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Question 1

Goose Bay Steel (GBS) has a market related βGBS = 1.05 and the company pays a regular dividend of $0.35 quarterly. a) If the risk-free rate is 3% and the market risk premium (return on market above the risk-free rate) is 5%, then what is the required return on GBS’ equity, based on the capital asset pricing model (CAPM). (2 marks) b) What is the value of the company’s stock, if 400,000 shares are outstanding? (2 marks) c) The firm also has 2,500 outstanding bonds with semi-annual coupons paying a coupon rate, CR = 6%. The face value is $1,000, the maturity is in 5 years and these are priced to yield 8%, compounded semi-annually. What is the price of each bond? (3 marks) d) What is the value of the firm? (2 marks) 2. An economy has three possible states: great, not as great, and poor. The returns on the market and two stocks are included in the table below.

Other information in the table can be used as required. Economy (probability) Market Snap Top GREAT (25%) 20% 30% 25% NAG (40%) 10% 7% 10% POOR (35%) -5% -5% 5% E(r) E(rs ) = 8.55% Risk = σ σM = 9.78% σT = 7.81% a) If the covariance between Snap and the market is CovS,M = 124.92 (%)2 , and the correlation between Top and the market is ρT,M = 0.9092, then which stock is more sensitive to changes in the market portfolio? (4 marks) b) What is the expected return of a portfolio invested 1/3 in the market, 1/3 in Snap, and 1/3 in Top? (2 marks) c) If CovS,T = 104.15 (%)2 , what is the risk of this portfolio? (5 marks) d) If you decide to invest 60% of your money in the market and 40% in Treasury Bills (which have a return of 2.5%), what is your expected risk and return? (2 marks) BUSI 4500 – Spring 2018 2 3. Pumpkin π Corporation is an established software development company that has debt and common stock in its capital structure. All questions below deal with the same company:

(a) The 3,000 company bonds (Face Value = 1000) that are still outstanding were issued several years ago and the coupon rate was set at 8% = $40 payment every six months, which was a competitive rate at the time. Since then interest rates have dropped and the bond price has risen to $1070.20. These bonds mature in four years exactly. What is the yield of these bonds? (3 marks) NOTE: You will need access to a spreadsheet or financial calculator for solution.

(b) As part of the Information Technology industry, Pumpkin π has a systematic risk that is above the TSX average: βPπ = 1.50 but the return (rPπ = 17%) is higher than the return on the market. The prevailing risk-free rate, rrf = 4%. What is the return on the market portfolio in this case? (3 marks)

(c) Pumpkin π corporate stock is priced at 20x earnings and there are 200,000 shares outstanding. The Gordon Growth model cannot be used as this high-tech. firm pays no dividend, but it has positive earnings and new communication device called the Pea-Pod is being developed. The return from part b) is a reasonable choice for the discount rate. Research investment this year is $2 million and the production investment next year is $4 million. The cash in-flows in the following four years are $3.5 million, $4 million, $4 million, and $2 million, after which the device will need redesign. What are the company earnings per share this year? (5 marks) (d) What is the total value of Pumpkin π’s equity and what is the value of the firm? (2 marks) Total: 35 marks

Part 1 Beta   1.05                        
  Rf   0.03                        
  Risk Premium 0.05                        
                               
  To calculate required rate of return, CAPM will be applied                        
  ke = Rf+ Beta (Rp)                        
                               
      3 + 1.05 (5)                        
                               
  ke = 8.25%                        
                               
                               
Part 2 Dividend per quarter= 0.35                          
  No. of quarters in a year= 4                          
  Dividend in a year= 1.4                          
                               
  Assumption: As the question is silent about the growth rate of stock of company, it is assumed that no growth has been achieved by the firm.        
                               
  P0 = D1                        
      Ke                        
                               
  P0 = 1.4                        
      8.25%                        
                               
  P0 =  $                16.97                        
                               
  Total no. of stock 400000                        
                               
  Value of company's stock  $ 67,87,878.79                        
                               
Part 3   Terms Cash Flows PVAF @ 4% PV of Cash Flows                  
  Interest 1  $                30.00 0.962  $    28.85                    
  Interest 2  $                30.00 0.925  $    27.74                    
  Interest 3  $                30.00 0.889  $    26.67                    
  Interest 4  $                30.00 0.855  $    25.64                    
  Interest 5  $                30.00 0.822  $    24.66                    
  Interest 6  $                30.00 0.790  $    23.71                    
  Interest 7  $                30.00 0.760  $    22.80                    
  Interest 8  $                30.00 0.731  $    21.92                    
  Interest 9  $                30.00 0.703  $    21.08                    
  Interest + Principle 10  $          1,030.00 0.676  $  695.83                    
                               
  Price of bond      $  918.89                    
                               
Part 4 Value of firm No. of bonds   x    Prcice of bond                          
                               
    2500    *   918.89                          
                               
  Value of firm=  $                                     22,97,227.61                          
                               
                               
PART 1   Annual Interest payment +[ (  Bond par value - Current bond price )]/4                  
     ( Current bond price + bond par value)]/2                        
                               
