Question

Presented below are annual coupon rates, yield rates, and expected duration for a series of debentures.

Calculate the issuance price for each debenture assuming that the face value of each bond is $1,000 and that interest is paid semiannually.

Bond	Coupon Rate		Yield Rate		Duration
A	4.0	%	6.0	%	6	years
B	10.0	%	8.0	%	10	years
C	5.0	%	6.0	%	15	years
D	8.0	%	8.0	%	10	years
E	0.0	%	10.0	%	5	years

Do not round until your final answer. Round your answer to the nearest dollar.

A	$Answer
B	$Answer
C	$Answer
D	$Answer
E	$Answer

Answer 1

Present value of bond = Present value of bond value + present value of interest payment

A. Present value of bond = face value / (1+ yield)^{number of payment} + interest [1 - (1+yield)^{-number of payment}]/ yield

= 1000 / (1+ 0.03)^6*2 + (1000*0.02) [1 - (1+0.03)^-6*2]/ 0.03

= 1000 / (1.03)¹² + 20 *[1 - (1.03)^-12]/ 0.03

= 1000 / 1.425761 + 20 *[1 - 1/1.425761 ]/ 0.03

= 701.38 + 199.08

= $900.46

=$900

B .Present value of bond = face value / (1+ yield)^{number of payment} + interest [1 - (1+yield)^{-number of payment}]/ yield

= 1000 / (1+ 0.04)^10*2 + (1000*0.05) [1 - (1+0.04)^-10*2]/ 0.04

= 1000 / (1.04)²⁰ + 50 [1 - (1.04)^-20]/ 0.04

= 1000 / (1.04)²⁰ + 50 [1 - 1/(1.04)²⁰]/ 0.04

= $456.39 + 679.52

= $1135.91

= $1136

C Present value of bond = face value / (1+ yield)^{number of payment} + interest [1 - (1+yield)^{-number of payment}]/ yield

= 1000 / (1+ 0.03)^15*2 + (1000*0.025) [1 - (1+0.025)^-15*2]/ 0.03

= 1000 / (1.03)³⁰ + 25 [1 - (1.025)^-30]/ 0.03

= 1000 / (1.03)³⁰ + 25 [1 - 1/ (1.025)³⁰]/ 0.03

=411.99 + 490.01

= $902

D. Present value of bond = face value / (1+ yield)^{number of payment} + interest [1 - (1+yield)^{-number of payment}]/ yield

= 1000 / (1+ 0.04)^10*2 + (1000*0.04) [1 - (1+0.04)^-10*2]/ 0.04

= 1000 / (1.04)²⁰ + 40 [1 - (1.04)^-20]/ 0.04

= 1000 / (1.04)²⁰ + 40 [1 - 1/(1.04)²⁰]/ 0.04

= 456.39 + 543.61

= $1000

E. Present value of bond = face value / (1+ yield)^{number of payment} + interest [1 - (1+yield)^{-number of payment}]/ yield

= 1000 / (1+ 0.05)^5*2 + 0 * [1 - (1+0.05)^-5*2]/ 0.05

= 1000 / (1.05)¹⁰ + 0

= 1000 / (1.05)¹⁰ + 0

= 613.91 + 0

= 613.91

= $614