Question

A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 8.7%, and sells for $1,130. Interest is paid annually. (Assume a face value of $1,000 and annual coupon payments.)

a. If the bond has a yield to maturity of 9.3% 1 year from now, what will its price be at that time? (Do not round intermediate calculations. Round your answer to nearest whole number.)

b. What will be the 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. If the inflation rate during the year is 3%, what is the 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.)

Answer 1

Par/Face value	1000
Annual Coupon rate	0.087
Annual coupon	87
Present Value = Future value/ ((1+r)^t)
where r is the interest rate that is .093 and t is the time period in years.
price of the bond = sum of present values of future cash flows
r	0.093
t	1	2	3	4	5	6	7	8	9
future cash flow	87	87	87	87	87	87	87	87	1087
present value	79.59744	72.82474	66.62831	60.95911	55.77229	51.02679	46.68508	42.71279	488.2566
sum of present values	964.46
a) The price of this bond is $964 a year from now.
b) The rate of return on the bond 1 yr from now
[Ending price - Beginning price + annual coupon payment)/Beginning price]
[964.46 - 1130 + 87]/1130
(-96.54)/1130
-0.085433628
-8.54%
The rate of return on the bond is -8.54%.
c)
1 + nominal interest rate = (1+ real interest rate)*(1+ inflation)
Nominal interest rate	-8.54%
Inflation	3%
(1-.0854) = (1 + real interest rate)*(1.03)
(1+real interest rate)	.9146/1.03
(1+real interest rate)	0.887961
real interest rate	.887961 - 1
real interest rate	-0.11204
The real interest rate is -11.20%.