Question

On January 1, 20X1, WP Industries issued $200,000 (face value) of bonds with a stated (coupon) rate of 6%. The bonds pay interest semi-annually on June 30 and December 31 and mature in 15 years. If the market rate of interest on the issue date was 8%, the bonds will sell for

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Select one:

a. $171,420

b. $239,201

c. $165,762

d. $200,000

e. $165,416

Answer 1

Answer:- The bonds will sell for = $165416.

Explanation-Calculation of selling price of bond at issuance=

                B0 =C/2 {1-(1+r/2)-2t}/ r/2 +F/(1+r/2)-2t

Where:-

Bo = Bond price

C= Coupon payment

r = Interest Rate

F= Face value

t = Years/Periods

Since the interest is paid semi-annually the bond interest rate per period is 3% (= 6%/ 2), the market interest rate is 4% (= 8%/ 2) and number of time periods are 30 (= 2*15). Hence, the price of the bond is calculated as the present value of all future cash flows as shown below:-

Price of Bond =3%*$200000*{1-(1+4%)-30/4%} +$200000/(1+4%)30

= ($6000*17.29203)+ ($200000*0.30832)

= $103752+$61664

= $165416