Question

A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 7.6%, and sells for $1,140. 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 10.4% 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. The bond is currently trading at a price of $1140 which translates to a YTM of 5.72%

After 1 year, the bond will have 9 years left until maturity.

Its price at a YTM of 10.4% would be calculated as follows:

C/(1+r)^1 + C/(1+r)^2 +C/(1+r)^3 +C/(1+r)^4 +C/(1+r)^5 +C/(1+r)^6 +C/(1+r)^7 +C/(1+r)^8 +C+F/(1+r)^9

where C is the coupon = $76; F = $1000, r=10.4%

Substituting above values gives Price = $841.28

b. Rate of return on the bond can be decomposed into carry roll down component and capital gain/loss component

Carry Roll down component: If the YTM of the bond would have been the same after 1y, the bond would have returned 5.72%. In this case the price of the bond after 1y would have been: $1129.22 (as can be seen, the price of the bond moves towards its face value)

5.72% = 76/1140 + (1129.22-1140)/1140

The capital gain/loss = (841.28 - 1129.22)/1140 = -25.25%

Therefore total return = 5.72 - 25.25 = -19.53%

Alternatively, return = [76 + (841.28-1140)]/1140 = -19.53%

c. The return calculated above is the nominal return.

Real Return = Nominal Return - Inflation

= -19.78 - 3 = -22.53%