Introduction
Bonds look simple because they promise coupons and principal, but their market value is determined by the timing and risk of those cash flows. This article builds the foundation for understanding bond valuation.
The Basic Bond Structure
At its core, a bond is a contractual stream of future cash flows. The investor pays a market price today and receives coupons and principal according to the issue terms. Understanding those cash flows is the starting point for every fixed-income valuation.
The four concepts that appear repeatedly are face value, coupon, maturity and market price. They are related, but they are not interchangeable.
Face Value (Par Value)
Face value is the principal amount the issuer promises to repay at maturity, assuming no default. A common face value is $1,000, although institutional bonds can be quoted and traded in much larger denominations.
Bond prices are often quoted as a percentage of par. A price of 98.50 means 98.5% of face value, while 102.00 means 102% of face value.
Coupon: The Interest Payment
The coupon rate determines the contractual interest payment. Annual Coupon = Face Value × Coupon Rate. A $1,000 bond with a 6% annual coupon pays $60 per year. If coupons are semiannual, the investor normally receives two $30 payments.
The coupon rate is set by the bond contract. The bond’s yield, by contrast, changes with its market price.
Maturity: Repayment of Principal
Maturity is the date on which the principal is scheduled to be repaid. Shorter and longer maturities can behave very differently because the timing of cash flows affects interest-rate sensitivity.
All else equal, investors generally demand greater compensation for risks that become more uncertain over long horizons, although the shape of the yield curve can cause important exceptions.
Bond Price: Why Bonds Trade Above or Below Par
A bond can trade at par, at a premium or at a discount. If its coupon is attractive relative to prevailing market yields, it may trade above par. If its coupon is unattractive, it may trade below par.
Price therefore acts as the adjustment mechanism that makes the return on an existing bond competitive with current market conditions.
The Time Value of Money and Bond Pricing
A bond’s theoretical value is the present value of its future cash flows. For a plain fixed-rate bond:
\[
P = \sum_{t=1}^{n} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^n}
\]
where P is price, C is the coupon, y is the required yield per period, F is face value and n is the number of periods.
This formula explains the inverse relationship between yield and price. A higher discount rate reduces the present value of future cash flows; a lower discount rate increases it.
A Simple Pricing Example
Consider a three-year bond with $1,000 face value, a 5% annual coupon and a required market yield of 4%. The investor receives $50 in years one and two and $1,050 in year three. Discounting those cash flows at 4% produces a price above $1,000 because the 5% coupon exceeds the required 4% yield.
If the required yield were 6%, the same contractual cash flows would be discounted more heavily and the bond would trade below par.
Key Takeaways
Face value determines principal repayment, the coupon determines contractual interest, maturity determines when principal is due, and market price adjusts continuously to required yields and risk. Bond valuation is fundamentally a present-value problem.
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