Bond Cash-Flow Mechanics
Bond Cash-Flow Mechanics
A bond is a schedule of cash flows. Master the schedule—when you get paid, how much, and what it is worth today—and you understand the bond.
Key takeaways
- Coupons are periodic interest payments (usually semi-annually); principal is the lump-sum repayment at maturity.
- The coupon rate is fixed at issuance; a 5% coupon on a $1,000 bond always pays $50 per year, split across payment dates.
- Bond value is the present value of all future cash flows, discounted at the yield-to-maturity (YTM).
- When yields rise, bond prices fall; when yields fall, bond prices rise. This inverse relationship holds for all bonds.
- A bond trading at a discount (below par) has a YTM higher than its coupon; a bond trading at a premium (above par) has a YTM lower than its coupon.
The coupon schedule
The coupon is the periodic payment an issuer makes to a bondholder. It is calculated as a percentage of the bond's face value (principal, or par).
Consider a Treasury bond with these terms:
- Face value: $1,000
- Coupon rate: 4.5% per annum
- Payment frequency: Semi-annual
- Maturity: 10 years
The annual coupon is 4.5% × $1,000 = $45. Since payments are semi-annual, you receive $22.50 every six months. Over 10 years (20 payment periods), you receive 20 × $22.50 = $450 in coupons, plus $1,000 in principal repayment.
The coupon rate is set at issuance and does not change. The 4.5% is locked in. If you hold the bond for 10 years and interest rates rise to 6%, you still receive the 4.5% coupon, no more. If interest rates fall to 2%, you still receive the 4.5% coupon. This is the bond's most predictable feature.
Payment dates are standardized. U.S. Treasury bonds typically pay coupons on the 15th of the month, on set schedules (e.g., January 15 and July 15 for a bond with 10-year maturity issued in January). Corporate bonds usually pay on the 1st or 15th of the month. These dates are known at issuance, so you can plan around them.
The principal repayment at maturity
The principal (face value) is the amount borrowed and the amount repaid at maturity. When a 10-year bond matures, the issuer repays the principal in full (barring default). You get the full $1,000 back, in addition to the final coupon payment.
The maturity date is fixed. A bond issued in 2024 with 10-year maturity matures in 2034. You know this at the time of purchase. There is no ambiguity, no option for the issuer to extend or call (except in the case of callable bonds, which are discussed later).
The maturity date defines the lifespan of the bond. A 2-year bond matures soon; a 30-year bond is a long-term commitment. The longer the maturity, the more time for interest rates to change and the bond's price to fluctuate.
The complete cash-flow stream
For the Treasury bond example above (4.5% coupon, $1,000 principal, 10-year maturity, semi-annual payments), here are all the cash flows:
- Year 0.5: $22.50
- Year 1: $22.50
- Year 1.5: $22.50
- Year 2: $22.50
- ...
- Year 9.5: $22.50
- Year 10: $22.50 + $1,000 = $1,022.50 (final coupon plus principal)
You receive $22.50 semi-annually for 10 years, with the final payment bundled with the principal. If you hold the bond from issuance to maturity and there is no default, you receive exactly this stream.
If you sell the bond before maturity, you stop receiving its coupons; the new owner receives the remaining coupons and principal. The purchase price you receive depends on market interest rates and the bond's credit quality at the time of sale.
Bond pricing: present value of cash flows
The bond's market price is the present value of all future cash flows, discounted at the yield-to-maturity (YTM). The YTM is the discount rate that makes the bond's price equal to the present value of its coupons and principal.
Mathematically:
Price = C / (1 + y)^1 + C / (1 + y)^2 + ... + (C + FV) / (1 + y)^n
Where:
- C = coupon per period
- y = YTM per period (coupon rate divided by 2 for semi-annual bonds)
- FV = face value (principal)
- n = number of periods to maturity
At issuance, the bond's coupon rate is set such that the bond's price is approximately par ($1,000). The issuer wants the bond to sell at face value, so the coupon rate reflects the prevailing market interest rate.
If market interest rates rise after issuance, new bonds are issued with higher coupons. The old bond's 4.5% coupon is now below market. Investors will only buy it if the price falls enough that the overall yield (coupons plus price appreciation at maturity) becomes competitive. The bond's price falls below par.
Conversely, if market interest rates fall, new bonds are issued with lower coupons. The old bond's 4.5% coupon is now above market. Investors will pay a premium for the higher coupon. The bond's price rises above par.
The inverse relationship: price and yield
The fundamental relationship in bond investing is this: when yields rise, bond prices fall; when yields fall, bond prices rise.
This relationship is inverse and mechanical. If a bond is priced to yield 5%, and you want to know its value when yields rise to 6%, the present value of its cash flows at a 6% discount rate is lower than at a 5% discount rate. The price must fall for the yield to rise.
