Question

James Corporation is planning to issue bonds with a face value of $502,500 and a coupon rate of 6 percent. The bonds mature in 7 years and pay interest semiannually every June 30 and December 31. All of the bonds will be sold on January 1 of this year.
Required: Compute the issue (sale) price on January 1 of this year for each of the following independent cases:

a. Case A: Market interest rate (annual): 4 percent.
b. Case B: Market interest rate (annual): 6 percent.
c. Case C: Market interest rate (annual): 8.5 percent.

Answer 1

Answer:

a.

Bond Price  = $563,333.90007 rounded off to $563,333.90

b.

Bond Price  = $502500

c.

Bond Price  = $437232.16025 rounded off to $437232.16

Explanation:

To calculate the quote/price of the bond today, which is the present value of the bond, we will use the formula for the price of the bond. As the bond is a semi annual bond, we will use the semi annual coupon payment, semi annual number of periods and semi annual YTM. The formula to calculate the price of the bonds today is attached.

a. Case A: Market interest rate (annual): 4 percent

Coupon Payment (C) = 502500 * 0.06 * 6/12 = $15075

Total periods remaining (n) = 7 * 2 = 14

r or YTM = 4% * 6/12  =  0.02 or 2%    

 

Bond Price = 15075 * [( 1 - (1+0.02)^-14) / 0.02]  + 502500 / (1+0.02)^14

Bond Price  = $563,333.90007 rounded off to $563,333.90

 

b. Case B: Market interest rate (annual): 6 percent

Coupon Payment (C) = 502500 * 0.06 * 6/12 = $15075

Total periods remaining (n) = 7 * 2 = 14

r or YTM = 6% * 6/12  =  0.03 or 3%    

 

Bond Price = 15075 * [( 1 - (1+0.03)^-14) / 0.03]  + 502500 / (1+0.03)^14

Bond Price  = $502500

c. Case C: Market interest rate (annual): 8.5 percent.

Coupon Payment (C) = 502500 * 0.06 * 6/12 = $15075

Total periods remaining (n) = 7 * 2 = 14

r or YTM = 8.5% * 6/12  =  0.0425 or 4.25%    

 

Bond Price = 15075 * [( 1 - (1+0.0425)^-14) / 0.0425] + 502500/(1+0.0425)^14

Bond Price  = $437232.16025 rounded off to $437232.16