# Calculate the Price of a Bond

• Sep 13th 2011, 02:44 PM
RogueDemon
Calculate the Price of a Bond
2. (a) Find the price of the bonds or debentures given V = 100 and r, i, and n as stated.

(i) 20 years to maturity, interest at 10% p.a. to yield 11% p.a.

My attempt at a solution is as follows:

$\displaystyle P = V(1 + i)^{-n} + rV\frac{1 - (\frac{1}{1 + i})^n}{i}$

$\displaystyle = V(1 + 0.11)^{-20} + 0.10*100\frac{1 - (\frac{1}{1 + 0.11})^{20}}{0.11}$

$\displaystyle = \$92.04$. Though apparently I'm wrong since the correct answer is listed as$\displaystyle \$91.98$. Why am I getting a different answer? Almost none of my answers are the same as those on the answer page, as I am always off by quite a few cents. The only thing I can think of is that the values given above aren't actually the values supposed to be subbed in, and that I need to perform some other calculations in order to get such values.
• Sep 13th 2011, 03:35 PM
RogueDemon
Re: Calculate the Price of a Bond
Nvm, I got it. (Hi)
• Sep 14th 2011, 01:05 AM
dexteronline
Re: Calculate the Price of a Bond
Quote:

Originally Posted by RogueDemon
2. (a) Find the price of the bonds or debentures given V = 100 and r, i, and n as stated.

(i) 20 years to maturity, interest at 10% p.a. to yield 11% p.a.

My attempt at a solution is as follows:

$\displaystyle P = V(1 + i)^{-n} + rV\frac{1 - (\frac{1}{1 + i})^n}{i}$

$\displaystyle = V(1 + 0.11)^{-20} + 0.10*100\frac{1 - (\frac{1}{1 + 0.11})^{20}}{0.11}$

$\displaystyle = \$92.04$. Though apparently I'm wrong since the correct answer is listed as$\displaystyle \$91.98$. Why am I getting a different answer? Almost none of my answers are the same as those on the answer page, as I am always off by quite a few cents. The only thing I can think of is that the values given above aren't actually the values supposed to be subbed in, and that I need to perform some other calculations in order to get such values.

Just to write so others reading the post can see why there were two prices for the same par value bond. It has to do with the number of payments the bond makes. When the bond pays semi annual interest payment the price of the bond is $91.98 and when the bond makes an annual interest payment the price of the bond is$92.04

Compounding = semi annually
Par Value = 100
Coupon Rate = 0.05
Market Rate = 0.055
N = 40

Non Zero Bond Price Formula

Coupon Rate x Par Value x PVIFA(ytm%, n) + Par Value x PVIF(ytm%, n)

PVIFA Formula

PVIFA(ytm%, n) = [1 - v] / ytm%
v = 1 / (1 + ytm%)^n
PVIFA(ytm%, n) = [1 - { 1 / (1 + ytm%)^n }] / ytm%

PVIFA Calculation

v = 1 / (1+0.055)^40
v = 0.117463142305
PVIFA(0.055, 40) = [1 - 0.117463142305] / 0.055
PVIFA(0.055, 40) = 0.882536857695 / 0.055
PVIFA(0.055, 40) = 16.0461246854
PVIF Formula

PVIF(ytm%, n) = 1 / (1 + ytm%)^n
PVIF Calculation

PVIF(0.055, 40) = 1 / (1+0.055)^40
PVIF(0.055, 40) = 1 / 8.51330877398
PVIF(0.055, 40) = 0.117463142305
Non Zero Bond Price Calculation

Price = 0.05 x 100 x 16.0461246854 + 100 x 0.117463142305
Price = 80.2306234269 + 11.7463142305
Price = $91.98 Compounding = annually Par Value = 100 Coupon Rate = 0.1 Market Rate = 0.11 N = 20 Non Zero Bond Price Formula Coupon Rate x Par Value x PVIFA(ytm%, n) + Par Value x PVIF(ytm%, n) PVIFA Formula PVIFA(ytm%, n) = [1 - v] / ytm% v = 1 / (1 + ytm%)^n PVIFA(ytm%, n) = [1 - { 1 / (1 + ytm%)^n }] / ytm% PVIFA Calculation v = 1 / (1+0.11)^20 v = 0.12403390709 PVIFA(0.11, 20) = [1 - 0.12403390709] / 0.11 PVIFA(0.11, 20) = 0.87596609291 / 0.11 PVIFA(0.11, 20) = 7.96332811737 PVIF Formula PVIF(ytm%, n) = 1 / (1 + ytm%)^n PVIF Calculation PVIF(0.11, 20) = 1 / (1+0.11)^20 PVIF(0.11, 20) = 1 / 8.06231153613 PVIF(0.11, 20) = 0.12403390709 Non Zero Bond Price Calculation Price = 0.1 x 100 x 7.96332811737 + 100 x 0.12403390709 Price = 79.6332811737 + 12.403390709 Price =$92.04

Reference: Bond Price Calculator