Yield to maturity YTM Calculation

Written by:Abraham A.
Location:Bonds

Finance.ThinkAndDone.com provides you online tool to calculate yield to maturity on bonds when you provide the bond's maturity value, market price, coupon rate, and years till maturity. The online tool shows step by step workout for YTM calculation using Newton Raphson method. The YTM formula used in calculation is derived from Excel's TVM equation that sets equal the bond's market price to sum of discounted stream of interest payments and the maturity value of the bond. The use of Newton Raphson method ensures that an exact YTM value is found using a guess rate of 10% as seed value for the Newton Raphson method.

Location: Bonds

YTM Calculation

Developed by:Emma A.
Location:Financial Calculators
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Results

f(x) = 1000 + -900 * (1+x)^20 + 25 [(1+x)^20 - 1]/x

f'(x) = 20 * -900 * (1+x)^19 + 25 * (20 x (1 + x)^19 - (1 + x)^20 + 1) / (x^2)

x = 0.1
f(x) = -3622.875
f'(x) = -93825.5675
x1 = 0.1 - -3622.875/-93825.5675 = 0.0613871243704
Error Bound = 0.0613871243704 - 0.1 = 0.038613 > 0.000001

x1 = 0.0613871243704
f(x1) = -1029.441
f'(x1) = -45773.6536
x2 = 0.0613871243704 - -1029.441/-45773.6536 = 0.0388973087478
Error Bound = 0.0388973087478 - 0.0613871243704 = 0.02249 > 0.000001

x2 = 0.0388973087478
f(x2) = -194.6198
f'(x2) = -29546.1707
x3 = 0.0388973087478 - -194.6198/-29546.1707 = 0.0323103354988
Error Bound = 0.0323103354988 - 0.0388973087478 = 0.006587 > 0.000001

x3 = 0.0323103354988
f(x3) = -12.2251
f'(x3) = -25906.7145
x4 = 0.0323103354988 - -12.2251/-25906.7145 = 0.0318384467887
Error Bound = 0.0318384467887 - 0.0323103354988 = 0.000472 > 0.000001

x4 = 0.0318384467887
f(x4) = -0.0577
f'(x4) = -25662.321
x5 = 0.0318384467887 - -0.0577/-25662.321 = 0.0318361965686
Error Bound = 0.0318361965686 - 0.0318384467887 = 2.0E-6 > 0.000001

x5 = 0.0318361965686
f(x5) = -0
f'(x5) = -25661.1607
x6 = 0.0318361965686 - -0/-25661.1607 = 0.0318361965178
Error Bound = 0.0318361965178 - 0.0318361965686 = 0 < 0.000001

YTM = 3.18%
Annual YTM = 6.36%

Input Data

Please enter the maturity value of the bond (debt) 
Please enter the market price of the bond (debt) 
Please enter the coupon rate  
Please enter the years to maturity  

Instructions

You have to provide certain details about the bond for which you have find the yield to maturity. Assuming we have a 5% semiannual $1000 bond with market price of $900 having 10 years to maturity.

  1. You have to key in 1000 as par value of the bond
  2. You have to key in 900 as the market price
  3. You have to key in 5 as the coupon rate
  4. You have to key in 10 as years to maturity
  5. You have to select the frequency of interest payments
Location: Financial Calculators