Question 5. Default Risk Premia The present value of Scone Ltd's existing assets is $95 million with a standard deviation of 40 percent, while the firm's debt (with a weighted average duration of 10 years), when rendered into zero coupon bond form is worth $70 million. The 10-year treasury bond rate is 5 percent. When this information is inputted into the Black-Scholes Model, the value of the call option is calculated to be $63,991,219. The firm is considering taking on a new project that has a $6 million NPV with a degree of risk that will increase the overall variance of the firm's asset value by 9 percent. With the inclusion of this information, the value of the Black-Scholes call option changes to $74,714,217. Required: Given the call option outputs provided above, please calculate the wealth transfer that occurs as a result of the new project being taken on by Scone Ltd, stating clearly the overall change in value of the firm, the gain or loss to the shareholders and the gain or loss to the bondholders. (6 marks) (b) Please estimate the default risk premium associated with Scone Ltd's YTM before the risky new project is taken on. (4 marks) (C) Please estimate the new default risk premium after the new debt is taken on and, using a percentage calculation, estimate the change in size of the default risk premium. (5 marks) Question 5. Default Risk Premia The present value of Scone Ltd's existing assets is $95 million with a standard deviation of 40 percent, while the firm's debt (with a weighted average duration of 10 years), when rendered into zero coupon bond form is worth $70 million. The 10-year treasury bond rate is 5 percent. When this information is inputted into the Black-Scholes Model, the value of the call option is calculated to be $63,991,219. The firm is considering taking on a new project that has a $6 million NPV with a degree of risk that will increase the overall variance of the firm's asset value by 9 percent. With the inclusion of this information, the value of the Black-Scholes call option changes to $74,714,217. Required: Given the call option outputs provided above, please calculate the wealth transfer that occurs as a result of the new project being taken on by Scone Ltd, stating clearly the overall change in value of the firm, the gain or loss to the shareholders and the gain or loss to the bondholders. (6 marks) (b) Please estimate the default risk premium associated with Scone Ltd's YTM before the risky new project is taken on. (4 marks) (C) Please estimate the new default risk premium after the new debt is taken on and, using a percentage calculation, estimate the change in size of the default risk premium
