In: Finance
Bonds X and Y are identical, including the risk class. The only
difference between A and B is in the coupon payment as shown
below.
Bond X | Bond Y | |
Face value | $1,000 | $1,000 |
Annual Coupon Payment | $120 | $130 |
Payment Frequency | Semiannual | Annual |
Years to maturity | 15 | 15 |
Price | $904.55 | ? |
What
is the price of bond Y?
A. |
$925.88 |
|
B. |
$956.95 |
|
C. |
$940.92 |
|
D. |
$989.75 |
|
E. |
$973.44 |
|
F. |
$1,007.15 |
Current Price = 904.55
Coupon 12%
Maturity = 15 years
Let's assume the YTM be 13%
Value of Bond =
=
= 934.70662046
Now,
Let's assume the YTM be 14%
Value of Bond =
=
= 875.909588152
YTM =
= 13% + ((934.70662046 - 904.55) / (934.70662046 - 904.55) + (904.55 - 875.909588152 )) * (14-13)
= 13% + (30.15662046 / (30.15662046) + (28.640411875)) * 1
= 13% + (30.15662046 / 58.797032335) * 1
= 13% + 0.5129%
= 13.51%
Value of Bond =
Where r is the discounting rate of a compounding period i.e. 13.50%
And n is the no of Compounding periods 15 years
Coupon 130
=
= 818.860414713 + 149.64495395
= $ 973.44
Option E is correct.