Question

Consider a bond being sold in the primary market with the following characteristics: currently priced at $1,000 which has 3 years to maturity, a 6% annual coupon rate, and a face value of $1,000 at maturity. Suppose that one year after you buy the bond, the interest rate increases 3% from the interest rate last year. If you decide to sell the bond then, what is your rate of return? Please show work with formulas, not Excel.

Answer 1

Given about a bond,

Face value = $1000

coupon rate = 6%

So, annual coupon = 6% of 1000 = $60

years to maturity = 3 years

Price = $1000

Since price of the bond equals face value, bond is selling at Par. So Yield to maturity of the bond = coupon rate.

So, YTM of the bond = 6%

One year later, bond yield increase by 3%, so new YTM of the bond 1 year later is 9%.

Now, Years to maturity = 2 years

New price of the bond 1 year from now is C/(1+ytm) + C/(1+ytm)^2 + FV/(1+ytm)^2

=> price of the bond = 60/1.09 + 60/1.09^2 + 1000/1.06^2 = $947.23

total return on the bond = (final price - inital price + coupon)/initial price = (947.23 - 1000 + 60)/1000 = 0.72%