Solve Question 3 and 4 with details.

3. (Question 23.27 from the textbook) Rob wishes to buy a European put option on BioLabs Inc., a non-dividend paying common stock, with a strike price of $40 and six months until expiration. BioLabs' common stock is currently selling for $30 per share, and Rob expects that the stock price will either rise to $60 or fall to $15 in six months. Rob can borrow and lend at the risk-free EAR (effective annual interest rate) of 5 percent. a. What should the put option sell for today? b. If no options currently trade on the stock, is there a way to create a synthetic put option with identical payoffs to the put option just described? If there is, how would you do it? c. How much does the synthetic put cost? Is this greater than, less than, or equal to what the actual put option costs? Does this make sense? 4. (Question 23.31 from the textbook) Brozik Corp. has a zero-coupon bond that matures in five years with a face value of $60,000. The current value of the company's assets is $57,000, and the standard deviation of its ROA is 50 percent per year. The risk-free rate is 6 percent per year, compounded continuously. a. What is the value of a risk-free bond with the same face value and maturity as the current bond? b. What is the value of a put option on the firm's assets with a strike price equal to the face value of the debt? c. Using your answers from parts (a) and (b), what is the value of the firm's debt? What is the continuously compounded yield on the company's debt? d. Assume the company can restructure its assets so that the standard deviation of its ROA increases to 60 percent per year. What happens to the value of the debt? What is the new continuously compounded yield on the debt? Reconcile your answers in parts (c) and (d). e. What happens to bondholders if the company restructures its assets? What happens to shareholders? How does this create an agency