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 3.30% 3.80% 4.00% 4.40% 4.50% Consider a four-year, default-free security with annual coupon payments and a face value of $ 1 comma 000 that is issued at par. What is the coupon rate of this bond? The par coupon rate is nothing%. (Round to two decimal places.)
Let the annual Coupon of the bond be $x
Tenure of the bond = 4 years.
Face Value of the bond = $1,000
Issue price of the bond =Present Value of the bond $1,000 (at par)
Let coupon amount of the bond be $x
.
Present Value of the Coupons at zero-coupon yields on default-free securities (computed in table below):
Years | Zero Coupon Yields | Discounting Factor at Yeild-Working | Discounting Factor at Yeild | Coupon Amount | Present Value at Yeildd |
1 | 3.30% | 1/1.033^1 | 0.968054211 | x | 0.968054211x |
2 | 3.80% | 1/1.038^2 | 0.928122482 | x | 0.928122482x |
3 | 4% | 1/1.04^3 | 0.888996359 | x | 0.888996359x |
4 | 4.40% | 1/1.044^4 | 0.841778841 | x | 0.841778841x |
3.626951894 | 3.626951894x |
.
Present Value of the bond = Present Value of the Coupons at zero-coupon yields on default-free securities + Present Value of the Redemption Value at zero-coupon yields on default-free securities
1,000 = 3.626951894x + 1,000* 0.841778841
1,000 = 3.626951894x + 841.7788415
3.626951894x = 158.22
x = 158.22/3.626951894
x = 43.62
.
Therefore, annual coupon amount of the bond = $43.62
.
Therefore, Coupon Rate of the Bond = Annual coupon amount of the bond/Face Value of the Bond * 100
= 43.62/1,000 * 100
= 4.63%
Assume the zero-coupon yields on default-free securities are as summarized in the following table: Maturity 1...
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