# Define an efficient capital market.

FNCE 370v9: Assignment 4
Assignment 4 is worth 5% of your final mark. Complete and submit Assignment 4 after you complete Lesson 12.

Question Marks available Marks awarded Reference
1 5 Lesson 10
2 10 Lesson 10
3 7 Lesson 10
4 15 Lesson 11
5 6 Lesson 11
6 9 Lesson 11
7 11 Lesson 12
8 19 Lesson 12
9 18 Lesson 12
Total 100
Note on Decimal Places
When working through numerical problems, use as many decimal places as shown on your financial calculator. Do not round your calculated answers until you have reached the final answer. When you reach your final answer, round as follows, unless the question specifies otherwise.
Percentages: round to two decimal places
Dollars: round to two decimal places
Others: round to four decimal places
Questions
1. a. Define an efficient capital market. (1 mark) (5 marks total)
b. What is the main assertion of the efficient market hypothesis (EMH)? (1 mark)
c. What is the implication of an efficient capital market for stock prices? (1 mark)
d. What is the major factor that contributes to market efficiency? How does it cause a market to become efficient? (2 marks)
2. The stocks on ABC Company and XYZ Company have the following returns over the last four years. (10 marks)

Year ABC returns XYZ returns
1 -0.2 0.05
2 0.5 0.09
3 0.3 -0.12
4 0.1 0.2
a. Calculate the average return on ABC. (1 mark)
b. Calculate the average return on XYZ. (1 mark)
c. Calculate the variance and standard deviation on the ABC returns. (2.5 marks)
d. Calculate the variance and standard deviation on the XYZ returns. (2.5 marks)
e. Using the coefficient of variation (standard deviation/average return) to compare the two stocks, which stock is preferable? (3 marks)
3. Suppose that you bought 100 shares of ABC Inc., for \$25 per share exactly one year ago. You have just received \$1.50 in dividends, and the current share price is \$30 per share. (7 marks total)
a. Calculate the cash income component of your investment return on ABC shares. (1 mark)
b. Calculate the capital gain/loss component of your investment return on ABC shares. (1 mark)
c. Calculate the dividend yield on ABC shares. (1 mark)
d. Calculate the capital gains yield on ABC shares. (1 mark)
e. Calculate the total percentage return on ABC shares. (1 mark)
f. If you keep your ABC shares, should you still consider the capital gain/loss as part of your investment return, or as simply a “paper” gain? Explain? (2 marks)
4. Suppose we have one risky asset Stock I and a risk-free asset. Stock I has an expected return of 25% and a beta of 2. The risk-free asset’s return is 6%. (15 marks total)
a. Calculate the expected returns and betas on portfolios with x% invested in Stock I and the rest invested in the risk-free asset, where x% = 0%, 25%, 75%, 100%, 125%, and 150%. (3 marks)
b. What reward-to-risk ratio does Stock I offer? How do you interpret this ratio? (1.5 marks)
c. Suppose we have a second risky asset, Stock J. Stock J has an expected return of 20% and a beta of 1.7. Calculate the expected returns and betas on portfolios with x% invested in Stock J and the rest invested in the risk-free asset, where x% = 0%, 25%, 75%, 100%, 125%, and 150%. (3 marks)
d. What reward-to-risk ratio does Stock J offer? How do you interpret this ratio? (1.5 marks)
e. Plot the portfolio betas against the portfolio expected returns for Stock I on a graph, and link all the points together with a line. Then plot the portfolio betas against the portfolio expected returns for Stock J on the same graph, and link all these points together with another line. (This can be done easily with the charting function in Microsoft Excel.) (2 marks)
f. Use the graph in part (e) above, together with your answers to parts (b) and (d) above to explain why Stock J is an inferior investment to Stock I. (2 marks)
g. Can a situation in which one stock is inferior to another stock persist in a well-organized, active market? Why or why not? (2 marks)
5. Consider the following information on three stocks in four possible future states of the economy: (6 marks total)

