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Tutorial FiveProblems1. Periodic Interest Rates. In the following table, fill in the periodic rates and the effective annual rates.Semiannual10%2Quarterly12%4Monthly9%12Daily5.25%3652. Periodic Interest Rates. You have a savings account in which you leave the funds for one year without adding or withdrawing from the account. What would you rather have: a daily compounded rate of 0.045%, a weekly compounded rate of 0.305%, a monthly compounded rate of 1.5%, a quarterly compounded rate of 4.5%, a semiannually compounded rate of 9.75%, or an annually compounded rate of 19%?3. EAR. What is the effective annual rate of a mortgage rate that is advertised at 7.25% (APR) over the next twenty years and paid with quarterly payments?4. EAR. What is the effective rate of a monthly car loan that is advertised at 10% (APR)?5.Present value with periodic rates. Let’s follow up with Sam Hinds, the dentist, from Chapter 4 and his remodeling project (Problem 12). The cost of the equipment for the project is $18,000, and the purchase will be financed with a 7.5% loan over six years. Originally, the loan called for annual payments. Redo the payments based on quarterly payments (four per year) and monthly payments (twelve per year). Compare the annual cash outflow of the two payments. Why does the monthly payment plan have less total cash outflow each year?6.Present value with periodic rates. Cooley Landscaping needs to borrow $30,000 for a new front-end dirt loader. The bank is willing to loan the money at 8.5% interest for the next ten years with annual, semiannual, quarterly, or monthly payments. What are the different payments that Cooley Landscaping could choose for these different payment plans?7. Future Value with Periodic Rates. Matt Johnson delivers newspapers and is putting away $20.00 every month from his paper route collections. Matt is thirteen years old and will use the money when he goes to college in five years. What will be the value of Matt’s account in five years with his monthly payments if he is earning 6% (APR), 8% (APR), or 12% (APR)?8.Future value with periodic rates. We return to Denise, our hopeful millionaire from Chapter 4 (Example 4.3) and this chapter (Example 5.2). In Chapter 4, Denise was putting away $5,000 per year at the end of each year at 6% interest, with the expectation that in forty-four years she would be a millionaire. If Denise switches to a monthly savings plan and puts one-twelfth of the $5,000 away each month ($416.66), how much will she have in forty-four years at the 6% APR? Why is it more than the $1,000,000 goal? In this chapter, Denise was putting away $546.23 for thirty years at 9% to become a millionaire. Why does it take more per month when she is putting money away at 9% than when she was earning a lower rate of 6% over the forty-four years? Hint: what interest rate would she need for the 30 years putting away $416.66 to match the future value when she started fourteen years earlier at 6%?So Denise would have to find an investment rate of 10.62% for the next 30 years if she wanted to match the same future value. If she can only get 9%, she will need to increase her monthly contributions to reach the same $1,076,759.95 future value.9.Payments with periodic rates. What payment does Denise (from problem 8) need to make at the end of each month over the coming forty-four years at 6% to reach her retirement goal of $1,000,000?10. Savings with Periodic Rates. What investment per month does Patrick need to make at the end of each month into his savings account over the coming eighteen months to reach his vacation goal of $8,000 if he is getting 5% APR on his account?Tutorial SixProblemsBond Prices: Use the following table for problems 1 through 4.Par ValueCoupon RateYears to MaturityYield to MaturityPrice$1,000.008%106%?