Question

PKC Ltd is considering raising $120 million from the markets. In its recent management meeting, Winnie Poon, the CFO, suggested PKC to issue perpetual bonds with a face value of $1,000 each and a coupon rate of 8.1% paid annually. The current market interest rate is 8%. Winnie estimates a 0.3 probability that next year’s interest rate will increase to 10%, and a 0.7 probability that it will fall to 6%.

(a) Calculate the current market value of the perpetual bond If PKC issues perpetual bond based on Winnie’s suggestion . (Show your calculations).

(b) The CEO, John Lung, decides to include a call provision in the bond contract such that the bonds are callable in one year. Calculate the coupon rate of the callable bonds such that the bonds will be sold at par. Assume the bonds will be called if the interest rates fall and the call premium is $150. (Show your calculations).

Answer 1

(a) The annual coupon on a perpetual bond having a face value of $1000 and a coupon rate of 8.1% is $81. Since the current market interest rate is 8%, we shall divide the annual coupon by the market interest rate to arrive at the current market value of the bond.

Market value = $81 / 8%

=  $1012.5

(b) The scenario in which a bond with a call provision is issued has two possible future outcomes;

• The interest rate increases

In case the interest rate increases, the call option will not be exercised. In this case, the coupon rate such that the bonds will be sold at par will be equal to the current market rate which is 8%

• The interest rate decreases

​​​​​​​In case the interest rate decreases, the call option will be exercised and the bond-holders will receive the face value of the bonds ($1000) along with a call premium ($150).

The bond-holder will also receive the coupon for the first year if the bond is called. However, since the bond is callable in one year and the call premium yield is higher than the current market interest rate, the hypothetical bond yield on such a bond would have to be negative if the bonds are to be sold at par.

In such a case, let us assume that the bond is sold for nil coupon.

• The coupon rate of the callable bond

Since there is a 0.3 probability of the interest rate increasing and a 0.7 probability of the interest rate decreasing, the weighted average coupon rate of the callable bond would be 8% * 0.3 + 0% * 0.7

= 2.4%