Bond Pricing & Yield
A bond's price is the present value of all its future cash flows. Discount each coupon and the principal back to today — add them up — that's the price.
Bond Parameters
Cash Flow Waterfall — Nominal vs Present Value
Each bar shows the nominal cash flow (tall, faded) versus its present value (short, colored). The dashed red line is the time value of money — future money is worth less today.
Price-Yield Curve
Par, Premium & Discount
Coupon > Yield → Price > Face Value
Investors pay more because the coupon payments are higher than what the market requires.
Coupon = Yield → Price = Face Value
The coupon exactly compensates for the required yield. Price equals face value.
Coupon < Yield → Price < Face Value
The coupon is below market rates, so investors pay less to achieve the required yield.
The Bond Pricing Formula
Step-by-step: How it works
List all future cash flows
A 5-year bond with 5% coupon, semi-annual, $1,000 face → you receive $25 every 6 months + $1,000 at the end = 10 coupon payments + principal.
Discount each cash flow to today
Each payment is divided by — money further in the future is discounted more heavily. This is the time value of money: $25 received in 5 years is worth less than $25 today.
Sum them up = Bond Price
The sum of all discounted cash flows — that's in the formula. The bond price is literally the total present value.
Key Relationships
Price and Yield move inversely
When yields rise, you discount cash flows at a higher rate → each is worth less → price falls. When yields fall, the opposite: each cash flow is worth more → price rises. This is the most fundamental relationship in bond markets.
Longer maturity = More sensitivity
A 30-year bond's price moves much more for the same yield change than a 2-year bond. This is because more cash flows are being discounted over longer periods. This concept is formalized as duration.
The curve is convex, not linear
Notice the price-yield curve bends — it's not a straight line. A 1% yield drop gives a bigger price gain than the price loss from a 1% yield rise. This asymmetry is called convexity, and it's always positive for vanilla bonds.