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Problem 1 (10 marks) You have been provided with the following information zero coupon bonds with $1000 face value. Maturity – semi -annual periods semi-annual spot rates 1 4.25 2 4.15 3 3.95 4 3.70 5 3.50 6 3.25 7 3.05 8 2.90 1. Compute the forward interest rates. 2. Graph the yield curve. 3. Explain the factors that account for the shape of the curve. Problem 2 (10 marks) Company HTA had a free cash flow for the firm (FCFF) of $1,500,000 last year. It is expected the FCFF will keep a sustainable growth rate of 5%. The company has 2 million common shares outstanding. In addition, the following information has been gathered: Capital structure: D/E=0.2:0.8; Market value of Debt: VD =$5,000,000; Required return on equity: kE =15% Cost of debt before tax =6% Tax rate: tc =25%; Determine the fair value of HTA stock. Problem 3 (10 marks) Company JUK has a ROE of 25% and the company will not pay any dividend for the next 3 years. It is estimated that the company will pay $2 dividend per share after three years and then to level off to 5% per year forever. The company has a beta of 2. Assume the risk-free interest rate is 4%, and the market risk premium is 8%. 1. What is your estimate of the fair price of a share of the stock? 2. If the market price of a share is equal to this intrinsic value, what is the P/E ratio? 3. What do you expect its price to be 1 year from now? Is the implied capital gain consistent with your estimate of the dividend yield and the market capitalization rate? Problem 4 (10 marks) MicroSense, Inc., paid $2 dividends per share last year. It is estimated that the company’s ROEs will be 12% and 10%, respectively, next two years. The plowback rate in next two years will be 0.6. It is expected that the dividends will grow at a sustainable rate of 3% per year after two years. Assume that the expected return on the market is 8%, the risk-free rate is 4%, and the beta of the stock is 1.4.What is the fair price of the stock? Problem 5 (10marks): An analyst uses the constant growth model to evaluate a company with the following data for a company: Leverage ratio (asset/equity): 1.8 Total asset turnover: 1.5 Current ratio: 1.8 Net profit margin: 8% Dividend payout ratio: 40% Earnings per share in the past year: $0.85 The required rate on equity: 15% Based on an analysis, the growth rate of the company will drop by 25 percent per year in the next two years and then keep it afterward. Assume that the company will keep its dividend policy unchanged. 1. Determine the growth rate of the company for each of next three years. 2. Use the multi-period DDM to estimate the intrinsic value of the company’s stock. 3. Suppose after one year, everything else will be unchanged but the required rate on equity will decrease to 14%. What would be your holding period return for the year? Problem 6 (50 marks) Using theYahoo! Finance website, search the Bank of Nova Scotia (BNS.TO) by finding its stock symbol. If you are unable to locate the prices for BNS.TO, use prices for BNS (the Bank of Nova Scotia observed in US dollars at the New York Stock Exchange). For the purpose of this question, assume that the Canadian dollar and the US dollar had been exchanged one for one.Find historical prices for the stock (on the left-hand menu) and complete the following: 1. Download historical data for the stock prices (adj. close) from January 1, 2004 through January 1, 2012, on a monthly basis. You will also need to download corresponding monthly prices for the S&P/TSX Comp index (also available on the Yahoo! Finance site) as well as 3-month T-Bill rates (download this attachment: T-Bill Rates.xlsx). 2. Calculate returns for both series of prices downloaded from Yahoo site (BNS and S&P /TSX Comp Index). Prior to that, make sure the data is sorted in ascending order (i.e., first row has the oldest data). The final spreadsheet should have the two series of returns you downloaded and calculated from Yahoo! Finance. Make sure all data is expressed in same units. 3. Using the Tools menu in EXCEL, (Tool Pack has to be installed if EXCEL does not show it) perform regression analyses using the Market Model for BNS. 4. Clearly provide the regression results in a table with an explanation for the coefficients obtained, and clear interpretation. Specifically, for each regression provide: • Dependent Variable • Independent Variable • Intercept • Beta Value • Firm Specific Risk i. How well does the S&P/TSX Comp Index movement explain the variability of the return on BNS stock? ii. What is the alpha of the BNS stock? iii. Calculate the standard deviation of the stock return (using the equation for R2 =β2σM2/σ2,and the individual regression results). iv. Calculate systematic risk and firm specific risk for the stock.

Problem 1 (10 marks)

You have been provided with the following information zero coupon bonds with $1000 face value.

