receives 100 per period coupon can be converted into 05 shares at any time The

# Receives 100 per period coupon can be converted into

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- receives \$100 per period coupon. - can be converted into 0.5 shares at any time. The company pays no dividends, the t=0 coupon has just been paid, the risk free rate is 8% and it is constant. a) What would be the value of their debt without the conversion feature (straight debt)? b) What is the value of the convertible debt? Q2: It is often argued that convertible bonds are a cheap source of financing for the following reason: 1) They carry coupon rates below the market rates of interest on straight debt (or preferred) and 2)They allow companies to sell equity at a premium by setting the exercise price above the current shareprice.Are these arguments correct?
Q1. Step 1: Two period asset value tree after the periodic coupon has been paid (ex-coupon): t=0 t=1 t=2 ______________________________________________________________ A 2 =(590x1.5) - 10 = 875 A 1 = (400x1.5) - 10 = 590 A 2 =(590x0.5) - 10 = 285 A 0 = 400 A 2 =(190x1.5) - 10 = 275 A 1 = (400x0.5) - 10 = 190 A 2 =(190x0.5) - 10 = 85 Step 2: u = 1.5, d = 0.5 ð p r d u d = + - - = - - = 1 108 05 15 05 058 . . . . . Note also: n n n D D s + = + = 50 50 150 0 25 .
Value of straight bond after the periodic coupon has been paid (ex coupon): t=0 t=1 t=2 _______________________________________________________ A 2 = 875 B 2 = 100 A 1 = 590 B 1 = 110 108 10185 . . = A 2 = 285 B 2 = 100 A 0 = 400 B 0 = 058 10185 0 42 96 02 10 108 1013 . . . . . . * + * + = A 2 = 275 B 2 = 100 A 1 = 190 B 1 = 058 100 0 42 85 10 108 96 02 . . . . * + * + = A 2 = 85 B 2 = 85 The value of straight debt after the current period’s coupon has been paid is D Straight = 101.3.
3. Value of the convertible bond: t=0 t=1 t=2 _____________________________________________________________ A 2 = 875 if convert: 0.25 x 875 = 218.75 if don’t convert: 100 A 1 = 590 if convert: 0.25 x 590 = 147.5 market value: 058 218 75 0 42 100 10 108 16563 . . . . . * + * + = A 2 = 285 if convert: 0.25 x 285 = 71.25 if don’t convert: 100 A 0 = 400 if convert: 0.25 x 400 = 100 market value: 058 16563 0 42 96 02 10 108 13556 . . . . . . * + * + = A 2 = 275 if convert: if don’t convert: 100 A 1 = 190 if convert: 0.25 x 190 = 47.5 market value: 058 100 0 42 85 10 108 96 02 . . . . * + * + = A 2 = 85 if convert: if don’t convert: 85 So the value of the convertible bond is: D Convertible = 135.56
Q2: The argument is clearly flawed. The investors receive a valuable option (right to convert to equity) as a compensation for the lower coupon rate. Neither are the shareholders selling equity at a premium. In fact, compared to the share price that prevails at the time of conversion, if anything, they are issuing equity at a discount. J

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