a.Suppose that we have a firm whose current value is Kshs 1000 and that (given a multiplicative stochastic process) its value could go up by 12.75% or down by 11.31% and a standard deviation of 12% per annum and the risk free rate is 8%. The equity of this firm is subordinated to debt that has a face value of Kshs. 800 maturing in three years and that pays no coupon. What is the value of an American call option written on the equity if its exercise price is Kshs. 400 and its maturity is three years?

b.Using the definition of portfolio variance prove that a perfectly hedged stock portfolio that is 100 shares long and 100 shares short is perfectly risk free

c.When corporations issue liabilities we assume that they do so at fair market rates. This implies that on the day the liability is issued the cash received by the company is equal in value to the debt liability that is recorded on the balance sheet. Except for the possibility of tax shield, financing creates no value. Banks and insurance companies are different because their liabilities (for example demand deposit at a bank or insurance policy reserves at an insurance company) involve services. Consequently growth of deposits and of reserves actually creates value for shareholders. How would you construct a DCF Valuation differently for:-

i.For Banks

ii.For Insurance Company

d.Empirical evidence supports the existence of a clientele effect; this implies that every time a company revises its dividend policy to pay out a greater (or smaller) percentage of earnings the characteristics of its shareholders also change. For example a firm with a higher payout ratio may expect to have more shareholders in lower tax brackets. Suppose that lower-income people are also more risk averse. Would this have an effect on the value of the firm?