CODEWITHSUNDEEP
sympyfinancenewtons-methodirr
Flux
Flux

Reputation: 10950

How to calculate internal rate of return (IRR) and yield to maturity (YTM) in Sympy

How do I calculate internal rate of return (IRR) and yield to maturity (YTM) in Sympy? I am trying to calculate the YTM of a bond of $1000 face value that pays $50 in coupons every year. The bond is currently selling for $900, and matures in 3 years. Using the formula for the YTM:

900 = [50 / (1 + r)] + [50 / (1 + r)^2] + [50 / (1 + r)^3] + [1000 / (1 + r)^3]

How do I solve for r, the YTM? Does Sympy have a solver for this kind of problem, or do I have to do it in Python using Newton's method?

Upvotes: 0

Views: 234

Answers (1)

Luuk
Luuk

Reputation: 14978

When following the docs for Solvers

from sympy.solvers import solve
from sympy import Symbol
r = Symbol('r')
solve((50 / (1 + r)) + (50 / pow((1 + r),2)) + (50 / pow((1 + r),3)) + (1000 / pow((1 + r),3)) - 900)

returns:

[-53/54 + (-1/2 - sqrt(3)*I/2)*(sqrt(11594049)/5832 + 11492/19683)**(1/3) + 55/(2916*(-1/2 - sqrt(3)*I/2)*(sqrt(11594049)/5832 + 11492/19683)**(1/3)),
 -53/54 + 55/(2916*(-1/2 + sqrt(3)*I/2)*(sqrt(11594049)/5832 + 11492/19683)**(1/3)) + (-1/2 + sqrt(3)*I/2)*(sqrt(11594049)/5832 + 11492/19683)**(1/3),
 -53/54 + 55/(2916*(sqrt(11594049)/5832 + 11492/19683)**(1/3)) + (sqrt(11594049)/5832 + 11492/19683)**(1/3)]

P.S. I have no clue about what an YTM, IRR is...

Upvotes: 0

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