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 9.2%. Bond C pays a 10% annual coupon, while Bond Z is a zero coupon bond.

a. Assuming that the yield to maturity of each bond remains at 9.2% over the next 4 years, calculate the price of the bonds at each of the following years to maturity. Round your answer to the nearest cent.

Years to Maturity Price of Bond C Price of Bond Z

4 $ $

3 $ $

2 $ $

1 $ $

0 $ $

Answer 1

Answer :- calculation of price of bond C at maturity

Here, when maturity period is 4 years

Formula used :- Interest amount (PVAF @ YTM %, n years) + redemption value or face value (PVF @ YTM %, n^th year)

Given YTM = 9.2%, n = 4 years, Interest amount = 1000$*10% = 100$, face value = 1000$

Bond value at maturity will be

= 100 $(PVAF @ 9.2%,4 years) + 1000 $(PVF @ 9.2%,4^th year)

= 100$ * 3.225 + 1000$ * 0.703

= 1025.5 $

Calculation of price of zero coupon bond Z

Formula used :- redemption value or face value (PVF @ YTM %, n^th year)

Here YTM = 9.2 %, n = 4

= 1000 $ (PVF @ 9.2%, 4^th year)

= 1000 $ * 0.703

= 703 $

When maturity period of bond is 3 years then

Value of bond C at maturity will be

Here, n = 3 years, YTM = 9.2%,Interest amount = 100$

Face value = 1000$

= 100$(PVAF @ 9.2%, 3 Years) + 1000$ (PVF @ 9.2%,3^rd year)

= 100 $ * 2.522 + 1000 $ * 0.768

= 252.2 $ + 768 $

=1020.2 $

price of zero coupon bond Z at maturity

Here n = 3 years, YTM = 9.2%, Face value = 1000 $

= 1000 $ ( PVF @ 9.2%, 3^rd year)

= 1000 $ * 0.768

= 768 $

When maturity period of bond is 2 years

Price of bond C will be

n = 2 years, YTM = 9.2%, Interest amount = 100$, face value = 1000$

= 100$ (PVAF @9.2 %, 2 years) + 1000 $ ( PVF @ 9.2%,2^{nd year)}

^{= 100 $ * 1.754 + 1000 $ *0.838}

^{= 175.4 $ + 838 $}

^{= 1013.4 $}

^{Value of zero coupon bond Z at maturity}

^{Here, n = 2 years, face value = 1000 $, YTM = 9.2%}

= 1000 $( PVF @ 9.2%,2^nd year)

= 1000 $ * 0.838

= 838 $

When maturity period is 1 year

Value of bond C at maturity will be

n = 1 year, YTM = 9.2%, Interest amount = 100$, Face value = 1000 $

= 100$ ( PVAF @9.2 %, 1 year) + 1000 $( PVF @9.2%,1^st year)

= 100 $ * 0.916 + 1000 $ * 0.916

= 91.6$ + 916 $

= 1007.6 $

Value of zero coupon bond Z at maturity will y

n = 1 year, YTM = 9.2%, face value = 1000 $

= 1000 $ * 0.916

= 916 $

When maturity period is zero then the bond holders will get only redemption value of bond (face value of bond)