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.

Re: Calculate the Price of a Bond

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