Rate of return if state occurs
State of economy Probability of state of economy Stock A Stock B Stock C
Boom 0.4 0.35 0.45 0.38
Good 0.3 0.15 0.20 0.12
Poor 0.2 0.05 -0.10 -0.05
Bust 0.1 0.00 -0.30 -0.10
a. Your portfolio is invested 50% in A, 20% in B, and 30% in C. What is the expected return of your portfolio? (3 marks)
b. What is the variance of this portfolio? (2 marks)
c. What is the standard deviation of this portfolio? (1 mark)
6. You have \$10,000 to invest in a portfolio containing Stock R, Stock S, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 15% and that has only 120% of the risk of the overall market. If Stock R has an expected return of 25% and a beta of 1.6, Stock S has an expected return of 17.5% and a beta of 1.3, and the risk-free rate is 6%, how much money will you invest in Stock R? Explain your answer. (9 marks)
7. Given the following information on Ke-Ma-Gen Ltd., what is its WACC? (11 marks)
Debt:
Number of bonds = 10,000
Par value = \$1,000
Coupon rate = 9% (semi-annual coupons)
Time to maturity = 10 years
Market value = 98% of par
Common equity:
Number of shares outstanding = 1,000,000
Par value = \$1
Price per share = \$3.50
Dividends per share = \$0.70
Preferred equity:
Number of shares outstanding = 50,000
Price per share = \$20
Dividend yield = 5%
Other information:
Tax rate = 40%
Equity beta = 1.2
Risk-free rate = 5%
8. ABC Co. has the following dividend payment history for the last five years, with the most recent dividend being \$3.60. (19 marks total)

Dividend
\$2.00
\$2.50
\$2.90
\$3.20
\$3.60

Historical growth rate estimation
a. What is the compound growth rate of dividends based on the last five years of dividends data? (2 marks)
b. Calculate the year-to-year growth rates in dividends. (2 marks)
c. What is the average year-to-year dividend growth rate? (1 mark)
d. ABC has a retention ratio of 0.75 and a historical return on equity (ROE) of 0.2. Using these two additional pieces of information, calculate an alternative estimate of dividend growth rate, g. (1 mark)
Dividend growth model
e. Given that ABC’s share price is currently \$65, and the most recent dividend paid is \$3.60 per share, use the three growth rates estimated for historical growth (com-pound growth rate, average year-to-year growth rate, and alternative estimate) to calculate the cost of equity using the dividend growth model. (3 marks)
f. Average the three estimated costs of equity in part (e). (1 mark)
SML model
g. Given that the firm’s equity beta is 1.6, the risk-free rate is 5%, and the expected return on the market index is 13.5%, calculate its cost of equity using the SML model. (1 mark)
WACC calculation
h. Calculate the firm’s average cost of equity by averaging the answers in parts (f) and (g). (1 mark)
i. ABC’s capital structure contains only debt and equity. Given that its debt-equity ratio is 0.8, its cost of debt is 10%, and its marginal tax rate is 35%, calculate the firm’s WACC using the cost of equity calculated in part (h). (2 marks)
NPV calculation
j. The firm has a project with an initial cost of \$1 million, and annual cash savings of \$300,000 for the next five years. The risk adjustment for this project on the WACC is +5%. Calculate the net present value of this project using the WACC calculated above. (4 marks)
k. Should the firm go ahead with the project? (1 mark)
9. We find the following information on NPNG (No-Pain-No-Gain) Inc. (18 marks total)
EBIT = \$2,000,000
Depreciation = \$250,000
Change in net working capital = \$100,000
Net capital spending = \$300,000
These numbers are projected to increase at the following supernormal rates for the next three years, and 5% after the third year for the foreseeable future:
EBIT: 10%
Depreciation: 15%
Change in net working capital: 20%
Net capital spending: 15%
The firm’s tax rate is 35%, and it has 1,000,000 outstanding shares and \$6,000,000 in debt. We have estimated the WACC to be 15%.
a. Calculate the EBIT, Depreciation, Changes in NWC, and Net Capital Spending for the next four years. (8 marks)
b. Calculate the CFA* for each of the next four years, using the following formula:
CFA* = EBIT(1 – T) + Depr – ΔNWC – NCS (4 marks)
d. Calculate the present value of growing perpetuity at Year 3. (1 mark)
e. Calculate the firm’s value at time 0 using the WACC of the firm as the discount rate. (Note that the first CFA* to be discounted is the cash flow from one year into the future.) (3 marks)
f. Calculate the firm’s equity value at time 0. (1 mark)
g. Calculate the firm’s share price at time 0. (1 mark)