Question

Suppose the following bond quote for IOU Corporation appears in the financial page of today’s newspaper. Assume the bond has a face value of $1,000, and the current date is April 15, 2016.

Company (Ticker)	Coupon	Maturity	Last Price	Last Yield	EST Vol (000s)
IOU (IOU)	8.30	Apr 15, 2036	91.675	??	1,841

What is the yield to maturity of the bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Yield to maturity             %
  
What is the current yield? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
  
Current yield             %

Answer 1

1)	YTM is the IRR of the cash flows associated with the bond. In
	other words it is that discount rate which equates the
	PV of the expected cash inflows from the bond with
	its current price.
	The expected cash inflows from the bond are:
	1) the maturity value of $1000 receivable after 20 years.
	2) the annual interest of $83.00 which is an annuity for 20 years.
	Hence, 916.75 = 1000/(1+r)^20+83*((1+r)^20-1))/((r*(1+r)^20))
	The value of r is to be found out by trial and error such
	that the value of the RHS in the above equation equals 916.75.
	Discounting with 10%, RHS equals
	= 1000/(1.10)^20+83*((1.10^20-1))/((0.10*(1.10)^20))=	$         855.27
	Discounting with 9%, RHS equals
	= 1000/(1.09)^20+83*((1.09)^20-1)/((0.09*(1.09)^20))=	$         936.10
	The value of r lies between 9% and 10%.
	The exact value of r, can be found out by simple interpolation as below:
	r = 9+(936.10-916.75)/(936.10-855.27) =	9.24
	Using a financial calculator the YTM = 9.23%
2)	Current yield = 83.00/916.75 =	9.05%