Question

A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 8.9%, and sells for $1,110. 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 9.1% 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.

Face Value = $1,000

Annual Coupon Rate = 8.90%
Annual Coupon = 8.90% * $1,000
Annual Coupon = $89

Time to Maturity = 9 years
Annual YTM = 9.10%

Price in 1 Year = $89 * PVIFA(9.10%, 9) + $1,000 * PVIF(9.10%, 9)
Price in 1 Year = $89 * (1 - (1/1.091)^9) / 0.091 + $1,000 / 1.091^9
Price in 1 Year = $988.06

Answer b.

Rate of Return = [Price in 1 Year + Coupon Received - Current Price] / Current Price
Rate of Return = [$988.06 + $89.00 - $1,110] / $1,110
Rate of Return = -$32.94 / $1,110
Rate of Return = -0.0297 or -2.97%

Answer c.

Real Rate of Return = [Nominal Rate of Return - Inflation Rate] / [1 + Inflation Rate]
Real Rate of Return = [-0.0297 - 0.03] / [1 + 0.03]
Real Rate of Return = -0.0597 / 1.03
Real Rate of Return = -0.0580 or -5.80%