Question

(TCO D) A bond currently sells for $1,050 even though it has a par of $1,000. It was issued 2 years ago and had a maturity of 10 years. The coupon rate is 7% and the interest payments are made semiannually. What is its YTM? Show your work.

Answer 1

YTM is that discount rate which equates the cash flows from the
bond with the current price if, the bond is held for 8 (10-2) years.
The cash flows are the maturity value of $1000 at EOY 8 and
the semiannual interest of $35.00 for 16 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 =
= 1000/1.03^16+35.00*(1.03^16-1)/(0.03*1.03^16) =	$ 1,062.81
Discounting with 4% (half year rate), PV of the cash flows =
= 1000/1.04^16+35.00*(1.04^16-1)/(0.04*1.04^16) =	$     941.74
The value of r lies between 3% and 4%.
The value of r can be found out by simple interpolation as done
below:
r = 3+(1062.81-1050.00)/(1062.81-941.74) =	3.11	%
3.11 % is semi-annual rate; annual rate being = 3.11*2 =	6.21	%
Using an online calculator, the YTM is 6.20% (difference due to approximation)