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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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