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

issue price of bond can be calculated using following formula

B = C*{1-1/(1+r)^n}/r +FV/(1+r)^n

where B = current market price

r= current interest rate

C = coupon payment

FV = Face Value

n = periods

(a)

Coupon = C = 6% *1000 /2 = $30

B = C*{1-1/(1+r)^n}/r +FV/(1+r)^n

=30*{1-1/(1+.025)^20}/.025 + 1000/(1.025)^20

= 467.67 + 610.27 = 1077.94

b.

B = 30 *{1-1/(1.04)^14}/.04 + 1000 / (1.04)^14 = $ 894.37

c.

B = 30* {1-1/(1.035)^6}/.035 + 1000/ (1.035)^6 = $ 1141.12

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