Question

A. You are considering a 25-year, $1,000 par value bond. Its coupon rate is 8%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 9.2025%, how much should you be willing to pay for the bond? Do not round intermediate calculations. Round your answer to the nearest cent. $___

B. Nesmith Corporation's outstanding bonds have a $1,000 par value, a 10% semiannual coupon, 7 years to maturity, and a 13% YTM. What is the bond's price? Round your answer to the nearest cent. $___

Answer 1

A.Effective annual rate = 9.2025%

APR compounded semi-annually = n*((1 + EAR)^1/n - 1)

= 2*((1 + 0.092025)^0.5 - 1)

= 2*1.0450 - 1

= 2*0.0450

= 0.09*100

= 9%

Information provided:

Par value= future value= $1,000

Time= 25 years*2= 50 semi-annual periods

Coupon rate= 8%/2= 4%

Coupon payment= 0.04*1,000= $40 per semi-annual period

Yield to maturity= 9%/2= 4.50% per semi-annual period

The price of the bond is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 40

I/Y= 4.50

N= 50

Press the CPT key and PV to compute the present value.

The value obtained is 901.19.   

Therefore, I will be willing to pay $901.19 for the bond.   

B.Information provided:

Par value= future value= $1,000

Time= 7 years*2= 14 semi-annual periods

Coupon rate= 10%/2= 5%

Coupon payment= 0.05*1,000= $50 per semi-annual period

Yield to maturity= 13%/2= 6.50% per semi-annual period

The price of the bond is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 50

I/Y= 6.50

N= 14

Press the CPT key and PV to compute the present value.

The value obtained is 864.79.

Therefore, the price of the bond is $864.79.