                               
    Annual interest payment                          
    Current bond price                          
    Par Value                          
                               
                               
                               
                               
    YTM using formula                          
                               
    YTM using excel                           
                               
    Face Value  $                1,000                        
    Annual Coupon Rate 8.00%                        
                               
    Years to Maturity                         4.0                        
                              1.0                        
                               
    Payment Frequency                            2                        
                               
    Value of Bond  $          1,070.20                        
                               
                               
                               
    Yield to Maturity 5.9999%                        
                               
PART 2   ke = Rf+ Beta (Rp)                    
        4% + (1.50* 17%)                    
        23.5%                      
PART 3                              
                               
  Years Cash flows Amounts PVAF @23.5%                    
  0 Research Investment -2 1.000                      
  1 Production Investment -4 0.810                      
  2 Cash Inflows 3.5 0.656                      
  3 Cash Inflows 4 0.531                      
  4 Cash Inflows 4 0.430                      
  5 Cash Inflows 2 0.348                      
                               
    NPV                          
                               
    Earnings 20 x return                        
    PE Ratio 20 times                        
    Earnings in millions                          
    No. of shares                          
                               
    EPS                          
                               
    Value of firm's equity                          
                               
PART 4   MPS                          
                               
    P0 P1 + D1                        
      1+Ke                        
                               
    3190.02= P1 + D1                        
      1.235                        
                               
    3939.67 P1 + D1                        
                               
    Value of firm 787934262.5                        
                               
                               
PART 1                              
                               
  SNAP                            
  Beta= Covxm   124.92     124.92   1.31            
    varinancem   9.78 * 9.78   95.6484                
                               
  TOP                            
  Beta= Standard Deviation of top    x    Correlationtm                        
    Standard Deviation of market                          
                               
    7.81    x      .9092                          
    9.78                          
                               
    7.100852                          
    9.78                          
                               
    0.73                          
                               
  Since beta of Snap is higher than that of Top, Snap is more sensitive to changes in market portfolio. With each 1.31% change in market index, the value of Snap will vary by 1.31%
                               
PART 2                              
                               
  Expected Return of Portfolio=   (R1W1 + R2W2 + R3W3)                  
        (7.25*0.33)+(8.55*0.33)+(12*0.33)                
        9.27%                      
  Market         Snap         Top        
  Returns Probability Weighted Return   Returns Probability Weighted Return   Returns Probability Weighted Return  
  0.2 0.25 0.05     0.3 0.25 0.075     0.25 0.25 0.0625    
  0.1 0.4 0.04     0.07 0.4 0.028     0.1 0.4 0.04    
  -0.05 0.35 -0.0175     -0.05 0.35 -0.0175     0.05 0.35 0.0175    
  Expected Return 7.25%     Expected Return 8.55%     Expected Return 12.00%    
                               
PART 3                              
  Standard deviation of Snap                          
                               
    Returns Probability Weighted Return Deviation Deviation 2 Deviation * Probability                
    30.00 0.25 7.50 21.45 460.10 115.03                
    7.00 0.40 2.80 -1.55 2.40 0.96                
    -5.00 0.35 -1.75 -13.55 183.60 64.26                
    Variance         180.25                
    Return   8.55                      
    Variance   180.25                      
    Standard Deviation   13.43                      
                               
  Standard deviation of Snap   13.43                      
  Standard deviation of Top   7.81                      
  Standard deviation of Market   9.78                      
  Cov MS     124.92                      
  Weights     0.33                      
                               
  Correlation TS Cov TS                        
      SD T * SD S                        
                               
      104.15                        
      7.81 * 13.43                        
                               
      104.15                        
      104.8541584                        
                               
      0.9933                        
                               
  Correlation MS Cov MS                        
      SD M * SD S                        
                               
      124.92                        
      131.30                        
                               
      0.9514                        
                               
  Correlation MT 0.9092                        
                               
  Risk of portfolio= sqrt  (WT2SDT2 + WS2SDS2 + WM2SDM2 + 2 WT WS SDT SDS rts rms rmt)      
                               
      sqrt  6.78 + 20.03 + 10.63 + 65.27          
                               
  Risk of portfolio=   10.13                      
                               
PART 4                              
    Portfolio Return                          
      Assets Weights Returns Weighted Average Returns                  
      Money Market 0.6 7.25% 4.35%                  
      Tresury Bill 0.4 2.50% 1.00%                  
                               
      Portfolio Return   5.35%                  
                               
                               
    Portfolio Risk                          
                               
      Assets Weights Returns Weighted Average Returns D= R-X D2 D2P            
      Money Market 0.6 7.25 4.35 1.90 3.61 2.166            
      Tresury Bill 0.4 2.50 1.00 -2.85 8.12 3.249            
                               
      Portfolio Return, X   5.35   Variance 5.42            
                Standard Deviation 2.327015            
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