FNCE 370v10: 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 13 Lesson 11

5 8 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

1. Market efficiency (5 marks)

a. Identify and describe the three forms of market efficiency. Do not use more than five sentences for each form of market efficiency. Make sure your descriptions discuss information dispersion and identification of mispriced securities. (4 marks)

b. Based on your knowledge and understanding of the three forms of market efficiency, which form do you think most appropriately describes the Toronto Stock Exchange? Explain your answer. (1 mark)

2. The stocks on ABC Company and XYZ Company have the following returns over the last five years. (10 marks)

Year ABC returns XYZ returns

1 –0.2 0.2

2 –0.1 0.1

3 0.5 –0.1

4 0.3 0.05

5 0.1 0.08

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 returns on ABC. (2.5 marks)

d. Calculate the variance and standard deviation on the returns on XYZ. (2.5 marks)

e. Using the coefficient of variation (standard deviation/average return) as a measure of comparison between the two stocks, which stock is preferable? (3 marks)

3. You bought one of BB Co.’s 10% coupon bonds one year ago for $1100. These bonds make annual payments, have a face value of $1000 each, and mature seven years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 8%. If the inflation rate was 3% over the past year, what would be your total real return on investment according to the Exact Fisher Formula? (7 marks)

4. Suppose we have two risky assets, Stock I and Stock J, and a risk-free asset. Stock I has an expected return of 25% and a beta of 1.5. Stock J has an expected return of 20% and a beta of 0.8. The risk-free asset’s return is 5%. (13 marks)

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%, 50%, 100%, and 150%. (2 marks)

b. Using the four portfolio betas calculated in part (a), reverse engineer (i.e., derive mathematically) the portfolio weights for a portfolio consisting of only Stock J and the risk-free asset. (4 marks)

Hint: For example, if we wished to obtain a portfolio beta of 0.5, then the weights on Stock J and the risk-free asset must be 62.5% and 37.5%, respectively, and the expected return for this portfolio must be 14.375%.

c. Calculate the reward-to-risk ratios for Stock I and Stock J. (2 marks)

d. 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. Ensure that the x-axis and y-axis are clearly labelled. (Hint: This can be done easily with the charting function in Microsoft Excel.) (3 marks)

e. Using the graph in part (d) above, together with your answers in part (c) above, elaborate on the efficiency of the market containing Stock I and Stock J. (2 marks)

Rate of return if state occurs

State of economy Probability of state of economy Stock A Stock B Stock C

Boom 0.3 0.35 0.45 0.38

Good 0.3 0.15 0.20 0.12

Poor 0.3 0.05 –0.10 –0.05

Bust 0.1 0.00 –0.30 –0.10

5. Consider the following information on three stocks in four possible future states of the economy: (8 marks)

a. Your portfolio is invested 30% in A, 50% in B, and 20% in C. What is the expected return of your portfolio? (5 marks)

b. What is the variance of this portfolio? (2 marks)

c. What is the standard deviation of this portfolio? (1 mark)

Just For Fun (JFF):

See if you can find the optimal portfolio using the Solver function in MS Excel. To optimize the portfolio, you would want to find the optimal portfolio weights that will minimize the portfolio risk (standard deviation) while achieving a required rate of return (say, 15%). No marks are assigned for this problem, as it is JFF.

Stock Expected return Beta

K 20% 1.6

L 12% 0.9

6. Suppose we observe two stocks with the following characteristics: (9 marks)

a. An asset is said to be overvalued if its price is too high given its expected return and risk. The risk-free rate is currently 6%. Is one of the two stocks overvalued relative to the other? Explain your answer fully (i.e., provide reasons why you think the stock is or is not overvalued). (3.5 marks)

Stock Expected return Beta

M 20% 1.6

N 12% 0.9

b. Suppose we observe two stocks with the following characteristics:

An asset is said to be undervalued if its price is too low given its expected return and risk. The risk-free rate is currently 6%. Is one of the two stocks undervalued relative to the other? Explain your answer fully (i.e., provide reasons why you think the stock is or is not undervalued). (3.5 marks)

c. In a well-functioning, well-organized, active market, can a stock be persistently over- or undervalued relative to an average asset in the market? Explain why or why not. How and when is equilibrium achieved? (2 marks)

