The firms assets are currently worth 200000 Each period asset value can either

# The firms assets are currently worth 200000 each

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* The firm's assets are currently worth \$200,000. Each period asset value can either double or halve. ð u=2 and d=1/2. * There are 700 shares outstanding. * The firm has also issued 100 bonds. Each bond - has a face value of \$1000 and matures in 2 periods. - receives no periodic coupon. - can be converted into 3 shares at any time. - is callable for \$1150 after 1 period (i.e. at t=1). * The company pays no dividends, the risk free rate is 10% and it is constant.
1. Two period asset value tree (thousands): t=0 t=1 t=2 ________________________________________________ A 2 =(400x2) = 800 A 1 = (200x2) = 400 A 0 = 200 A 2 = (400x0.5) = 200 A 1 = (200x0.5) = 100 A 2 =(100x0.5) = 50
2. Value of a straight bond: t=0 t=1 t=2 ________________________________________________ A 2 = 800 D 2 = 100 A 1 = 400 D 1 = A 0 = 200 A 2 = 200 D 0 = D 2 = 100 A 1 = 100 D 1 = A 2 = 50 D 2 = 50 ð D straight =
3. Value of convertible bond (if not callable): t=0 t=1 t=2 ________________________________________________ A 2 = 800 if convert: if don’t convert: 100 A 1 = 400 if convert: market value: A 0 = 200 A 2 = 200 if convert: if convert: market value: if don’t convert: 100 A 1 = 100 if convert: market value: A 2 = 50 if convert: if don’t convert: 50 ð D convertible =
4. Value of callable, convertible bond (callable at t=1): t=0 t=1 t=2 ________________________________________________ A 2 = 800 convert: 240 A 1 = 400 if convert: 120 market value: 142 if called: A 0 = 200 A 0 = 200 if convert: 60 don’t convert: 100 market value: A 1 = 100 if convert: 30 market value: 63.63 if called: A 2 = 50 don’t convert: 50 ð D callable and convertible =
Summary At t= 0: Value straight bond = \$ 67.8 Value convertible bond = \$ 86.3 Value callable, convertible bond = \$ 78.3 Therefore: Value of conversion feature = Value of callability = Market value of equity at t=0 =
Example 2: General case Par value of the bond: \$40.00 Maturity: 20 years Semi-annual coupon: \$1.00 Quarterly dividend: \$1.00 Convertible into 10% of the shares outstanding after conversion. Variance of asset value: .001 per month Risk free rate: .005 per month Call terms: non callable for the first 5 years callable at - 43 for following 5 years - 42 for following 5 years - 41 for last 5 years.
D=0
0.001 0.002
0%
WHY ISSUE CONVERTIBLE BONDS? Convertible bonds are an important source of financing especially for young growth firms. Two main reasons: * It is very difficult to estimate the level of risk for such companies. As we saw, the price of convertible debt can be fairly insensitive to risk. It is thus easier to price than other securities. * These companies may also have an incentive to take too many risky projects if financed with straight debt. As we saw, equity is then an option on the assets and, as for any option, its value is increasing in volatility. Because of this, the shareholders may have an incentive to take excessive risks. With convertible debt the shareholders do not have similar benefits from taking take large risks, as by making the debt convertible, the shareholders are also writing a call option, whose value is increasing in volatility.
Summer may be over, but top-down, hit-the-accelerator time has arrived for companies selling convertible bonds. The bonds get their name from the feature that separates them from conventional debt: They can be converted into the issuer’s stock at a specified price, often at the buyer’s option.They are popular among companies looking to raise money at rates lower than those on ordinary bonds.

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