1. Test 2
Spring 2014, 9 am Class

2. Multiple Choice #1
Stephanie owns stock in CF134AA, Inc. The stock pays a $10 dividend every year forever, beginning six months from now. Each dividend is 8% higher than the previous one, and the effective annual interest rate is 12%. What is the present value of this stock? 𝑷𝑽= 𝑪 𝒓−𝒈 x 𝟏+𝒓 𝟏 𝟐 = 𝟏𝟎 .𝟏𝟐−.𝟎𝟖 𝟏.𝟏𝟐 =$𝟐𝟔𝟒.𝟓𝟖

3. Multiple Choice #2
Stock X and Stock Y are perfectly positively correlated. Stock X has an expected return of 12% and a standard deviation of 14%. Stock Y has an expected return of 18% and a standard deviation of 16%. If a portfolio has a positive % of both stocks, which of the following could be the portfolio standard deviation – 12%, 14%, 15%, 16%, or 18%?

4. Multiple Choice #2
Any combination of the two stocks must be strictly between the two endpoints, which denote Stock X and Stock Y.
This means the portfolio standard deviation, 𝝈 𝑷 , must fall within .𝟏𝟔> 𝝈 𝑷 >.𝟏𝟒. The only option satisfying this is 15%.

5. Multiple Choice #3
In 2012 the nominal return for large-company stocks was 16% and the Consumer Price Index (CPI) increased by 1.74%. Assuming the CPI represents the inflation rate, what was the real rate of return for large-company stocks in 2012? 𝟏+real 𝟏+inflation =𝟏+nominal 𝟏+real 𝟏.𝟎𝟏𝟕𝟒=𝟏.𝟏𝟔 real=.𝟏𝟒𝟎𝟏𝟔 OR 𝟏𝟒.𝟎𝟏𝟔%

6. Multiple Choice #4 & #5
Badda Star Books stock is currently valued at $50 and acts as a random walk. The value of the stock either goes up by $2 or down by $3 every day. The probability that the value increases is 60%.
4. What is the probability that Badda Star Books will be exactly $49 two days from today?
Only two possible outcomes can produce $49 in two days:
the stock goes up, then down;
the stock goes down, then up.
𝑷 Up,Down =.𝟔∗.𝟒=.𝟐𝟒; 𝑷 Down,Up =.𝟒∗.𝟔=.𝟐𝟒
The total probability of either event occurring:
𝑷 Up,Down +𝑷 Down,Up =.𝟐𝟒+.𝟐𝟒=.𝟒𝟖

7. Multiple Choice #4 & #5
Badda Star Books stock is currently valued at $50 and acts as a random walk. The value of the stock either goes up by $2 or down by $3 every day. The probability that the value increases is 60%. 5. What is the probability that Badda Star Books stock will be higher 3 days from today? Only 4 outcomes produce a higher stock value: 1) Up, Up, Up; 2) Up, Up, Down; 3) Up, Down, Up; 4) Down, Up, Up Individual Probabilities: 𝑷 Up, Up, Up = .𝟔 𝟑 =.𝟐𝟏𝟔; 𝑷 𝟐 Up, 𝟏 Down = .𝟔 𝟐 x .𝟒=.𝟏𝟒𝟒 The total probability of any of these events occurring: 𝑷 Up, Up, Up +𝟑 x 𝑷 𝟐 Up, 𝟏 Down =.𝟐𝟏𝟔+𝟑 .𝟏𝟒𝟒 =.𝟔𝟒𝟖

8. Free Response #6
Windy Tree Pizza paid out its annual dividend of $10 earlier today. The annual dividend increases by 15% each of the next 6 years and then remains constant forever. If the effective annual discount rate is 16%, what will be the price of the stock 4 years from today? 𝑫 𝟓 =𝟏𝟎 𝟏+.𝟏𝟓 𝟓 =$𝟐𝟎.𝟏𝟏𝟑𝟔 𝑫 𝟔 = 𝑫 𝟕 =…= 𝑫 ∞ =𝟏𝟎 𝟏+.𝟏𝟓 𝟔 =$𝟐𝟑.𝟏𝟑𝟎𝟔 𝑭 𝑽 𝟒 = $𝟐𝟎.𝟏𝟏𝟑𝟔 𝟏.𝟏𝟔 + $𝟐𝟑.𝟏𝟑𝟎𝟔 .𝟏𝟔 𝟏 𝟏.𝟏𝟔 =$𝟏𝟒𝟏.𝟗𝟕

9. Free Response #7
San Hearst Swimming Supplies, Inc. has stock issued with a beta value of 2 and pays dividends of $6 per year forever, starting one year from today. The risk-free rate is 5%, and the rate of return to the market is 8%. What is the present value of this stock? 𝒓= 𝑹 𝒇 +𝜷 𝑹 𝑴 − 𝑹 𝒇 =.𝟎𝟓+𝟐 .𝟎𝟖−.𝟎𝟓 =.𝟏𝟏 Present Value: $𝟔 .𝟏𝟏 =$𝟓𝟒.𝟓𝟓