Question

Consider a 6¼%-annual coupon bond, with a 30-year time-to-maturity and a face value of $1,000 that you buy right now. At the time of the purchase the YTM is 10%. Your plan is to sell the bond immediately after you receive the 27^th coupon payment. The YTM is expected to remain constant.

1. What is the minimum selling price for the bond at the time of the sale?
   1. $906.74
   2. $653.60
   3. $1,099.78
   4. 646.49
2. What is the duration at the time of the sale? Assume the selling price (regardless of your previous answer) is $P.
   1. $906.74/ $P
   2. $P / $2,554.94
   3. $2,554.94/ $P
   4. $P / $301.00
   5. $301.00 / $P

Answer 1

Solution

A. Minimum Selling Price of the bond after receiving 27th Coupon payment

The minimum selling is present value of all cash flows that will be received after 27th Coupon payment

Therefore Present Value is calculated as follows

Coupon Amount/(1+ytm)¹ + Coupon Amount/(1+ytm)² + Coupon Amount/(1+ytm)³ + Maturity Value /(1+ytm)³

=$62.5/(1+.10)¹ + $62.5/(1+.10)² + $62.5/(1+.10)³ + $1000(1+.10)³

=$906.74 i.e Option (a) is correct

B. Duration at the time of sell

Duration of bond is calculated as follows

=1/P * (1 * Coupon Amount/(1+ytm)¹ + 2 * Coupon Amount/(1+ytm)² + 3 * Coupon Amount/(1+ytm)³ + 3 * Maturity Value /(1+ytm)³

  =1/P * (1 * $62.5/(1+.10)¹ + 2 * $62.5/(1+.10)² + 3 * $62.5/(1+.10)³ + 3 * $1000(1+.10)³

=1/P * $2554.94

=$2554.94/P i.e Option (c) is correct