John Co. issues a series of bonds with a par value of $1,000 and a maturity of 1

Question

John Co. issues a series of bonds with a par value of $1,000 and a maturity of 10 years. The bonds pay interest based upon an annual fixed coupon rate of 6%, but coupon payments are made on a semi-annual basis. The bonds are issued when the going rate in the market for similar bonds is 5%. (a) What price will one John Co. bond sell for at the issuance date? $_______________ (b) Three years pass since the issuance date and the going rate in the market for similar bonds is 8%. If a John Co. bondholder is looking to sell his fixed coupon bond, how much will he be able to sell the bond for? $_______________ (c) Seven years pass since the issuance date and the going rate in the market for similar bonds is 7%. If a John Co. bondholder is looking to sell his fixed coupon bond, how much will he be able to sell the bond for? $_______________

Explanation / Answer

a)

                    K =Nx2         
BOND PRICE= [(Semi-annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^(Nx2)
                   k=1

                    K= 10x2          
BOND PRICE= [(6*1000/(100*2))/(1 + 5/200)^k]     +   1000/(1 + 5/200)^10x2
                   k=1

Price = 1077.95

b

K =Nx2          
BOND PRICE= [(Semi-annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^(Nx2)
                   k=1

                    K= 7x2           
BOND PRICE= [(6*1000/(100*2))/(1 + 8/200)^k]     +   1000/(1 + 8/200)^7x2
                   k=1

Price = 894.37

c)

K =Nx2          
BOND PRICE= [(Semi-annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^(Nx2)
                   k=1

                    K= 3x2           
BOND PRICE= [(6*1000/(100*2))/(1 + 7/200)^k]     +   1000/(1 + 7/200)^3x2
                   k=1

=973.36

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