Question

Consider a 1 year reverse convertible bond issued by sumsung. The coupon rate is 20% (only pay once a year) and face value is 100,000 USD . At the maturity date, the firm has the option to convert it to 1000 shares of sumsung stock.

1. Suppose at the maturity date, the sumsung stock price is 167 USD. What is debtholder’s payoff?

2. Explain why the reverse convertible bond promises high coupon rate

3. Should the coupon rate be higher/lower when the underlying firm stock is more volatile?

4. Suppose at the maturity date, the sumsung stock price is 79 USD. What is debtholder’s payoff?

Answer 1

A reverse convertible bond is a bond which is issued by issuer with a right with the issuer to convert the bonds into cash, debt or equity at the option of issuer.

1) If value of share is 167, then equivalent value of bond = 1000 * 167 = 167,000

Firm has an option to either pay 100000 cash or issue 1000 equity shares. As we observe paying cash is more beneficial for the firm payoff to the debtholder will be 100000

2) As we observe if the share price rises, then benefit does not accrue to the debtholder but if the share price falls, debtholder has to suffer by getting lower value at the time of redemption. As there is higher risk faced by the debtholder, it demands higher return. Hence reverse convertible bond promises high coupon rate.

3) If the stocks are more volatile, there is higher chances for the share price to go very low. Hence it results in higher risk and indeed will coupon rate should be higher.

4) If share price is 79, then equivalent value of debenture = 1000 *79 = 79000

Hence now the issuer shall choose to issue equity rather than pay cash of 100000

Debenture payoff is 79000