Use the tabs in the calculator to compute a bond’s yield to maturity (often called the “constant yield”), compute price from yield, or generate a constant-yield (effective interest) amortization schedule. Inputs may include face value, market/purchase price (clean), annual coupon rate, coupon frequency, and years to maturity.
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Approximate Constant Yield (Approximate YTM) Formula
The following formula is a common approximation for a bond’s yield to maturity (sometimes called the “approximate YTM”). The exact yield to maturity is the discount rate that solves the full bond pricing equation and typically must be found using iteration or a financial calculator (like the one above).
Y_{\text{approx}} = \frac{C + \frac{F - P}{T}}{\frac{F + P}{2}}Variables:
- Yapprox is the approximate yield to maturity (constant yield), as a decimal per year
- C is the annual coupon payment (in dollars). If you have an annual coupon rate r, then C = r × F.
- F is the face (par) value of the bond
- P is the bond’s price (typically the clean price)
- T is the years to maturity
To estimate the yield, add the annual coupon payment to the average annual price change toward par, (F − P) / T. Then divide by the average of the face value and the price, (F + P) / 2. This estimate is most accurate for bonds near par and with moderate maturities; for more accurate results, compute YTM by solving the bond pricing equation (as the calculator above does).
What is a Constant Yield?
In bond investing and accounting, “constant yield” commonly refers to the bond’s yield to maturity (YTM)—the effective interest rate implied by the bond’s current price and its promised cash flows (coupon payments and principal repayment), assuming the bond is held to maturity and payments are made as scheduled. The yield is treated as “constant” in the sense that the same yield rate is applied over time (for example, in the constant-yield/effective-interest method of amortizing bond premiums and discounts), and coupon cash flows are typically assumed to be reinvested at the yield to maturity.
How to Calculate Constant Yield?
The following steps outline how to calculate the Constant Yield.
- First, determine the annual coupon payment (C) or the annual coupon rate and face value (so you can compute C).
- Next, determine the face value of the bond (F).
- Next, determine the bond’s price (P) (often quoted as the clean price).
- Next, determine the years to maturity (T).
- To estimate the yield quickly, you can use the approximation: Yapprox = (C + (F − P) / T) / ((F + P) / 2). For the exact yield to maturity, solve for the yield rate that makes the present value of the bond’s future cash flows equal to its price (this generally requires iteration).
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Annual Coupon Payment (C) = 50
Face Value (F) = 1000
Purchase Price (P) = 950
Years to Maturity (T) = 10