Question

1. Assume Uber Technologies Inc., just issued a zero-coupon convertible bond due in 10 years. The face amount of the bond is $1,000. The conversion ratio is 25 shares. The appropriate interest rate (Kd) is 12%. The current stock price is $12 per share. Each convertible is trading at $400 in the market. – 5 marks
   1. What is the Macaulay duration of the Uber Technologies Inc. bond?
   2. What is the conversion value?
   3. What is the straight bond value?
   4. What is the option value of the bond?

Answer 1

Because zero coupon bonds make no coupon payments, a zero coupon bond's duration will be equal to its maturity. The longer a bond's maturity, the longer its duration, because it takes more time to receive full payment.

DUration = 10 years

Conversion value is the amount an investor would received if a convertible security is changed into common stock. This value is arrived at by multiplying the conversion ratio (how many shares received per bond) by the market price of the common stock.

Conversion value = 12*25=300

In convertible security, the value of the security itself (usually a bond or preferred stock) without considering the fact that it may be converted to common stock.

Straight bond value =1000

Option value of the bond = 400