Question

Consider the Leverage Unlimited, Inc., zero coupon bonds of Year 22. The bonds were issued in Year 1 for $100. Determine the yield-to-maturity if the bonds are purchased at the following price. Round PVIF value in intermediate calculations to three decimal places. Use Table II to answer the question. Round your answers to one decimal place.

A). Issue price of $100 in Year 1. (Note: To avoid a fractional year holding period, assume that the issue and maturity dates are at the midpoint—July 1—of the respective years.   %

B). Market price as of July 1, Year 19, of $850. %

c). Explain why the returns calculated in Parts a and b are different. Over the period from Year 1 to Year 19, the general level of interest rates declined, causing bond prices to ______and yields to_______ .

Answer 1

A)	Yield to maturity			11.59%
Working:
	Bonds maturity value is the future value of bond's price at its yield to maturity rate.
	Future Value		=	Present Value*(1+i)^n		Where,
	1000		=	100*(1+i)^21		i	=	Yield to maturity
	10		=	(1+i)^21		n	=	Time
	10	^(1/21)	=	1+i
	1.1159		=	1+i		Note:
	0.1159		=	i
						July 1, year 1 to July 1, 2022 is 21 years.
	So, Yield to maturity	=	11.59%
B)	Yield to maturity			5.57%
Working:
	Bonds maturity value is the future value of bond's price at its yield to maturity rate.
	Future Value		=	Present Value*(1+i)^n		Where,
	1000		=	850*(1+i)^3		i	=	Yield to maturity
	1.176470588		=	(1+i)^3		n	=	Time
	1.176470588	^(1/3)	=	1+i
	1.0557		=	1+i		Note:
	0.0557		=	i
						July 1, year 19 to July 1, 2022 is 3 years.
	So, Yield to maturity	=	5.57%
c.	Return of bonds depend upon three factor-(i) Price, (ii) Time and (iii) Future Value.
	Future value (Face Value) of bond is always 1000.
	Price of bond increases as number of period reduced.
	Therefore, return of bond decreased in part b than part a because price increases.
	Over the period from Year 1 to Year 19, the general level of interest rates declined, causing bond prices to $ 850 and yields to 5.57%.