Bond valuation

What is a bond?

A bond is a debt instrument: the issuer (a government or company) borrows money from the investor and promises fixed interest payments and repayment of the principal on a set date. Bond terms:

• Face value (par value), F: the amount repaid at maturity, often ₹1,000 or ₹100.
• Coupon rate: the annual interest rate paid on the face value.
• Coupon payment, C: face value × coupon rate (for example, 8% of ₹1,000 = ₹80 a year).
• Maturity: the date the face value is repaid; n is the number of periods left.
• Yield to maturity (market rate), r: the return investors currently require on similar bonds.

Valuing a bond

The fair price (value) of a bond is the present value of all its future cash flows, discounted at the market rate r: V = C/(1 + r) + C/(1 + r)² + … + C/(1 + r)ⁿ + F/(1 + r)ⁿ = C × [1 − (1 + r)⁻ⁿ]/r + F/(1 + r)ⁿ. For semi-annual coupons, use C/2, r/2 and 2n periods.

Examples

• F = ₹1,000, coupon 10% annually, 2 years, r = 8%: V = 100/1.08 + 1100/1.08² ≈ 92.59 + 943.07 = ₹1,035.67. The bond sells at a premium.
• F = ₹1,000, coupon 6% annually, 3 years, r = 10%: V = 60/1.1 + 60/1.21 + 1060/1.331 ≈ ₹900.53. The bond sells at a discount.

Price and yield

• Coupon rate = market rate ⇒ price = face value (at par).
• Coupon rate > market rate ⇒ price > face value (premium).
• Coupon rate < market rate ⇒ price < face value (discount).

Bond prices and market interest rates move in opposite directions: when rates rise, existing bonds with fixed coupons become less attractive, so their prices fall.

Key points

• Coupon = face value × coupon rate.
• Bond value = PV of coupons + PV of face value.
• Price and yield are inversely related.
• Premium if coupon rate > yield; discount if coupon rate < yield.

Common mistakes

• Discounting at the coupon rate instead of the market rate.
• Forgetting the face value in the final period's cash flow.