Respuesta :
Answer:
a. Price 1 year later = $810
b. Annual rate of return on the bond = -24.53%
c. Since -24.79% is lower than -24.53% obtained part b, this implies that annual rate of return is slightly less than our part b answer.
d. Annual real rate of return on the bond = -26.73%
Explanation:
a. If the bond has a yield to maturity of 10.7% 1 year from now, what will its price be at that time? (Do not round intermediate calculations. Round your answer to nearest whole number.)
This can be calculated as follows:
Price 1 year later = Coupon rate * Par value / Yield to maturity * (1 - 1 / (100% + Yield to maturity)^Years to maturity) + Par value / (100% + Yield to maturity)^Years to maturity = 7.3% * 1000 / 10.7% * (1 - 1 / (100% + 10.7%)^9) + 1000 / (100% + 10.7%)^9 = $810
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.)
This can be calculated as follows:
Annual rate of return on the bond = (Price 1 year later + Coupon rate * Par value) / Price now - 1 = (810 + 7.3% * 1000) / 1170 - 1 = -24.53%
c. Now assume that interest is paid semiannually. What will be the annual rate of return on the bond?Slightly greater than your part b answer Slightly less than your part b answer
This can be determined as follows:
Price 1 year later = (Coupon rate / 2) * Par value / (Yield to maturity / 2) * (1 - 1 / (100% + (Yield to maturity / 2))^(Years to maturity * 2)) + Par value / (100% + (Yield to maturity / 2))^(Years to maturity * 2) = (7.3% / 2) * 1000 / (10.7% / 2) * (1 - 1 / (100% + (10.7% / 2))^(9 * 2)) + 1000 / (100% + (10.7% / 2))^(9 * 2) = $807
Annual rate of return on the bond = (Price 1 year later + Coupon rate * Par value) / Price now - 1 = (807 + (7.3% / 2) * 1000) / 1170 - 1 = -24.79%
Since -24.79% is lower than -24.53% obtained part b, this implies that annual rate of return is slightly less than our part b answer.
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.)
This can be calculated as follows:
Annual real rate of return on the bond = (1 + nominal return) / (1 + inflation)-1 = (1 - 24.53%) / (1 +3 %) - 1 = -26.73%
