Assume the zero-coupon yields on default-free securities are as summarized in th

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

3.00%

3.60%

4.00%

4.30%

4.60%

Consider a four-year, default-free security with annual coupon payments and a face value of $1,000 that is issued at par. What is the coupon rate of this bond?

The par coupon rate is________.

(Round to two decimal places.)

Maturity

1 year

2 years

3 years

4 years

5 years

Zero-Coupon Yields

3.00%

3.60%

4.00%

4.30%

4.60%

Explanation / Answer

Let the annual coupon amount be P

Price of bond = Present value of coupon payments + Present value of face value of bond

Present value of annual coupon payments = P/1.03 + P/1.0362 + P/1.043 + P/1.0434 = P*3.63659

Present value of face value of bond = $1,000/1.0434 = $845.01

Price of bond = $1,000 = P*3.63659 + $845.01

P*3.63659 = $1,000 - $845,.01 = $154.99

P = $154.99/3.63659 = $42.62

Annual coupon amount = $42.62

Coupon rate = $42.62/$1,000 = 0.0426 = 4.26%

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