Let us use a concrete example. Consider a bond with:
- Face value: $1,000
- Coupon rate: 5% per annum
- Maturity: 5 years
If market yields are 5%, the bond trades at par ($1,000).
If market yields rise to 6%, the present value of the cash flows (using 6% as the discount rate) is approximately $957. The bond trades at a discount.
If market yields fall to 4%, the present value of the cash flows (using 4% as the discount rate) is approximately $1,045. The bond trades at a premium.
This relationship holds for all bonds. Long-term bonds are more sensitive to yield changes than short-term bonds (duration effect). High-coupon bonds are less sensitive than low-coupon bonds (because coupons return cash faster, reducing the impact of price changes).
Premium and discount bonds
When a bond trades above par, it is trading at a premium. This happens when its coupon is above the prevailing market yield. An investor buying a premium bond will receive the full coupon for the life of the bond, plus the principal at maturity. But the purchase price is higher than $1,000, so the overall return (YTM) is lower than the coupon rate.
When a bond trades below par, it is trading at a discount. This happens when its coupon is below the prevailing market yield. An investor buying a discount bond will receive coupon payments lower than what new bonds pay, but because the purchase price is less than $1,000, the overall return (YTM) is higher than the coupon rate. The capital gain (from purchase price to par at maturity) offsets the lower coupons.
Both premium and discount bonds eventually return to par at maturity. If you hold a bond to maturity, the price movements that happened while you held it are realized. A discount bond held to maturity gives you capital gains; a premium bond held to maturity gives you capital losses (relative to the coupon yield).
An investor choosing between a discount bond (4% coupon, trading at $960) and a premium bond (6% coupon, trading at $1,050) will receive the same total return if held to maturity, assuming no default. The difference is in the pattern: one front-loads price gains, the other front-loads coupon income.
Duration: the time-weighted sensitivity to yields
Duration is a measure of a bond's sensitivity to interest-rate changes. It is also the weighted-average time to receive the bond's cash flows.
A zero-coupon bond (a bond that pays no coupons, only principal at maturity) has a duration equal to its maturity. A 10-year zero-coupon bond has a 10-year duration. If yields rise 1%, the price falls approximately 10%.
A coupon bond has a duration shorter than its maturity because coupons are received throughout the life of the bond. A 10-year bond with a 5% coupon might have a duration of 7.5 years. If yields rise 1%, the price falls approximately 7.5%.
Duration is useful for comparing bonds. A portfolio of 5-year bonds has lower interest-rate risk than a portfolio of 20-year bonds. A portfolio of high-coupon bonds has lower duration than a portfolio of low-coupon bonds with the same maturity.
For individual investors, the practical takeaway is simple: longer-maturity bonds are more sensitive to interest-rate changes. If you expect rates to rise, shorter-duration bonds are safer. If you expect rates to fall, longer-duration bonds will appreciate more.
Convexity: the second-order effect
Bonds exhibit a property called convexity. The relationship between price and yield is not perfectly linear; it curves. This curvature is convexity.
For practical purposes, beginners can ignore convexity. Duration captures most of the interest-rate sensitivity. Convexity is a second-order refinement that matters more to traders than to long-term portfolio managers.
The only practical insight is that bonds with more convexity (which is often the case for bonds with lower coupons) respond more favorably to large drops in interest rates. But this is a small effect compared to duration.
Real-world pricing: bid-ask spreads and transaction costs
In reality, bonds are not always priced at exact present value. The bond market has bid-ask spreads—the difference between what dealers bid (what they will pay to buy from you) and what they ask (what they will sell to you for).
For U.S. Treasury bonds, spreads are very tight (often under 0.01%). For less liquid corporate bonds, spreads can be 0.25% or more. If you buy a bond at the ask price and immediately sell at the bid price, you lose money to the spread.
For long-term investors, spreads are a minor cost. You absorb the spread once at purchase, and the coupon income and price appreciation should exceed it over time. But for traders or frequent sellers, spreads matter.
Additionally, when you sell a bond before maturity, you may face accrued interest adjustments. If you sell between coupon dates, the seller collects accrued interest from the buyer. This is a mechanical adjustment but can affect the net proceeds.
Summary: cash flows and valuation
A bond's cash flows are determined at issuance: coupons on fixed dates, principal at maturity. The bond's market price is the present value of those cash flows, discounted at the prevailing yield. As interest rates change, the discount rate changes, and the bond's price changes inversely. Understanding this mechanism—cash flows fixed, price flexible—is the foundation of bond investing.
Related concepts
Next
Bond cash flows are predictable and can be valued using present-value mechanics. But bonds are not uniform—they vary by issuer type, term, and credit quality. The next step is to understand fixed income as an asset class: how different bonds serve different purposes in a portfolio.