Question

A 13-year bond with a 7 percent semiannual coupon and a $1,000 face

value has a nominal yield to maturity of 9.9 percent.  The bond currently sells for

$790.48. The bond, which may be called after 3 years, has a nominal yield to

call of 18.23% percent.  What is the bond’s call price?

Answer 1

Yield to call is IRR till the Bond is called. at YTC, PV of Cashflows will be equal to bond price.

Let "X" be the call Price.

Bond Price:

Period	CF	PVF @9.115%	Disc CF
1	35	0.916464281	$                    32.08
2	35	0.839906778	$                    29.40
3	35	0.769744561	$                    26.94
4	35	0.705443396	$                    24.69
5	35	0.646513674	$                    22.63
6	35	0.59250669	$                    20.74
6	X	0.59250669	0.5925X
Bond Price	156.47 + 0.5925X

Thus 156.47 + 0.5925X = 790.48

0.5925X = 790.48 - 156.47

= 634.01

X = 634.01 / 0.5925

= 1070.06

Call Price is $ 1070.06