Question

Assume zero-coupon yields on default-free securities are as summarized in the following table:

Maturity (years)	1	2	3
Zero-coupon YTM	4%	4,5%	4,75%

Consider a three-year, default-free security with annual coupon payments and a face value of $1000 that is issued at par. What is the coupon rate of this bond (EAR)? (hint: you can solve this question algebraically but also you can use “goal seek” in Excel)

A. 4.73%

B. 4.75%

C. 4.55%

D. 4.81%

Answer 1

Coupon price of bond must be such so that bond is issued at par or bond price is equal to $1000

so bond issue or market price = $1000

Bond price = PV of all coupon and matuirty payments = C/(1+YTM year 1)^1 + C/(1+YTM year 2)^2 + (C+Face value)/(1+YTM year 3)^3

1000 = C/(1+4%)^1 + C/(1+4.5%)^2 + (C+1000)/(1+4.75%)^3

1000 = (C*0.9615384615)+(C*0.9157299512)+(C*0.8700373663)+870.0373663

1000-870.0373663 =2.747305779*C

C =129.9626337/2.747305779

=47.3054855

Annual coupon amount =47.3054855

Coupon rate = coupon amount/face value

=47.3054855/1000

=4.73%

So Answer is a, 4.73%