A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 7%, and sells for $1,160. Interest is paid annually.

A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 7%, and sells for $1,160. Interest is paid annually.

a. If the bond has a yield to maturity of 9% 1 year from now, what will its price be at that time? (Do not round intermediate calculations.)


 b. What will be the annual rate of return on the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)
 

c. Now assume that interest is paid semiannually. What will be the annual rate of return on the bond?


d. If the inflation rate during the year is 3%, what is the annual real rate of return on the bond? (Assume annual interest payments.) (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)

Explanation

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.

Bond price	=	PV of coupon payments + PV of face value
	=	C × ((1 / r) – {1 / [r(1 + r)t]}) + FV / (1 + r)t
	=	(0.11 × $1,000) × ((1 / 0.11) – {1 / [0.11(1.11)(10 – 1)]}) + $1,000 / 1.11(10 – 1)
	=	$820

Since yield to maturity equals the coupon rate, the bond must be priced at par.

b.

Rate of return	=	[Annual interest + (Ending price – Beginning price)] / Beginning price
	=	($74 + 1,000 – 1,160) / $1,160
	=	–0.2293, or –22.93%

c.
The rate of return will be slightly higher above −22.93%, since the midyear coupon can be reinvested:

Rate of return =	$37 + $37 × (7.30).5 + ($1,000 -$1,160)	= –(expression error)%
	$1,160

d.

Rate of return	=	(1 + Nominal return) / (1 + Inflation rate) – 1
	=	[1 + (–0.2293)] / 1.03 – 1
	=	–0.2517, or –25.17%