Question

 

Five years ago XYZ International issued some 26​-year ​zero-coupon bonds that were priced with a​ market's required yield to maturity of 8 percent and a par value of ​$1,000.What did these bonds sell for when they were​ issued? Now that 5 years have passed and the​ market's required yield to maturity on these bonds has climbed to 10 percent, what are they selling​ for? If the​ market's required yield to maturity had fallen to 6 ​percent, what would they have been selling​ for?

a.  What did these bonds sell for when they were​ issued? ($) (Round to the nearest​ cent.)

b.  Now that 5 years have passed and the​ market's required yield to maturity on these bonds has climbed to 10​%, what are they selling​ for? ​($)​ (Round to the nearest​ cent.)

c.  If the​ market's required yield to maturity had fallen to 6 percent, what would they have been selling​ for? ($) ​​(Round to the nearest​ cent.)

Answer 1

a

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =26

Bond Price =∑ [(0*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^26

k=1

Bond Price = 135.2

Using Calculator: press buttons "2ND"+"FV" then assign

PMT = Par value * coupon %=1000*0/(100)

I/Y =8

N =26

FV =1000

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(8/(100),26,-0*1000/(100),-1000,)

b

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =21

Bond Price =∑ [(0*1000/100)/(1 + 10/100)^k]     +   1000/(1 + 10/100)^21

k=1

Bond Price = 135.13

Using Calculator: press buttons "2ND"+"FV" then assign

PMT = Par value * coupon %=1000*0/(100)

I/Y =10

N =21

FV =1000

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(10/(100),21,-0*1000/(100),-1000,)

c

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =21

Bond Price =∑ [(0*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^21

k=1

Bond Price = 294.16

Using Calculator: press buttons "2ND"+"FV" then assign

PMT = Par value * coupon %=1000*0/(100)

I/Y =6

N =21

FV =1000

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(6/(100),21,-0*1000/(100),-1000,)