Maturity – semi -annual periods

semi-annual spot rates

1

4.25

2

4.15

3

3.95

4

3.70

5

3.50

6

3.25

7

3.05

8

2.90

 

  1. Compute the forward interest rates.
  2. Graph the yield curve.
  3. Explain the factors that account for the shape of the curve.

 

Problem 2 (10 marks) 

Company HTA had a free cash flow for the firm (FCFF) of $1,500,000 last year. It is expected the FCFF will keep a sustainable growth rate of 5%. The company has 2 million common shares outstanding. In addition, the following information has been gathered:

Capital structure: D/E=0.2:0.8;

Market value of Debt: VD =$5,000,000;

Required return on equity: kE =15%

Cost of debt before tax =6%

Tax rate: tc =25%;

Determine the fair value of HTA stock.

 

 

 

 

Problem 3 (10 marks)

Company JUK has a ROE of 25% and the company will not pay any dividend for the next 3 years. It is estimated that the company will pay $2 dividend per share after three years and then to level off to 5% per year forever.

The company has a beta of 2. Assume the risk-free interest rate is 4%, and the market risk premium is 8%.

  1. What is your estimate of the fair price of a share of the stock?
  2. If the market price of a share is equal to this intrinsic value, what is the P/E ratio?
  3. What do you expect its price to be 1 year from now? Is the implied capital gain consistent with your estimate of the dividend yield and the market capitalization rate?

 

Problem 4 (10 marks)

MicroSense, Inc., paid $2 dividends per share last year. It is estimated that the company’s ROEs will be 12% and 10%, respectively, next two years. The plowback rate in next two years will be 0.6. It is expected that the dividends will grow at a sustainable rate of 3% per year after two years. Assume that the expected return on the market is 8%, the risk-free rate is 4%, and the beta of the stock is 1.4.What is the fair price of the stock?

Problem 5 (10marks):

An analyst uses the constant growth model to evaluate a company with the following data for a company:

Leverage ratio (asset/equity): 1.8

Total asset turnover:      1.5

Current ratio: 1.8

Net profit margin: 8%

Dividend payout ratio: 40%

Earnings per share in the past year: $0.85

The required rate on equity: 15%

Based on an analysis, the growth rate of the company will drop by 25 percent per year in the next two years and then keep it afterward.  Assume that the company will keep its dividend policy unchanged.

  1. Determine the growth rate of the company for each of next three years.
  2. Use the multi-period DDM to estimate the intrinsic value of the company’s stock.
  3. Suppose after one year, everything else will be unchanged but the required rate on equity will decrease to 14%. What would be your holding period return for the year?

 

Problem 6 (50 marks)

Using theYahoo! Finance website, search the Bank of Nova Scotia (BNS.TO) by finding its stock symbol. If you are unable to locate the prices for BNS.TO, use prices for BNS (the Bank of Nova Scotia observed in US dollars at the New York Stock Exchange). For the purpose of this question, assume that the Canadian dollar and the US dollar had been exchanged one for one.Find historical prices for the stock (on the left-hand menu) and complete the following:

  1. Download historical data for the stock prices (adj. close) from January 1, 2004 through January 1, 2012, on a monthly basis.  You will also need to download corresponding monthly prices for the S&P/TSX Comp index (also available on the Yahoo! Finance site) as well as 3-month T-Bill rates (download this attachment: T-Bill Rates.xlsx).
  2. Calculate returns for both series of prices downloaded from Yahoo site (BNS and S&P /TSX Comp Index). Prior to that, make sure the data is sorted in ascending order (i.e., first row has the oldest data).  The final spreadsheet should have the two series of returns you downloaded and calculated from Yahoo! Finance.  Make sure all data is expressed in same units.
  3. Using the Tools menu in EXCEL, (Tool Pack has to be installed if EXCEL does not show it) perform regression analyses using the Market Model for BNS.
  4. Clearly provide the regression results in a table with an explanation for the coefficients obtained, and clear interpretation. Specifically, for each regression provide:
  • Dependent Variable
  • Independent Variable
  • Intercept
  • Beta Value
  • Firm Specific Risk

i.            How well does the S&P/TSX Comp Index movement explain the variability of the return on BNS stock?

ii.            What is the alpha of the BNS stock?

iii.            Calculate the standard deviation of the stock return (using the equation for R2 2σM22,and the individual regression results).

iv.            Calculate systematic risk and firm specific risk for the stock.

 

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