Finance 100: Corporate Finance

Transcription

1 Finance 100: Corporate Finance Professor Michael R. Roberts Quiz 2 October 31, 2007 Name: Section: Question Maximum Student Score Total 100 Instructions: Please read each question carefully Formula sheets are attached to the back of the quiz To receive credit you must: (1) show all work, (2) clearly circle or box your final answers, and (3) express all numeric answer with at least 2 decimal places of precisions. Good luck 1

2 1. (30 Points) GM is expected to pay dividends per share equal to $1.40 and $1.50 at the end of this year and the end of the following year, respectively. You expect GM s stock price to be $25.00 at the end of two years (and just after the second dividend is paid out) and assume that GM s equity cost of capital is 10%. (a) (5 Points) How much would you be willing to pay, per share, today for GM s stock if you plan on holding the stock for two years? D 1 P 0 = + D 2 + P r e (1 + r e ) 2 = ( ) 2 = (b) (5 Points) Now suppose that you plan on holding GM s stock for just one year. At what price do you anticipate being able to sell GM s stock in one year from today? P 1 = D 2 + P r e = =

3 (c) (5 Points) If you only hold GM s stock for one year starting from today, what is the dollar value of your capital gains and the rate of capital gain (i.e., relative price appreciation). Capital Gain Dollars = P 1 P 0 = = 0.92 Capital Gain Rate = P 1 P = = 3.97% P (d) (5 Points) If you only hold GM s stock for one year starting from today, what is your prospective dividend yield from holding GM s stock as of today? Dividend Yield = D 1 P 0 = = 6.04% 3

4 (e) (5 Points) Now suppose that you plan on purchasing GM s stock one year from today, just after the $1.40 dividend is paid. You then plan on selling your stock at the end of year two, right after the $1.50 dividend is paid. What is the capital gains rate that you will receive on your investment? P 1 = D 2 + P r e = = Capital Gain Rate = P 2 P 1 P 1 = = 3.78% (f) (5 Points) Now suppose that you plan on purchasing GM s stock one year from today, just after the $1.40 dividend is paid. You then plan on selling your stock at the end of year two, right after the $1.50 dividend is paid. What is the total return on your investment? Total return is just the sum of dividend yield and capital gains: Capital Gain Rate = P 2 P 1 P 1 = = 3.78% Dividend Yield = D 2 P 1 = = 6.22% So the total return is: = 10.00% 4

5 2. (40 Points) The table below contains information for three securities (denoted A, B and C), the market portfolio, and a risk-free security. You may assume the following: The assumptions of the CAPM are true. Stocks A and B are uncorrelated and an equal-weighted portfolio of these two stocks has a standard deviation equal to The Sharpe ratio of the market is The variance of a portfolio consisting of 30% invested in security B and 70% invested in the risk-free security has a standard deviation equal to Cells in the table containing X i correspond to missing information for which you must solve in the following problems, which are organized in increasing level of difficulty (approximately). For example, X 3 is the unknown quantity corresponding to the expected return on the risk-free security, X 8 is the unknown quantity corresponding to the beta on security A, etc. A B C Market Risk-Free Expected Return (E(R)) X 1 X X 3 Standard Deviation (σ) X 4 X X 6 X 7 Beta (β) X X 9 X 10 X 11 Correlation with Market (ρ im ) 0.30 X 12 0 X 13 X 14 (a) (8 Points) What are the four unknown quantities in the Risk-Free column of the table (i.e., X 3, X 7, X 11, X 14 )? X 3 = 0.05 X 7 = 0 X 11 = 0 X 14 = 0 5

6 (b) (6 Points) What are the three unknown quantities in the Market column of the table (i.e., X 6, X 10, X 13 )? X 10 = 1 X 13 = 1 To get X 6 we need to use the information about the Sharpe ratio of the market, which implies: 0.35 = σ M = σ M = 0.20 So, X 6 = 0.20 (c) (2 Points) What is the unknown quantity in the C column of the table (i.e., X 9 )? X 9 = 0. 6

7 (d) (12 Points) What are the unknown quantities in the B column of the table (i.e., X 2, X 5, X 12 )? The expected return follows from the SML and beta: X 2 = ( ) = The standard deviation follows from the fourth assumption above: X 5 = = 0.30 Now we can get the correlation with the market: X 12 = βσ2 M σ B σ M = 1.2(0.2)2 0.30(0.20) = 0.8 (e) (12 Points) What are the unknown quantities in the A column of the table (i.e., X 1, X 4, X 8 )? We can find the variance (and SD) from the second assumption above: (0.25) 2 = (X 2 4) (0.3) 2 = X 4 = 0.4 With the SD and correlation, we can find the beta: X 8 = 0.30(0.4)(0.2) (0.2) 2 = 0.6 With beta we can find the expected return: X 1 = ( ) =

8 3. (30 Points) Consider the following information about Kodak and Nikon stocks: Stocks Kodak Nikon Beta Standard Deviation Suppose the expected rate of return on the market portfolio is 12%, the standard deviation of the return on the market portfolio is 24%, and the riskless interest rate is 6%. (a) (6 Points) Find the expected returns to Kodak and Nikon. Using the SML we get: R K = ( ) = R N = ( ) = (b) (3 Points) Construct a portfolio of Kodak and Nikon that offers an expected return of 14.58% = x(0.0954) + (1 x)(0.129) = x = 0.5 Short 50% of wealth in Kodak and long 150% in Nikon. 8

9 (c) (3 Points) What is the standard deviation of this portfolio, if the correlation between Kodak and Nikon is 0.6? σ 2 = ( 0.5) 2 (0.2) 2 + (1.5) 2 (0.4) 2 + 2( 0.5)(1.5)(0.6)(0.2)(0.4) = = So the SD = (d) (6 Points) Find the efficient portfolio offering the same return as the above portfolio of Kodak and Nikon? = x(0.12) + (1 x)(0.06) = x = 1.43 Invest 143% in the market and -43% in the risk-free security. (e) (4 Points) What is the standard deviation of the efficient portfolio found in part (d)? σ p = 1.43(0.24) =

10 (f) (8 Points) Suppose that you can borrow or lend at the riskless rate, but can only invest in the stock of either Kodak or Nikon. Which of these two stocks would you prefer and why? Pick the stock with the highest Sharpe ratio: Sharpe K = Sharpe N = 0.40 = = Pick Nikon, which has a (slightly) higher Sharpe ratio. 10