$1,000.006%108%?$5,000.009%207%?$5,000.0012%305%?1.Price the bonds from the above table with annual coupon payments.2.Price the bonds from the above table with semiannual coupon payments.ANSWERPrice = $1,000.00 × 1/(1.03)20 + $40.00 (1 – 1/(1.03)20)/ 0.03Price = $1,000.00 × 0.5537 + $40.00 × 14.8775Price = $553.67 + $595.10 = $1,148.77Price = $1,000.00 × 1/(1.04)20 + $30.00 (1 – 1/(1.04)20)/ 0.04Price = $1,000.00 × 0.4564 + $30.00 × 13.5903Price = $456.39 + $407.71 = $864.10Price = $5,000.00 × 1/(1.035)40 + $225.00 (1 – 1/(1.035)40)/ 0.035Price = $5,000.00 × 0.2526 + $225.00 × 21.3551Price = $1,262.86 + $4,804.90 = $6,067.75Price = $5,000.00 × 1/(1.025)60 + $300.00 (1 – 1/(1.025)60)/ 0.025Price = $5,000.00 × 0.2273 + $300.00 × 30.9087Price = $1,136.41 + $9,272.60 = $10,409.013.Price the bonds from the above table with quarterly coupon payments.ANSWERPrice = $1,000.00 × 1/(1.015)40 + $20.00 (1 – 1/(1.015)40)/ 0.015Price = $1,000.00 × 0.5584 + $20.00 × 7.3601Price = $558.39 + $588.81 = $1,085.84Price = $1,000.00 × 1/(1.02)40 + $15.00 (1 – 1/(1.02)40)/ 0.02Price = $1,000.00 × 0.4632 + $15.00 × 6.7101Price = $463.19 + $402.60 = $863.22Price = $5,000.00 × 1/(1.0175)80 + $75.00 (1 – 1/(1.0175)80)/ 0.0175Price = $5,000.00 × 0.2584 + $75.00 × 10.5940Price = $1,292.10 + $3,178.20 = $4,464Price = $5,000.00 × 1/(1.0125)120 + $150.00 (1 – 1/(1.0125)120)/ 0.0125Price = $5,000.00 × 0.2314 + $150.00 × 15.3725Price = $1,156.89 + $9,223.47 = $10,423.504.Price the bonds from the above table with monthly coupon payments.ANSWERPrice = $1,000.00 × 1/(1.005)120 + $6.67 (1 – 1/(1.005)120)/ 0.005Price = $1,000.00 × 0.5584 + $6.67 × 7.3601Price = $558.39 + $588.81 = $1,150.42Price = $1,000.00 × 1/(1.0067)120 + $5.00 (1 – 1/(1.0067)120)/ 0.0067Price = $1,000.00 × 0.4632 + $5.00 × 6.7101Price = $463.19 + $402.60 = $860.13Price = $5,000.00 × 1/(1.0058)240 + $37.50 (1 – 1/(1.0058)240)/ 0.0058Price = $5,000.00 × 0.2476 + $37.50 × 128.98Price = $1,238.01 + $4,836.84 = $6,074.85Price = $5,000.00 × 1/(1.0042)360 + $50.00 (1 – 1/(1.0042)360)/ 0.0042Price = $5,000.00 × 0.2314 + $50.00 × 15.3725Price = $1,156.89 + $9,223.47 = 10,377.65Yield-to-Maturity: Use the following table for problems 5 through 8.Par ValueCoupon RateYears to MaturityYield to MaturityPrice$1,000.008%10?$1000.00$1,000.006%10?$850.00$5,000.009%20?$5,400.00$5,000.0012%30?$4,300.005.What is the yield of the above bonds if interest (coupon) is paid annually?ANSWER(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1INPUT10?-1000.0080.001000.00KEYSNI/YPVPMTFVCPT8.0(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1INPUT10?-850.0060.001000.00KEYSNI/YPVPMTFVCPT8.2619(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1INPUT20?-5400.00450.005000.00KEYSNI/YPVPMTFVCPT8.1746(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1INPUT30?-4300.00600.005000.00KEYSNI/YPVPMTFVCPT13.99916.What is the yield of the above bonds if interest (coupon) is paid semiannually?ANSWER(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2INPUT20?-1000.0040.001000.00KEYSNI/YPVPMTFVCPT8.0(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2INPUT20?-850.0030.001000.00KEYSNI/YPVPMTFVCPT8.2300(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2INPUT40?-5400.00225.005000.00KEYSNI/YPVPMTFVCPT8.1807(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2INPUT60?-4300.00300.005000.00KEYSNI/YPVPMTFVCPT13.99367.What is the yield of the above bonds if interest (coupon) is paid quarterly?ANSWER(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4INPUT40?-1000.0020.001000.00KEYSNI/YPVPMTFVCPT8.0(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4INPUT40?