7. Given the following information on Ke-Ma-Gen Ltd., what is its WACC? Retain as many decimal places as possible in your intermediate answers, and round your final answer (in percentage) to two decimal places. (11 marks)

Debt:

Number of bonds = 6000

Par value = $1000

Coupon rate = 8% (semi-annual coupons)

Time to maturity = 10 years

Market value = 97.5% of par

Common Equity:

Number of shares outstanding = 1,000,000

Par value = $1

Price per share = $5.00

Dividends per share = $0.70

Preferred Equity:

Number of shares outstanding = 50,000

Price per share = $20

Dividend yield = 5%

Other information:

Tax rate = 35%

Equity beta = 2

Market risk premium = 11%

Risk-free rate = 5%

8. ABC Co. has the following dividend payment history for the last five years, with the most recent dividend being $1.10: $0.50, $0.60, $0.80, $1.00, $1.10. (19 marks)

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 0.9 and a historical return on equity (ROE) of 0.25. Using these two additional pieces of information, calculate an alternative estimate of dividend growth rate, g. (1 mark)

e. Calculate the expected growth rate of dividends by averaging the growth rates in parts (a), (c), and (d). (1 mark)

Dividend growth model

f. ABC’s share price is currently $70, and the most recent dividend paid is $1.10 per share. Using the expected growth rate estimated in (e) above, calculate the cost of equity using the dividend growth model. (3 marks)

SML model

g. Given that the firm’s equity beta is 2, 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 1, 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 seven years. The risk adjustment for this project on the WACC is +5%. Calculate the net present value of this project using the WACC calculated in (i) 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.:

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: 20%

Depreciation: 10%

Change in net working capital: 15%

Net capital spending: 10%

The firm’s tax rate is 35%, and it has 1,000,000 outstanding shares and $8,000,000 in debt. We have estimated the WACC to be 15%. (18 marks)

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 formula

CFA* = EBIT(1 – T) + Depr – ?NWC – NCS. (4 marks)

c. Calculate the firm’s share price at time 0. (6 marks)

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 13 Lesson 11

5 8 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

1. Market efficiency (5 marks)

a. Identify and describe the three forms of market efficiency. Do not use more than five sentences for each form of market efficiency. Make sure your descriptions discuss information dispersion and identification of mispriced securities. (4 marks)

b. Based on your knowledge and understanding of the three forms of market efficiency, which form do you think most appropriately describes the Toronto Stock Exchange? Explain your answer. (1 mark)

2. The stocks on ABC Company and XYZ Company have the following returns over the last five years. (10 marks)

Year ABC returns XYZ returns

1 –0.2 0.2

2 –0.1 0.1

3 0.5 –0.1

4 0.3 0.05

5 0.1 0.08

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 returns on ABC. (2.5 marks)

d. Calculate the variance and standard deviation on the returns on XYZ. (2.5 marks)

e. Using the coefficient of variation (standard deviation/average return) as a measure of comparison between the two stocks, which stock is preferable? (3 marks)

3. You bought one of BB Co.’s 10% coupon bonds one year ago for $1100. These bonds make annual payments, have a face value of $1000 each, and mature seven years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 8%. If the inflation rate was 3% over the past year, what would be your total real return on investment according to the Exact Fisher Formula? (7 marks)

4. Suppose we have two risky assets, Stock I and Stock J, and a risk-free asset. Stock I has an expected return of 25% and a beta of 1.5. Stock J has an expected return of 20% and a beta of 0.8. The risk-free asset’s return is 5%. (13 marks)

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%, 50%, 100%, and 150%. (2 marks)

b. Using the four portfolio betas calculated in part (a), reverse engineer (i.e., derive mathematically) the portfolio weights for a portfolio consisting of only Stock J and the risk-free asset. (4 marks)

Hint: For example, if we wished to obtain a portfolio beta of 0.5, then the weights on Stock J and the risk-free asset must be 62.5% and 37.5%, respectively, and the expected return for this portfolio must be 14.375%.

