Fixed income YTM Bonds

Bond YTM calculator

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Yield to Maturity (YTM) is the single discount rate that equates a bond’s future cash flows (coupons + principal) to its current market price.

Formula

Price = sum(Coupon_t / (1 + YTM)^t) + FaceValue / (1 + YTM)^T

Where:

  • Coupon_t = coupon paid at time t.
  • T = time to maturity in periods.
  • FaceValue = principal at maturity.

YTM is solved numerically (no closed-form for general bonds).

Worked example

7.18% coupon, semi-annual, Rs 100 face value, 8 years to maturity, current price Rs 97.

Semi-annual coupon = Rs 3.59. Periods = 16.

97 = sum(3.59 / (1+r)^t) + 100 / (1+r)^16, for t = 1 to 16

Solve: r ~ 3.84% per period → YTM = 7.68% annualised.

Calculators

  • Excel: =RATE(periods, coupon, -price, face_value) * 2 (semi-annual).
  • Online: Many financial calculator websites.
  • Zerodha Console: Auto-displays YTM for bond holdings.

Caveats

  • Assumes coupons reinvested at YTM (rarely true).
  • Doesn’t reflect default risk.
  • Doesn’t reflect inflation / real rates.

For real-world bond comparison, also consider modified duration, credit rating, and liquidity.

See also

External references

References

  1. CFA Institute, YTM methodology, cfainstitute.org.
  2. RBI, Bond pricing convention, rbi.org.in.

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