Bond Horizon Return & Reinvestment Calculator
Enter the bond’s coupon, purchase yield, holding period, reinvestment rate, and expected sale yield. The calculator decomposes the horizon return into coupon cash, reinvestment income, and price change.
Annualized horizon yield4.61%
- Purchase price per $100 par
- $96.19
- Initial position cost
- $9,619.32
- Coupon cash received
- $1,500.00
- Reinvestment income
- $77.03
- Sale or redemption value
- $9,435.20
- Price-change component
- -$184.12
- Ending horizon value
- $11,012.23
- Total dollar gain
- $1,392.91
- Holding-period total return
- 14.48%
- Break-even sale YTM for target return
- 5.78%
Return-source breakdown
| Source | Amount | How it is measured |
|---|---|---|
| Coupon cash received | $1,500.00 | Undiscounted coupons paid through the horizon |
| Reinvestment income | $77.03 | Accumulated coupon value minus coupon cash received |
| Price-change component | -$184.12 | Sale or redemption value minus initial position cost |
| Total dollar gain | $1,392.91 | Ending value minus initial cost |
Assumes purchase and sale occur on coupon dates, with no accrued interest or settlement-day adjustment.
Assumes scheduled fixed coupons, one constant coupon reinvestment rate, and no taxes, spreads, fees, or credit losses.
How to use this calculator
- Enter the total par value, stated coupon rate, purchase yield, maturity, and coupon frequency.
- Enter the planned holding period, making sure it ends on a coupon date and does not run past maturity.
- Enter the coupon reinvestment rate and the expected yield used to price the bond at sale.
- Enter a target annual return to solve the sale yield that would break even with that target.
How the horizon return is calculated
A bond’s yield to maturity is a promised-cash-flow discount rate. A horizon return asks a different question: what happens if you own the bond for a shorter period, reinvest the coupons, and sell the remaining cash flows at a new yield? This calculator follows that horizon-return structure and shows the three sources separately.
Let F be position par value, c the annual coupon rate, f coupon payments per year, T years to maturity, and H years held. The number of maturity periods is N = fT, the number of held periods is K = fH, and each coupon is C = F × c / f.
The initial cost discounts all remaining coupons and principal at the purchase yield y0:
B0 = sum(C / (1 + y0 / f)^t) + F / (1 + y0 / f)^N
Coupons received by the horizon are accumulated at the reinvestment rate r:
A = sum(C × (1 + r / f)^(K - t))
If the bond is sold before maturity, the horizon sale value discounts the remaining cash flows at the sale yield ys. If the holding period reaches maturity, the horizon value is par redemption instead. Ending wealth is W = A + BH, holding-period return is W / B0 - 1, and annualized horizon yield is (W / B0)^(1 / H) - 1.
What moves the result
The sale yield usually dominates shorter holding periods because it reprices the remaining principal and coupons. Coupon reinvestment matters more when the coupon rate is high, the holding period is long, or the reinvestment rate differs sharply from the purchase yield. A zero-coupon bond has no coupon reinvestment component, so its horizon result comes entirely from the price paid and the sale or redemption value.
Break-even sale yield
For the target return, the calculator first finds the sale value required to earn the entered annual return: Btarget = B0 × (1 + g)^H - A. It then solves the sale yield that prices the remaining cash flows to that required value. If the required sale value is zero or negative, there is no finite break-even sale yield. If the bond is held to maturity, sale yield is not part of the result.
What this calculator leaves out
The model assumes purchase and sale happen exactly on coupon dates. It omits accrued interest, day-count conventions, odd coupon periods, taxes, commissions, bid-ask spreads, default losses, and transaction costs. It also assumes fixed scheduled cash flows, so callable, putable, convertible, floating-rate, and amortizing bonds need separate option or cash-flow modeling.
Worked example
Suppose you buy $10,000 par value of a 5% semiannual coupon bond with 10 years to maturity at a 5.5% yield. You plan to hold it for 3 years, reinvest coupons at 4%, and expect the sale yield to be 6%.
The purchase price is $96.19 per $100 of par, so the initial position cost is $9,619.32. Six coupons produce $1,500.00 of cash, which grows to $1,577.03 with reinvestment income of $77.03. Pricing the remaining 7 years of cash flows at a 6% sale yield gives a sale value of $9,435.20.
Ending horizon value is $11,012.23, for a total gain of $1,392.91. That is a 14.48% holding-period return, or 4.61% annualized. To earn a 5% target annual return in this scenario, the break-even sale yield is about 5.78%.
Common questions
What is a bond's horizon yield?
A bond horizon yield is the annualized return over a chosen holding period, not necessarily the return to maturity. It combines the purchase price, coupons received and reinvested, and the sale or redemption value at the horizon.
Why can realized return differ from yield to maturity?
Yield to maturity assumes the bond is held to maturity and that coupons are effectively reinvested at that same yield. A shorter holding period exposes the investor to the yield available when the bond is sold and to the rate actually earned on coupons.
How do coupon reinvestment and sale yield affect total return?
The reinvestment rate changes the future value of coupons received before the horizon. The sale yield changes the market value of the remaining cash flows, so a higher sale yield generally lowers the sale price and a lower sale yield generally raises it.
What happens if I hold the bond to maturity?
The sale value is replaced by par redemption, and the entered sale yield is not used. The result still includes coupon cash and reinvestment income through maturity, but there is no break-even sale yield because no sale price has to be solved.
Why is reinvestment risk greater for high-coupon bonds?
High-coupon bonds return more cash before maturity, so more of the final wealth depends on the rate earned on interim coupons. Low-coupon and zero-coupon bonds have less interim cash flow, so their horizon return depends more on price change.
Should I use yield to maturity or yield to worst for a callable bond?
For a callable bond, yield to worst is often more relevant than yield to maturity because the issuer may redeem the bond before maturity. This calculator does not model optional redemption, so callable bonds should be evaluated with their call schedule and option risk separately.