Question

A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 8.8%, and sells for $1,120. 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 9.2% 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

a)
FV = 1000
Nper = 10 - 1 = 9
PMT = 1000 * 8.8% = 88
Rate = 9.2%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(9.2%,9,-88,-1000)
= $976.21

Price of the bond = $976.21

b)
Rate of return = (Price 1 year from now - Purchase Price + coupon) / Purchase Price
= ($976.21 - $1,120 + $88) / $1,120
= -4.98%

Rate of return = -4.98%

c)
Real rate of return = (1 + nominal rate of return) / (1 + inflation rate) - 1
= (1 - 0.0498) / (1 + 0.03) - 1
= -7.75%

Real rate of return = -7.75%