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Bond Valuation (Coupon Bond Price) Calculator

Calculates the present value of a coupon bond's future cash flows.

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Bond Price

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Overview

The Bond Valuation formula determines the fair price of a coupon bond by discounting all its future cash flows—coupon payments and the face value at maturity—back to the present. It sums the present value of each periodic coupon payment (an annuity) and the present value of the bond's face value received at maturity. This valuation is crucial for investors to assess whether a bond is underpriced, overpriced, or fairly priced relative to its yield to maturity.

Symbols

Variables

C = Coupon Payment, r = Yield to Maturity (YTM), n = Number of Periods, FV = Face Value (Par Value), P = Bond Price

Coupon Payment
USD
Yield to Maturity (YTM)
%
Number of Periods
years
FV
Face Value (Par Value)
USD
Bond Price
USD

Apply it well

When To Use

When to use: Use this equation when you need to determine the theoretical fair price of a bond that pays periodic interest (coupons) and returns its face value at maturity. It's essential for investors, portfolio managers, and financial analysts to evaluate bond investments, compare different bonds, or understand how changes in interest rates affect bond prices.

Why it matters: Bond valuation is fundamental to fixed income investing, allowing market participants to make informed decisions. It helps in understanding the relationship between bond prices, interest rates, and time to maturity, which is critical for managing interest rate risk and constructing diversified portfolios. Accurate valuation ensures efficient capital allocation in debt markets.

Avoid these traps

Common Mistakes

  • Not adjusting the coupon payment (C), yield (r), and number of periods (n) to match the compounding frequency (e.g., using annual 'r' for semi-annual coupons).
  • Confusing the coupon rate with the yield to maturity (r); 'r' is the market required rate of return, not the stated coupon rate.

One free problem

Practice Problem

A company issues a 5-year bond with a face value of $1,000 and an annual coupon rate of 5%. If the market's required yield to maturity (YTM) for similar bonds is 6%, what is the current market price of this bond?

Coupon Payment50 USD
Yield to Maturity (YTM)0.06 %
Number of Periods5 years
Face Value (Par Value)1000 USD

Solve for:

Hint: Calculate the present value of each annual coupon payment and the present value of the face value separately, then sum them up.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Investments (11th Edition) by Bodie, Kane, Marcus
  2. Principles of Corporate Finance (13th Edition) by Brealey, Myers, Allen
  3. Wikipedia: Bond valuation
  4. Bodie, Z., Kane, A., & Marcus, A. J. (2021). Investments (12th ed.). McGraw-Hill Education.
  5. Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  6. Bodie, Zvi, Alex Kane, and Alan J. Marcus. Investments. 12th ed. McGraw-Hill Education, 2021.
  7. Ross, Stephen A., Randolph W. Westerfield, and Jeffrey F. Jaffe. Corporate Finance. 13th ed. McGraw-Hill Education, 2022.
  8. Fabozzi, Frank J. The Handbook of Fixed Income Securities. 8th ed. McGraw-Hill Education, 2012.