Question

A 15-year, $1,000 par value, 10% semiannual coupon bond has a price of $1,190 and it is callable in 5 years at a call price of $1,050. What is the bond’s nominal yield to call (YTC)?

	a.	6.37%
	b.	6.73%
	c.	7.60%
	d.	7.83%
	e.	3.18%

Answer 1

YTC is that discount rate which equates the cash flows from the
bond with the price if it is held for 5 years, the time when the
call can be made.
The cash flows are the call price of $1050 at EOY 5 and
the semiannual interest of $50 for 10 half years.
The relevant discount rate has to be found by trial and error.
Discounting with 3% (half year rate), PV of the cash flows =
= 1050/1.03^10+50*(1.03^10-1)/(0.03*1.03^10) =	$       1,207.81
Discounting with 4% (half year rate), PV of the cash flows =
= 1050/1.04^10+50*(1.04^10-1)/(0.04*1.04^10) =	$       1,114.89
The value of r lies between 3% and 4%.
The exact value can be ascertained by simple interpoltaion as
below:
r = 3+(1207.81-1190)/(1207.81-1114.89) =	3.1917
3.1917 is semi-annual rate; annual rate being = 3.1917*2 =	6.38
Closest option = Option [a] 6.37%/ (Difference due to approximation)