Question

A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 8.5%, and sells for $1,150. 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 9.5% 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

Answer:

a. Coupon payment = 8.5% of $1000 = $85

i = 9.5%

n = 9

m =$1,000

Price of the bond after one year P1 = C* [1- 1/ (1+i)^n] /i + M / (1+i)^n

P1 = $85 * [1 – 1 / (1+9.5%) ^9] /9.5% + 1000 / (1+9.5%) ^9

P1 = $499.40 + $441.85

P1 = $941.25

b. The rate of return on the bond = (Income from one coupon payment + capital appreciation)/ Initial price of the bond

The rate of return on the bond = [$85 + ($941.25 - $1,150)]/ $1,150

The rate of return on the bond = ($85 - $208.75)/ $1,150

The rate of return on the bond = - $123.75/ $1,150

The rate of return on the bond = - 0.1076

The rate of return on the bond = -10.76%

c. f the inflation rate during the year is 3%

Real rate of return =  [(1+ Nominal rate of return)/ (1+ Inflation rate)]-1

Where Nominal rate of return = - 10.76%, Inflation rate = 3%

Real rate of return =   [(1-10.76%)/ (1+ 3%)]-1

Real rate of return = 0.08664 -1

Real rate of return = - 0.1336

Real rate of return = -13.36%