Question

Addison company will issue a zero-coupon bond this coming month. The projected yield for the bond is 7%. If the par value of the bond is $1,000, what is the price of the bond using a semiannual convention if:
a. the maturity is 20 years
b. the maturity is 30 years
c. the maturity is 50 years
d. the maturity is 100 years

Answer 1

Answer:

If the bond is zero coupon then there only be one lump sum payment at the end of the bond period and we will have to discount is back using the yield of the  bond to find its present value or price. Because the convention is semi annual we will divide interest by 2 to find the semi annual interest rate and to number of periods we will multiply years by 2 because of semi annual convention.

Yield= 7/2= 3.5%

a. the maturity is 20 years

We have to discount 1,000 20 years back which means 40 periods back as 20*2= 40

1,000/1.035^40=252.5725

The present value of a zero coupon $1000 bond will be $252.5725 when the yield is 7% and maturity is 20 years.

b. the maturity is 30 years

We have to discount 1,000 30 years back which means 60 periods back as 30*2= 60

1000/1.035^60=126.93

The present value of a zero coupon $1000 bond will be 126.93 when the yield is 7% and maturity is 30 years.

c. the maturity is 50 years

We have to discount 1,000 50 years back which means 100 periods back as 50*2= 100

1000/1.035^100= 32.06

The present value of a zero coupon $1000 bond will be $32.06 when the yield is 7% and maturity is 50 years.

d. the maturity is 100 years

We have to discount 1,000 100 years back which means 200 periods back as 50*2= 200

1000/1.035^200= 1.02

The present value of a zero coupon $1000 bond will be $1.02 when the yield is 7% and maturity is 100 years.

Explanation: