Question

An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity of 9.4%. Bond C pays a 11.5% annual coupon, while Bond Z is a zero coupon bond.

1. Assuming that the yield to maturity of each bond remains at 9.4% over the next 4 years, calculate the price of the bonds at each of the following years to maturity. Round your answers to the nearest cent.

   Years to Maturity	Price of Bond C	Price of Bond Z
   4	$	$
   3	$	$
   2	$	$
   1	$	$
   0	$	$

2. Select the correct graph based on the time path of prices for each bond.

Answer 1

Solution:

1.a)Calculation of Price of Bond C

Price of bond is the sum of the present value of coupon amount and maturity value of bond.

Price=Annual coupon amount/(1+YTM)^n+Annual coupon amount+Maturity value/(1+YTM)^Maturity year

Annual coupon amount=$1000*11.5%=$115

n=no.of year

Thus price of bond,when maturity year is;

4 years=$115/(1+0.0940)^1+$115/(1+0.0940)^2+$115/(1+0.0940)^3+($115+$1000)/(1+0.0940)^4

=$1067.44

3 years=$115/(1+0.0940)^1+$115/(1+0.0940)^2+($115+$1000)/(1+0.0940)^3

=$1052.78

2 Years=$115/(1+0.0940)^1+($115+$1000)/(1+0.0940)^2

=$1036.74

1 year=($115+$1000)/(1+0.0940)^1

=$1019.20

0 Year=If the bond will be mature right now(i.e 0 year),then no coupon will be paid.Thus in that case,bond price will be equal to its maturity value.

Therefore price of bonnd in case of 0 year maturity is $1000

b)Calculation of Price of Zero coupon bond

In case of zero coupon bond,no coupon will be paid,thus formula for calculating price of zero coupon bond is;

Price=Maturity Value/(1+YTM)^n

n=No. of years to maturity

Thus price of bond,when maturity year is;

4 years=$1000/(1+0.094)^4

=$698.12

3 years=$1000/(1+0.094)^3

=$763.74

2 years=$1000/(1+0.094)^2

=$835.54

1 year=$1000/(1+0.094)^1

=$914.08

0 year=$1000