Finish this question. (Corporate Finance)

I. Short answer: 1. What are the perfectmarket assumptions? 2. Explain whether the following statements are true or false. In each case, provide justification for your answer: In a perfect capital market, expected returns on all bonds must be equal to the risk-free (T-bill) rate. In a perfect capital market with risk-neutral investors, expected returns on all bondsmust equal the risk-free rate. 3. Write down the CAPM formula. What are the economy-wide inputs and what are the firm-specific inputs? II. The table below describes the return rates for a stock X and a market index fund, call itM. Find the (true, as opposed to estimated) beta of stock X. Assume the probability of the good state is 1/3 (bad has probability 2/3). Good Bad M 10% 6% Asset X 4% 10% III. Suppose Intels stock has an expected return of 10%and a volatility (standard deviation) of 5%, while Coca-Colas has an expected return of 5% and volatility of 2%. Assume these two stocks have correlation coefficient 1. 1. Calculate the portfolio weights that remove all risk. 2. If there are no arbitrage opportunities, what is the risk-free rate of interest in this economy? IV. A biotech company has a drug in development that will allow you to sell your firm for $10 billion next year. Assume your boss wants you to use the CAPM. Your firm has a beta of 4, the risk-free rate is 5% per year, and the equity premiumis 2% per year. What do you think the firmis worth today? V. Your borrowing rate is 15% per year. Your lending rate is 5% per year. The project costs $1,000 and has a rate of return of 10%. 1. Assume you have $500 of your own money to invest. Should you invest in this project? 1 2. Find themaximal amount the investor would bewilling to borrow in order to invest in the project?1 VI. Option pricing: 1. Consider a European call option on a single share of stock in company X. The strike price is $25 and the maturity date is 1 year. Call this a 25- call for simplicity (and, generally, a K-call, where K is the strike price). Draw the payoff diagram in the two cases where (i) an investor goes long on a single 25-call, and (ii) an investor shorts both a 25-call and a 20-call. 2. Consider (European) call and put options on a single share of stock in company X. Each has a strike price of $25 and matures in 1 year. Assume the (per share) stock price at the time the options are written is $22 and that the cost of the put is $2. Also assume that the risk-free rate is 10%. Find the price of the call.

Exam 2 - Economics 134 Professor Madhav Chandrasekher Directions: This exam consists of 8 questions, with point allocations as noted. Please write your answers in the provided space and also show work for your answers. You have 80 minutes. Good luck. 1. (5 pts) List the conditions under which a market is considered \"perfect\". 2. Explain whether the following statements are either true or false. Provide brief reasoning for your answer: i. (3 pts) In a perfect capital market, the expected return rate on all bonds must be equal to the risk-free (T-bill) rate. ii. (2 pts) In a perfect capital market with risk-neutral investors, expected return rate on all bonds must equal the risk-free rate. 3. (5 pts) Write down the CAPM formula. What are the economy-wide inputs and what are the firm-specific inputs? 4. (5 pts) A Fortune 100 firm is initially financed by 20 billion dollars debt and 20 billion dollars equity, i.e. a debt/equity ratio of 1. It has a historical equity beta of 4. Assume the firm never defaults on its debt. Say the firm repurchases some shares by issuing more debt, with the result being that the new debt/equity ratio is 2/1. Find the beta of (levered) equity under this new capital structure. 5. (5 pts) A corporate zero-bond promises to pay $100 in one year. The bond has a default probability of .3 and its market beta is 0.3. The equity premium is 4%; the equivalent Treasury rate is 3%. Assume that the bonds pays out nothing in the default state. Find the appropriate bond price today.1 6. The table below describes the return rates for a stock X and an equivalent to the S&P 100 index fund, call it M. Assume both \"good\" and \"bad\" states are equally likely. M Stock X Good Bad 8% 4% 4% 8% i. (3 pts) Find the beta of stock X. 1 Maintain the assumption that capital markets are perfect. 1 2 ii. (2 pts) For a random variable X, we let X , X denote (resp.) its mean and variance. Assume an investor's preferences over random variables (bets) is a function only of their mean and variance and takes the following functional form, 1 2 2 . u(X , X ) = X X 4 Assume that the investor has a dollar to invest and that the price of one share of X or of the index fund M is equal to $1. Find the utility-maximizing (affordable) portfolio choice of the investor.2 7. Your borrowing rate is 20% per year. Your lending rate is 10% per year. The project costs $2,000 and has a rate of return of 15%. i. (3 pts) Assume you have $500 of your own money to invest. Should you invest in this project? ii. (2 pts) Find the maximal amount the investor would be willing to borrow in order to invest in the project?3 8. (5 pts) You are in the 10% tax bracket.4 A project will return $30,000 next year for a $20,000 investment today. The equivalent tax-exempt bond yields 15%, and the equivalent taxable bond yields 20%. What is the NPV of this project? 2 The set of budget-feasbile portfolios in this problem is the set of shares, {, 1 } in (resp.) stocks X and M , where 0 1. 3 An equivalent way to phrase this turns out to be: Find the threshold wealth level such that the investor would select the project whenever his(her) wealth is at or above this level. 4 As in the examples from lecture 10, this is a capital gains tax. 2