Question

Three years ago, PurpX issued 10,000 bonds with the following specifications:

10-year bond with 10% coupon rate and $1000 face value.

PurpX made its third coupon payment today with 7 more coupon payments as well as the face value left to be paid.

The current market rate is 6%.

One board member suggests to take advantage of the low rates and purchase back all the bonds to reissue them at 6% coupon rate.

1. How much does PurpX need today to purchase back all of its bonds?

2. How many new 7-year, 6%-coupon, $1,000-face-value bond does PurpX

   need to issue to finance this purchase?

3. Would you be supporting the board member who makes this suggestion?

   Why or why not?

Answer 1

In the absence of call option, purchase of bonds will be at the current market value which is the PV of future cash flows, discounted at the new interest rate. The purchase price of 10,000 bonds is $12,233,000.

Since the interest rate (YTM) and coupon rate are equal at 6%, the new bonds will be issued at par, at $1,000 per bond. Number of new bonds to be issued is 12,233.

Details of calculation as follows:

Present value of all bonds together, discounted at the new interest rate of 6% is $12,233,000 as stated above. Present value of the bonds to be issued, on buy back of existing bonds, is also $12,233,000 since the new bonds are issued at par, to be redeemed at par and since YTM is equal to coupon rate. Therefore, there is no benefit of purchasing back the existing bonds, to be financed by new bonds as stated.