 Econ 134A Fall 2015 Test 3 Based on Form A

Q1  If Joe believes that all information(including private information) relevant to a stock is incorporated in to a stock’s price, then he believes in what form(s) of efficiency?  A. Weak form efficiency only  B. Semi-strong efficiency only  C. Strong form efficiency only  D. Both weak and strong form efficiency only  E. Weak and semi-strong, and strong form efficiency  E

Q2  A stock has a value right now of $80. Each day starting tomorrow, the stock’s price changes in the same fashion as a random walk as follows: there is a 50% chance that the price goes up by $2, and a 50% change that the price goes down by $2. Each day’s movement in price is independent of the previous day’s movement. You own a call option with an exercise price of $83.50, and the call option can only be exercised three days from now. What is the probability that the call option will have positive value three days from now?

Q3  Assume an effective annual discount rate of 10%. If someone invests $500 in a project today, and then receives $700 3 years later from the investment, what is the profitability index of this investment?

Q4  A zero-coupon bond has a face value of $600, to be paid 8 months from today. If the yield to maturity is 5% (as an effective annual interest rate), what is the current price of the bond?

Q5 An asset promises to pay $20 per year forever, starting six months from today. The stated annual discount rate for this asset is $14, compounded twice per year. What is the present value of this stream of payments?

Q6  Suppose that the daily price of each share of Paradise Profit Walk Shoe stock is a random walk with each day’s movement in price independent of the previous’ price change. Every day, the stock can either go up or down by $5, each with 50% probability. The stock is currently valued at $50. What is the probability that the value of the stock three days from now will be exactly $60? Pr($60)=0 No path sets to exactly $60.

Q7  Which supermarket chain talked about in lecture is selling its Santa Barbara area stores? Haggen

Q8  Joanna owns an investment in which she receives $1,000 today, she must pay $2,200 one year from today, and she receives $1,202 two years from today. She finds that there are two internal rates of return, L and U. Both L and U are positive and L < U. For which positive discount rates will the net present value of this investment be positive? Plug in values to solve $; Less than L and More than U

Q9  An asset’s returns were analyzed over a four- year time period. During these four years, the rates of return were 5%, 12%, and 5%. What is the standard deviation of this sample?

Q10  Hal borrows $10,000 today and will make 10 monthly payments to completely pay back the loan, starting one month from today. He will reduce the principal by the same amount each month. How much will the payment be 5 months from today if Hal’s stated annual interest rate is 24%, compounded monthly?

Q11  Stock Z has a 40% probability of a 2% return in a given year, a 50% probability of a 15% return in a given year, and a 10% probability of a 20% return in a given year. The beta value for stock Z is 2. The return of a risk-free asset is 8%. What is the return of an asset with a beta value equal to 1?

Q12  Carlos is about to uy a $1,000,000 house in a small Iowa town. He will pay off the loan over 40 years, and he will make yearly payments to pay off the mortgage starting one year from today. Carlos will pay back the loan with a partial amortization repayment schedule over the first 20 years, followed by a new financing schedule to completely pay off the balloon payment 20 years from today over the following 20 years.  The loan for the first 20 years has 40-year amortization with a 5% interest rate. This will result in a balloon payment 20 years from today, which will be financed with a new loan over the following 20 years/ The first payment for the second loan will occur 21 years from today. The interest rate over the last 20 years will be 7.5%. (Note that the last payment 40 years from today will completely pay off the loan.)

Q12

Q13  Stock Q’s value today is $50. Over the course of the next year, the value of the stock could go up by $2, $4, $6, $8, $10, each with 20% probability. Hillary holds a European call option for Stock Q with an exercise price of $55.50, and an expiration date of one year from today. What is the present value of the option if the appropriate discount rate for the option is 20%?

Q14  Laura has run a regression of the security market line, just as you did in your econometric assignment, with beta and expected returns entered as decimals. (For example, an expected return of 5% is entered as 0.05 for the regression.) Based on her sample size, she finds in her regression results that her point estimate for the slope is 0.1 with a standard error of Her point estimate for the y-intercept is 0.06 with a standard error of Explain all answers below with words, an equation, and/or a graph.  a) What is the estimated rate of return for a risk-free asset?  b) What is the estimated rate of return for an asset with beta equal to 1? (Note: I am referring to the meaning of beta referred to in this class, not the beta meaning that is commonly referred to in econometric class.)

Q15  There are three known states of the world, L, M, and N. Each state occurs with one-third probability.  When state L occurs, Stock A has a rate of return of 6% and Stock B has a rate of return of 19%.  When state M occurs, Stock A has a rate of return of 14% and Stock B has a rate of return of 2%.  When state N occurs, Stock A has a rate of return of 10% and Stock B has a rate of return of 15%.  a) What is the average rate of return for each stock.  b) What is the standard deviation for the rate of return of each stock?  c) What is the correlation coefficient for the rate of return for these two stocks?

Q15

Q16  Lesley buys two shares of stock at a price of $100 today, and one put option with an exercise price of $90 two years from today. (In other words, the expiration date of the option is two years from now.) The put option is for selling one share. For simplicity in this problem, you can assume that the discount rate is 0%. Draw a well-labeled graph that shows the value of a combination of the two shares of stock and the put option as a function of the value of stock at expiration. The vertical intercept should have the value of the combination of the stock and the put. The horizontal intercept should have the value of the stock at the expiration.

Q16

Q17  Aubrey’s Waffles currently has $200,000 of stock issued, with no bonds. The current cost of equity is 10%. If the company sells $25,000 of bonds and uses this money to purchase $25,000 worth of stock, what is the new cost of equity? Assume that the cost of debt is 5% and that there are no other securities issued by Aubrey’s Waffles. You can also assume that the weighted average cost of capital is constant.