A 1000 par value, 8 percent bond with quarterly coupons is callable five years after issue. The bond matures for 1000 at the end of ten years and is sold to yield a nominal rate of 6 percent compounded quarterly under the assumption that the bond will not be called. Calculate the redemption value, at the end of five years, that will yield the purchaser the same nominal rate of 6 percent compounded quarterly.

Question

Yusuf

Business

3 May, 03:05

A 1000 par value, 8 percent bond with quarterly coupons is callable five years after issue. The bond matures for 1000 at the end of ten years and is sold to yield a nominal rate of 6 percent compounded quarterly under the assumption that the bond will not be called. Calculate the redemption value, at the end of five years, that will yield the purchaser the same nominal rate of 6 percent compounded quarterly.

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Misael Madden · Answer 1

85.84

Explanation:

•At a 1000 par value, 8%, the coupon

will be 80 (1000*0.08).

•It is also compounded quaterly = 80/4 = 20 per quarter.

•Nominal interest rate = 6%, = 1.5% per quater.

•Face value = 1000

•Since it is cimpounded quaterly, n = 5years*4 = 20

To find the redemption value at the end of five years, we need to first find the present value of the bond.

= 20 / (1+0.015) + 20 / (1+0.015) ² + 20 / (1+0.015) ³+20 / (1+0.015) ⁴ ... + 20 (1+0.015) ^20

= 1085.84

Therefore the redemption value after five years will be:

Present value - face value

1085.84-1000 = 85.84