Question

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

Maturity	1 year	2 years	3 years	4 years	5 years
​Zero-Coupon Yields	3.603.60​%	4.204.20​%	4.404.40​%	4.804.80​%	5.205.20​%

Consider a​ four-year, default-free security with annual coupon payments and a face value of

$ 1 comma 000$1,000

that is issued at par. What is the coupon rate of this​ bond?

Answer 1

Given yield on zero coupon default free bond

Maturity yield

1 year 3.60%

2 year 4.20%

3 year 4.40%

4 year 4.80%

So for a coupon bond, that has a face value of $1000 and sells on par, its price = $1000

let coupon payment be C

then, Price = C/(1+r1) + C/(1+r2)^2 + C/(1+r3)^3 + C/(1+r4)^4 + 1000/(1+r4)^4

So, 1000 = C/1.036 + C/1.042^2 + C/1.044^3 + C/1.048^4 + 1000/1.048^4

1000 = 0.9653C + 0.9210C + 0.8788C + 0.8290C + 829.0

So, 171 = 3.5941C or, C = 171/3.5941

C = $47.58

or coupon rate = 47.58/1000 = 4.76%