c. Calculate the reward-to-risk ratios for Stock I and Stock J. (2 marks)

d. 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. Ensure that the x-axis and y-axis are clearly labelled. (Hint: This can be done easily with the charting function in Microsoft Excel.) (3 marks)

e. Using the graph in part (d) above, together with your answers in part (c) above, elaborate on the efficiency of the market containing Stock I and Stock J. (2 marks)

Rate of return if state occurs

State of economy Probability of state of economy Stock A Stock B Stock C

Boom 0.3 0.35 0.45 0.38

Good 0.3 0.15 0.20 0.12

Poor 0.3 0.05 –0.10 –0.05

Bust 0.1 0.00 –0.30 –0.10

5. Consider the following information on three stocks in four possible future states of the economy: (8 marks)

a. Your portfolio is invested 30% in A, 50% in B, and 20% in C. What is the expected return of your portfolio? (5 marks)

b. What is the variance of this portfolio? (2 marks)

c. What is the standard deviation of this portfolio? (1 mark)

Just For Fun (JFF):

See if you can find the optimal portfolio using the Solver function in MS Excel. To optimize the portfolio, you would want to find the optimal portfolio weights that will minimize the portfolio risk (standard deviation) while achieving a required rate of return (say, 15%). No marks are assigned for this problem, as it is JFF.

Stock Expected return Beta

K 20% 1.6

L 12% 0.9

6. Suppose we observe two stocks with the following characteristics: (9 marks)

a. An asset is said to be overvalued if its price is too high given its expected return and risk. The risk-free rate is currently 6%. Is one of the two stocks overvalued relative to the other? Explain your answer fully (i.e., provide reasons why you think the stock is or is not overvalued). (3.5 marks)

Stock Expected return Beta

M 20% 1.6

N 12% 0.9

b. Suppose we observe two stocks with the following characteristics:

An asset is said to be undervalued if its price is too low given its expected return and risk. The risk-free rate is currently 6%. Is one of the two stocks undervalued relative to the other? Explain your answer fully (i.e., provide reasons why you think the stock is or is not undervalued). (3.5 marks)

c. In a well-functioning, well-organized, active market, can a stock be persistently over- or undervalued relative to an average asset in the market? Explain why or why not. How and when is equilibrium achieved? (2 marks)

7. Given the following information on Ke-Ma-Gen Ltd., what is its WACC? Retain as many decimal places as possible in your intermediate answers, and round your final answer (in percentage) to two decimal places. (11 marks)

Debt:

Number of bonds = 6000

Par value = $1000

Coupon rate = 8% (semi-annual coupons)

Time to maturity = 10 years

Market value = 97.5% of par

Common Equity:

Number of shares outstanding = 1,000,000

Par value = $1

Price per share = $5.00

Dividends per share = $0.70

Preferred Equity:

Number of shares outstanding = 50,000

Price per share = $20

Dividend yield = 5%

Other information:

Tax rate = 35%

Equity beta = 2

Market risk premium = 11%

Risk-free rate = 5%

8. ABC Co. has the following dividend payment history for the last five years, with the most recent dividend being $1.10: $0.50, $0.60, $0.80, $1.00, $1.10. (19 marks)

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 0.9 and a historical return on equity (ROE) of 0.25. Using these two additional pieces of information, calculate an alternative estimate of dividend growth rate, g. (1 mark)

e. Calculate the expected growth rate of dividends by averaging the growth rates in parts (a), (c), and (d). (1 mark)

Dividend growth model

f. ABC’s share price is currently $70, and the most recent dividend paid is $1.10 per share. Using the expected growth rate estimated in (e) above, calculate the cost of equity using the dividend growth model. (3 marks)

SML model

g. Given that the firm’s equity beta is 2, 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 1, 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 seven years. The risk adjustment for this project on the WACC is +5%. Calculate the net present value of this project using the WACC calculated in (i) 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.:

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: 20%

Depreciation: 10%

Change in net working capital: 15%

Net capital spending: 10%

The firm’s tax rate is 35%, and it has 1,000,000 outstanding shares and $8,000,000 in debt. We have estimated the WACC to be 15%. (18 marks)

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 formula

CFA* = EBIT(1 – T) + Depr – ?NWC – NCS. (4 marks)

c. Calculate the firm’s share price at time 0. (6 marks)

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