For a levered firm, firm's assets are financed by equity and debt. That is, A_t=E_t+D_t, where A_t, D_t & E_t represents asset value, debt value and equity value at time t. Suppose the firm makes no dividend payment and has a zero-coupon debt maturing at time T. At maturity, if the value of the company asset is greater than the maturity value of the debt (A_t > D_t ), the company will simply pay off the debt. Otherwise, the company will declare bankruptcy and debt holders will own the firm.

(i) At maturity t=T. From an equity holder perspective, describe a company's equity as a call option. Identify the underlying asset, strike price, maturity, and the payoff function of the call option.

(ii) At maturity t=T. From a debt holder perspective, describe a company's debt using a call option. Identify the positions that the debt holder takes on each asset (e.g. long or short?)

(iii) At time t =0. Suppose c and p are option prices (i.e. premium) for call and put options. Using the result from part (i) and put-call parity, describe a company's debt using a put option from a debt holder perspective. Identify the position that the debt holder takes on each asset (i.e. long or short ?)

(iv) Energy Dynamic is a company with 10 million shares outstanding. The current asset value is $90 million and is has a zero-coupon corporate debt of $100 million face vale due in 5 years. Suppose company's asset volatility is 25% and the risk-free interest rate is 6% per annum with continuous compounding. The company makes no dividend payment. Apply the Black-Scholes model to estimate company's equity value. What os the share price?

(v) Base on part (iv), what is the yield to maturity on the debt?