Week4_FIN2062a_Feb2_PracticeQs_Ch1516_Answers

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QUIZ #2 FINANCIAL CALCULATION REVIEW CHAPTER 15: INTRODUCTION TO PORTFOLIO MANAGEMENT Rate of Return (Individual Security) Question #1 : On January 1, 2020, an investor purchases one share of Canadian Pacific Ltd on the TSX for $20.00. On January 1, 2021, the share was sold at a price of $22.00. It’s dividend yield for the most recent period is 3%. What is the rate of return for the investor? Formula: Rate of Return (%) = Cash Flow ($) + (Sale Price – Purchase Price) Purchase Price Rate of Return (%) = $0.60 + ($22.00 - $20.00) $20.00 Rate of Return (%) = $0.60 + $2.00 $20.00 Rate of Return (%) = $2.60 = 13.0% $20.00 Question #2 : On October 12, 2019, an investor purchases a bond with a face value of $100.00 with one year to maturity. It pays an interest rate of 6% annually and the purchase price is $101.50. What is the rate of return for the investor? Formula: Rate of Return (%) = Face Value ($) + Interest ($) - Sale Price Purchase Price Rate of Return (%) = $100.00 + $6 - $101.50 $101.50 Rate of Return (%) = $106.00 - $101.50

$101.50 Rate of Return (%) = $4.50 = 4.43% $101.50 “Real” Rate of Return (Individual Security) Formula: “Real” Rate of Return (%) = “Nominal” Rate of Return - Inflation Rate of Return (Portfolio) Question #3 : Michael and Terry are comparing the rates of return on their stock portfolios to see whose advisor is doing a better job. They have exactly the same rates of return for the equities (10%), fixed income (6%) and cash (3%) in each of their portfolios. But Michael’s portfolio has a 70% equity, 25% fixed income and 5% cash allocation while Terry’s portfolio has a 30% equity, 60% fixed income and 10% cash allocation. Which advisor has generated a better rate of return? Formula: Rate of Return (%) = (r-1 x w-1) + (r-2 x w-2) + …. (r-n x w-n) Michael = (70% x .10) + (25% x .06) + (5% x .03) = (0.07) + (0.015) + (0.0015) = (0.087) = 8.7% Terry = (30% x .10) + (60% x .06) + (10% x .03) = (0.03) + (0.036) + (0.003) = (0.069) = 6.9%

Sharpe Ratio Question #4 : So, we now know that Michael’s portfolio generated the higher rate of return last year. But, we have also learned that we should take into account the level of “risk” that each portfolio is subject to. If Michael’s advisor tells him that the “standard deviation” for his portfolio = 20 and Terry learns that the “standard deviation” for his portfolio = 10, then which advisor has constructed the better portfolio based on a current “risk-free rate of return” of 1.5%? Formula: Sharpe Ratio = Portfolio Return (%) - “Risk Free” Return) Standard Deviation Michael = (0.087) - (0.015) 20 = 0.072 = 0.0036 20 Terry = (0.069) - (0.015) 10 = 0.054 = 0.0054 (Larger is better!!) 10 Portfolio Re-Balancing Question #5 :

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Following this discussion, Michael decides to talk with his advisor (who he hasn’t seen in 3 years). Together they decide that Michael’ portfolio needs to be re-balanced. Remember that his base portfolio is 70% equity, 25% fixed income and 5% cash and the annual rates of return for each asset class has been: equities 10%, fixed income 6% and cash (3%). Michael’s original investment 3 years ago was $100,000. What is the process for re-balancing Michael’s portfolio? Step #1: Determine the original dollar value invested in each asset class. Equities = $100,000 X 70% = $ 70,000.00 Fixed Income = $100,000 X 25% = $ 25,000.00 Cash = $100,000 X 5% = $ 5,000.00 Total = $100,000.00 Step #2: Determine the current weighting and dollar value in each asset class. Equities = $70,000 X 10% = $ 77,000.00 Fixed Income = $25,000 X 6% = $ 26,500.00 Cash = $5,000 X 3% = $ 5,150.00 Total = $108,650.00 Step #3: Using the base portfolio allocation, determine what the proper amount of money should be in each asset class for the current portfolio value. Equities = $108,650 X 70% = $ 76,055.00 Fixed Income = $108,650 X 25% = $ 27,162.50 Cash = $108,650 X 5% = $ 5,432.50 Total = $108,650.00 Step #4: Determine necessary adjustments by asset class. Current Target Value Value Action Equities $77,000.00 $76,055.00 Sell $945.00 Fixed Income $26,500.00 $27,162.50 Buy $662.50

