond that only pays 8%? No — you'd demand a discount. If you could only earn 6% elsewhere, that same 8% bond becomes more valuable, and you'd pay a premium.
Bond valuation is simply the process of calculating the fair price of a bond today, given the current interest rates in the market.
The Precise Statement
Bond Price=∑t=1n(1+r)tC+(1+r)nF
Where:
- C = annual coupon payment (face value × coupon rate)
- F = face value (principal repaid at maturity)
- r = market interest rate (yield to maturity)
- n = number of years to maturity
This formula says: The bond's price equals the present value of all future cash flows — both the periodic coupon payments and the final face value repayment.
Why This Works: The Logic
You're essentially asking: "If I want to earn a return of r per year, what should I pay today for a stream of future payments?"
Each future payment is discounted back to today using the market rate r. The sum of these discounted values gives the fair price.
When the coupon rate equals the market rate, the bond sells at par (face value). When the coupon rate is higher than the market rate, the bond sells at a premium (above face value). When lower, it sells at a discount (below face value).
A Worked Example
Consider a 3-year bond with face value ₹1,000, coupon rate 10%, and market interest rate 8%.
Step 1: Identify the cash flows
- Annual coupon: C=0.10×1000=₹100
- Year 1: ₹100
- Year 2: ₹100
- Year 3: ₹100 + ₹1,000 = ₹1,100
Step 2: Discount each cash flow at 8%
- Year 1: (1.08)1100=₹92.59
- Year 2: (1.08)2100=₹85.73
- Year 3: (1.08)31100=₹873.22
Step 3: Sum them
Price=92.59+85.73+873.22=₹1,051.54
The bond sells at a premium (₹1,051.54 > ₹1,000) because its 10% coupon beats the market's 8%.
A common mistake is forgetting to include the face value repayment in the final year's cash flow. The bond doesn't just stop paying coupons — it also returns your principal.
The Big Picture
Bond valuation is present value in action. Every time you see a bond price, you're seeing the market's collective judgment about how much those future payments are worth today, given current interest rates.
The same logic applies to any fixed-income investment: the price is always the present value of promised future cash flows, discounted at the prevailing market rate.