Question

Suppose a ten-year bond $1,000 bond with a 5% coupon rate that pays annual coupons is initially trading at par (at $1,000). After 5 years time, the bond’s yield to maturity falls to 4%. If you sell the bond after 5 years, what price will you receive

Answer 1

Ans)- Given a ten-year $1000 bond with a 5% coupon rate.

So, annual coupon payment would be = 1000*5% = 1000*5/100 = $50

Now, if after 5 years, yield to maturity falls to 4%. Then the price received or the value of bond in 5^th year for this bond would be the present value (value in year 5) of all future payments received on this bond after year 5 at yield rate of 4%.

i.e. this bond would pay the annual coupon payment of $50 in year 6, 7, 8 and 9. And in year 10, the bond will pay face value of $1000 along with $50 coupon payment.

So, the value of all this future payment in 5^th year (i.e. by discounting this payments) would be the price of bond in 5^th year.

Hence,

Hence, the required price of bond in year 5 after fall in yield rate would be $1,045. i.e. if we sell bond in year 5, we will receive $1,045.