(33 points) i) a) A trader holds two calls and one put on the same share, all of which expiring in three months. The exercise price of both calls is $70 and the exercise of the put is $80. Each option is sold as a 100-share contract. Find the payoff at the expiration date if the stock sells for $65 and if it sells for 90$

. Draw the payoff diagram (profile) for your option position

. b) Which of the following features affect the value of a call option, other things equal, and how?

 Explain and justify your answer 

i. A high expected return on the underlying stock 

ii. A high interest rate

 iii. A highly variable stock price

 iv. A long time to maturity 

v. A high exercise price 

vi. None of the above affects the value of a call ii) The current price of the nine-month futures on the Hungary Stock Market index (BUX) is 7,330, while the index spot price is 7,111. The interest rate is 8 percent and the dividend yield is 4 percent. Is there an arbitrage opportunity?

 If no, explain. If yes, explain and state the respective investment position

. How robust is your answer to different methodologies?

 iii) A firm whose fixed and perpetual annual EBITDA cash flows are 2300£ is taxed at a rate of 35% while the risk-free rate is 3.5%. Each year, capital expenditures are equal to depreciation expenditures and working capital is constant.

 a) In the case of an all-equity firm that pays its net income as dividend annually, what is the value of equity?

 b) In the case of a firm that holds debt and pays 500£ in interest per year, what are the values of equity and debt? Does total firm value differ between (i) and (ii)? 

c) Based on your previous findings, what is the difference in firm value expressed as a fraction of debt? Interpret the finding.