Cash $ 5,150.00 $ 5,432.50 Buy $282.50 Total $108,650.00 $108,650.00 Question #6 : A company is projected to pay a dividend next year of $0.50 per share and have a growth rate of 6%. The target return on capital (ie. rate of return) is 9% and inflation is currently running at 2%. If the shares are currently trading at $15.00 per share on the TSX and you are a potential investor, would you buy the shares? Formula: FMV = Current Dividend ($) X (1 + Growth Rate %) Expected Rate of Return - Expected Dividend Growth Rate FMV = $0.50 X (1 + .06) .90 - .06 FMV = $0.50 X 1.06 .03 FMV = $0.53 = $17.67 .03 Question #7 : A company is projected to make $3.50 in earnings per share next year and to have a payout ratio of 7%. The company has a long term growth rate is 8%. If a potential investor is targeting a 12% return on capital (ie. rate of return), what is the fair market value for the price of this company’s shares? Formula: FMV = Current Dividend ($) X (1 + Growth Rate %) Expected Rate of Return - Expected Dividend Growth Rate FMV = $0.25 X (1 + .08) .12 - .08 FMV = $0.25 X 1.08 .04 FMV = $0.27 = $6.75 .04

Question #8 : An investor purchased a $1000 per value bond, with a 5% coupon, for $98. The bond matured at par, a year later. What rate of return did the investor earn? Formula: Rate of Return (%) = Price ($) + Interest ($) - Par Purchase Price Rate of Return (%) = $100.00 + $5.00 - $98.00 $98.00 Rate of Return (%) = $105.00 - $98.00 $98.00 Rate of Return (%) = $7.00 = 7.14% $98.00 Question #9 : In 2019, Robert got a hot tip from a friend and invested $1,200 in three securities: $200 in High Flyer Inc., $300 in Skyrocket Ltd., and $700 in Sure-Thing Enterprises. At year-end High Flyer Inc. is up 10%, Skyrocket Ltd. is down 5% and Sure-Thing Enterprises is up 12%. What is the return that Robert earned on his portfolio measured in dollars? Formula: Determine the current dollar value in each asset class. Rate of Return ($) = ($ x %) + ($ x %) + ($ x %) High Flyer Inc. = $200 X 10% (1.1) = $ 220.00 Skyrocket Ltd. = $300 X -5% (.95) = $ 285.00 Sure-Thing Ent. = $700 X 12% (1.12) = $ 784.00 Total = $1,289.00

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Initial Investment = $1,200 Current Value = $1,289 Increase = $ 89 Question #10 : On December 31, 2020, Robert wins $200,000 in Lotto 649. He invests it 50% in equities, 40% in fixed income and keeps 10% in cash. So far, in 2021, the rates of return for each asset class have been: equities are up 20%, fixed income are up 5% and cash is unchanged. How should the portfolio be re-balanced? Step #1: Determine the original dollar value invested in each asset class. Equities = $200,000 X 50% = $ 100,000 Fixed Income = $200,000 X 40% = $ 80,000 Cash = $200,000 X 10% = $ 20,000 Total = $200,000 Step #2: Determine the current weighting and dollar value in each asset class. Equities = $100,000 X 20% = $ 120,000 Fixed Income = $ 80,000 X 5% = $ 84,000 Cash = $ 20,000 X 0% = $ 20,000 Total = $224,000 Step #3: Using the base portfolio allocation, determine what the proper amount of money should be in each asset class for the current portfolio value. Equities = $224,000 X 50% = $ 112,000 Fixed Income = $224,000 X 40% = $ 89,600 Cash = $224,000 X 10% = $ 22,400 Total = $224,000 Step #4: Determine necessary adjustments by asset class. Current Target Value Value Action

Equities $120,000 $112,000 Sell $8,000 Fixed Income $ 84,000 $ 89,600 Buy $5,600 Cash $ 20,000 $ 22,400 Buy $2,400 Total $224,000 $224,000 Question #11: An investor’s $400,000 portfolio has a long-term strategic asset allocation of 50% in equities, 30% in bonds and 20% in cash. By the time of the next portfolio review date between the investor and her advisor, the equity portion of the portfolio had fallen in value by 10% and the bond holdings had risen in value of 10%. The cash value had remained unchanged. In order the re-balance the portfolio back to the initially agreed strategic allocation, how should the advisor make this change Step #1: Determine the original dollar value invested in each asset class. Equities = $400,000 X 50% = $ 200,000 Fixed Income = $400,000 X 30% = $ 120,000 Cash = $400,000 X 20% = $ 80,000 Total = $400,000 Step #2: Determine the current weighting and dollar value in each asset class. Equities = $200,000 X -10% = $ 180,000 Fixed Income = $120,000 X 10% = $ 132,000 Cash = $ 80,000 X 0% = $ 80,000 Total = $392,000 Step #3: Using the base portfolio allocation, determine what the proper amount of money should be in each asset class for the current portfolio value. Equities = $392,000 X 50% = $ 196,000 Fixed Income = $392,000 X 30% = $ 117,600 Cash = $392,000 X 20% = $ 78,400 Total = $392,000 Step #4: Determine necessary adjustments by asset class.

Current Target Value Value Action Equities $ 180,000 $ 196,000 Buy $16,000 Fixed Income $ 132,000 $ 117,600 Sell $14,400 Cash $ 80,000 $ 78,400 Sell $ 1,600 Total $392,000 $392,000

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