Question

A 7% semiannual coupon bond matures in 5 years. The bond has a face value of $1,000 and a current yield of 7.4658%. What are the bond's price and YTM? (Hint: Refer to Footnote 6 for the definition of the current yield and to Table 7.1) Do not round intermediate calculations. Round your answer for the bond's price to the nearest cent and for YTM to two decimal places.

Bond’s price: $  

YTM:   %

Answer 1

1]	Bond price = Coupon in dollars/Current yield
	Substituting available values:
	Bond price = 70/7.4658% =	$          937.61
2]	YTM is that discount rate which equates the PV of the
	expected cash flows from the bond with its current price.
	The expected cash flows are:
	*The maturity value of the bond of $1000 at EOY5, and
	*The semiannual interest payments of $35 receivable for
	10 half years. It is an annuity.
	Such a discount rate is to be found out by trial and error.
	Discounting with 4.5% [half yearly rate]:
	PV = 1000/1.045^10+35*(1.045^10-1)/(0.045*1.045^10) =	$ 920.87
	With 3.5% half yearly compounding price =	$      1,000.00
	YTM [half yearly] = 3.5%+1%*(1000-937.61)/(1000-920.87) =	4.29%
	YTM = 4.29*2 =	8.58%
	Using a financial calculator it is 8.56%