-850.0015.001000.00KEYSNI/YPVPMTFVCPT8.2140(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4INPUT80?-5400.00112.505000.00KEYSNI/YPVPMTFVCPT8.1838(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4INPUT120?-4300.00150.005000.00KEYSNI/YPVPMTFVCPT13.99098.What is the yield of the above bonds if interest (coupon) is paid monthly?ANSWER(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12INPUT120?-1000.006.671000.00KEYSNI/YPVPMTFVCPT8.0(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12INPUT120?-850.0030.001000.00KEYSNI/YPVPMTFVCPT8.2033(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12INPUT240?-5400.0037.505000.00KEYSNI/YPVPMTFVCPT8.1859(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12INPUT360?-4300.0050.005000.00KEYSNI/YPVPMTFVCPT13.9891Tutorial Seven1.Anderson Motors Inc. has just set the company dividend policy at $0.80 per year. The company plans to be in business forever. What is the price of this stock ifa. An investor wants a 5% return?b. An investor wants an 8% return?c. An investor wants a 10% return?d. An investor wants a 12.5% return?e. An investor wants a 20% return?ANSWERUse the constant dividend infinite dividend stream model:Price ??Dividend/ra. Price ??$0.80/0.05 ??$16.00b. Price ??$0.80/0.08 ??$10.00c. Price ??$0.80/0.10 ??$8.00d. Price ??$0.80/0.125 ??$6.40e. Price ??$0.80/0.20 ??$4.002.Diettreich Electronics wants its shareholders to earn a 16% return on their investment in the company. At what price would the stock need to be priced today if Diettreich had aa. $0.40 constant annual dividend forever?b. $1.00 constant annual dividend forever?c. $1.80 constant annual dividend forever?d. $2.40 constant annual dividend forever?ANSWERUse the constant dividend with infinite horizon model:Price ??Dividend/ra. Price ??$0.40/0.16 ??$2.50b. Price ??$1.00/0.16 ??$6.25c. Price ??$1.80/0.16 ??$11.25d. Price ??$2.40/0.16 ??$15.003.Singing Fish Fine Foods has a current annual cash dividend policy of $2.25. The price of the stock is set to yield a 12% return. What is the price of this stock if the dividend will be paida.for 10 years?b.for 15 years?c.for 40 years?d.for 60 years?e.for 100 years?f.forever?ANSWERUse the finite constant dividend model except with f (use infinite constant dividend model)Price = Dividend × (1 – 1/(1+r)n) / r a.Price = $2.25 × (1 – 1/(1.12)10 / 0.12 = $2.25 × 5.6502 = $12.71b.Price = $2.25 × (1 – 1/(1.12)15 / 0.12 = $2.25 × 6.8109 = $15.32c.Price = $2.25 × (1 – 1/(1.12)40 / 0.12 = $2.25 × 8.2438 = $18.54d.Price = $2.25 × (1 – 1/(1.12)60 / 0.12 = $2.25 × 8.3240 = $18.73e.Price = $2.25 × (1 – 1/(1.12)100 / 0.12 = $2.25 × 8.3332 = $18.75f.Price = $2.25 / 0.12 = $18.754.Pfender Guitars has a current annual cash dividend policy of $4.00. The price of the stock is set to yield an 8% return. What is the price of this stock if the dividend will be paida.for 10 years and then a liquidating or final dividend of $25.00?b.for 15 years and then a liquidating or final dividend of $25.00?c.for 40 years and then a liquidating or final dividend of $25.00?d.for 60 years and then a liquidating or final dividend of $25.00?e.for 100 years and then a liquidating or final dividend of $25.00?f.forever with no liquidating dividend?ANSWERUse the finite constant dividend model liquidating dividend except with f (use infinite constant dividend model)Price = Dividend × (1 – 1/(1 + r)n) / r + Liquidating Dividend × (1/(1 + r)n)a.Price = $4.00 × (1 – 1/(1.08)10 / 0.08 + $25.00 × 1/1.0810= $4.00 × 6.7101 + $25 × 0.4632 = $26.84 + $11.58 = $38.42b.Price = $4.00 × (1 – 1/(1.08)15 / 0.08 + $25.00 × 1/1.0815= $4.00 × 8.5595 + $25 × 0.3152 = $34.24 + $7.88 = $42.12c.Price = $4.00 × (1 – 1/(1.08)40 / 0.08 + $25.00 × 1/1.0840= $4.00 × 11.9246 + $25 × 0.0460 = $47.70 + $1.15 = $48.85d.Price = $4.00 × (1 – 1/(1.08)60 / 0.08 + $25.00 × 1/1.0860= $4.00 × 12.3766 + $25 × 0.0099 = $49.51 + $0.24 = $49.75e.Price = $4.00 × (1 – 1/(1.08)100 / 0.08 + $25.00 × 1/1.08100= $4.00 × 12.4943 + $25 × 0.0005 = $49.98 + $0.01 = $49.99f.Price = $4.00 / 0.08 = $50.005.King Waterbeds has an annual cash dividend policy that raises the dividend each year by 4%.Last year’s dividend was $0.50 per share. What is the price of this stock ifa. an investor wants a 6% return?b. an investor wants an 9% return?c. an investor wants a 10% return?d. an investor wants a 14% return?e. an investor wants a 20% return?ANSWERUse the constant growth dividend model with infinite horizon:Price ??Last Dividend X?(1 ??g)/(r ??g)a. Price ??$0.50 X?(1.04)/(0.06 ??0.04) ??$0.52/0.02 ??$26.00b. Price ??$0.50 X?(1.04)/(0.09 ??0.04) ??$0. 52/0.05 ??$10.40c. Price ??$0.50 X?(1.04)/(0.10 ??0.04) ??$0. 52/0.06 ??$8.67d. Price ??$0.50 X?(1.04)/(0.14 ??0.04) ??$0. 52/0.10 ??$5.20e. Price ??$0.50 X?(1.04)/(0.20 ??0.04) ??$0. 52/0.16 ??$3.256.Seitz Glassware is trying to determine its growth rate for an annual cash dividend. Last year’sdividend was $0.35 per share. The target return rate for the stock is 12%. What is the price ofthis stock ifa. the annual growth rate is 2%?b. the annual growth rate is 4%?c. the annual growth rate is 5%?d. the annual growth rate is 8%?e. the annual growth rate is 10%?ANSWERUse the constant growth dividend model with infinite horizon:Price ??Last Dividend X?(1 ??g)/(r ??g)a. Price ??$0.35 X?(1.02)/(0.12 ??0.02) ??$0.357/0.10 ??$3.57b. Price ??$0.35 X?(1.04)/(0.12 ??0.04) ??$0.364/0.08 ??$4.55c. Price ??$0.35 X?(1.05)/(0.12 ??0.05) ??$0.3675/0.07 ??$5.25d. Price ??$0.35 X?(1.08)/(0.12 ??0.08) ??$0.378/0.04 ??$9.45e. Price ??$0.35 X?(1.10)/(0.12 ??0.10) ??$0.385/0.02 ??$19.257.Miles Hardware has an annual cash dividend policy that raises the dividend each year by 3%. Last year’s dividend was $1.00 per share. Investors want a 15% return on this stock. What is the stock’s price if a.the company will be in business for 5 years and not have a liquidating dividend?b.the company will be in business for 15 years and not have a liquidating dividend?c.the company will be in business for 25 years and not have a liquidating dividend?d.the company will be in business for 35 years and not have a liquidating dividend?e.the company will be in business for 75 years and not have a liquidating dividend?f.forever?ANSWERUse the constant growth dividend model with a finite dividend stream:Price = Last Dividend × (1 + g) / (r – g) × [1 – ((1+g) / (1+r))n]a.Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))5]= $1.03 / 0.12 × [1 - 0.5764] = $8.58 × [0.4236] = $3.64b.Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))15]= $1.03 / 0.12 × [1 - 0.1915] = $8.58 × [0.8085] = $6.94c.Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))25]= $1.03 / 0.12 × [1 - 0.0636] = $8.58 × [0.9364] = $8.03d.Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))35]= $1.03 / 0.12 × [1 - 0.0211] = $8.58 × [0.9789] = $8.40e.Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))75]= $1.03 / 0.12 × [1 - 0.0003] = $8.58 × [0.9997] = $8.58f.Price = $1.00 × (1.03) / (0.15 – 0.03) = $1.03 / 0.12 = $8.588.Sia Dance Studios has an annual cash dividend policy that raises the dividend each year by 2%. Last year’s dividend was $3.00 per share. The company will be in business for forty years with no liquidating dividend. What is the price of this stock if a.an investor wants a 9% return?b.an investor wants an 11% return?c.an investor wants a 13% return?d.an investor wants a 15% return?e.an investor wants a 17% return?ANSWERUse the constant growth dividend model with a finite dividend stream:Price = Last Dividend × (1 + g) / (r – g) × [1 – ((1+g) / (1+r))n]a.Price = $3.00 × (1.02) / (0.09 – 0.02) × [1 – ((1.02) / (1.09))40]= $3.06 / 0.07 × [1 - 0.0703] = $43.71 × [0.9297] = $40.64b.Price = $3.00 × (1.02) / (0.11 – 0.02) × [1 – ((1.02) / (1.11))40]= $3.06 / 0.09 × [1 - 0.0340] = $34.00 × [0.9660] = $32.85c.Price = $3.00 × (1.02) / (0.13 – 0.02) × [1 – ((1.02) / (1.13))40]= $3.06 / 0.11 × [1 - 0.0166] = $27.82 × [0.9834] = $27.35d.Price = $3.00 × (1.02) / (0.15 – 0.02) × [1 – ((1.02) / (1.15))40]= $3.06 / 0.13 × [1 - 0.0082] = $23.54 × [0.9918] = $23.35e.Price = $3.00 × (1.02) / (0.17 – 0.02) × [1 – ((1.02) / (1.17))40]= $3.06 / 0.15 × [1 - 0.0041] = $20.40 × [0.9959] = $20.329.Fey Fashions expects the following dividend pattern over the next seven years:Year 1Year 2Year 3Year 4Year 5Year 6Year 7$1.00$1.10$1.21$1.33$1.46$1.61$1.77Then the company will have a constant dividend of $2.00 forever. What is the price of this stock today if an investor wants to earn a.15%?b.20%?ANSWERThere are two dividend patterns here; the first is a constant growth pattern for the next seven years and then a constant dividend forever. Solve each part separately and then add the two parts.Part one: Constant growth for seven years, first find growth rate and note that there are six changes in the dividend stream over the seven years.g = ($1.77 / $1.00)1/6 – 1 = 1.771/6 – 1 = 10%Next, use the finite dividend growth modelPrice = Dividend × (1 + g) / (r – g) × [1 – ((1+g) / (1+r))n]Part two: Use the constant dividend (infinite period) model and then discount the price at period 7 back to the presentPrice7 = Dividend8 / rPrice0 = Price7 / (1 + r)7a.Part One Price = $1.00 (1.10) / (0.15 – 0.10) × [ 1 – (1.10/1.15)7]Part One Price = $22.00 × 0.2674 = $5.88Part Two Price = ($2.00 / 0.15) / (1.15)7 = $13.33 / 2.66 = $5.01Price = $5.88 + $5.01 = $10.89b.Part One Price = $1.00 (1.10) / (0.20 – 0.10) × [ 1 – (1.10/1.20)7]Part One Price = $11.00 × 0.4561 = $5.02Part Two Price = ($2.00 / 0.20) / (1.20)7 = $10.00 / 3.5832 = $2.79Price = $5.02 + $2.79 = $7.8110.Staton-Smith Software is a new up-start company and will not pay dividends for the first five years of operation. It will then institute an annual cash dividend policy of $2.50 with a constant growth rate of 5% with the first dividend at the end of year six. The company will be in business for 25 years total. What is the price of this stock if an investor wantsa.a 10% return?b.a 15% return?c.a 20% return?d.a 40% return?ANSWERCalculate the price at the beginning of the sixth year (end of the fifth year) with the finite constant growth dividend model and then discount the price by five years to the present value.a.Price5 = $2.50 / (0.10 – 0.05) × [1 – (1.05/1.10)20]Price5 = $50.00 × 0.6056 = $30.28Price0 = $30.28 / 1.105 = $30.28 / 1.6105 = $18.80b.Price5 = $2.50 / (0.15 – 0.05) × [1 – (1.05/1.15)20]Price5 = $25.00 × 0.8379 = $20.95Price0 = $20.95 / 1.155 = $20.95 / 2.0114 = $10.41c.Price5 = $2.50 / (0.20 – 0.05) × [1 – (1.05/1.20)20]Price5 = $16.67 × 0.9308 = $15.51Price0 = $15.51 / 1.205 = $15.51 / 2.4883 = $6.23d.Price5 = $2.50 / (0.40 – 0.05) × [1 – (1.05/1.40)20]Price5 = $7.14 × 0.9968 = $7.12Price0 = $7.12 / 1.405 = $7.12 / 5.3782 = $1.32Tutorial Eight1.Profits. What are the profits on the following investments?InvestmentOriginal Cost or Invested $Selling Price of InvestmentDistributions Received $Dollar ProfitCD$500.00$540.00$0.00Stock$23.00$34.00$2.00Bond$1,040.00$980.00$80.00Bike$400.00$220.00$0.00ANSWERInvestmentOriginal Cost or Invested $Selling Price of InvestmentDistributions Received $Dollar ProfitCD$500.00$540.00$0.00$40Stock$23.00$34.00$2.00$13Bond$1,040.00$980.00$80.00$20Bike$400.00$220.00$0.00-$180CD Dollar Return = $540 + $0 – $500 = $40Stock Dollar Return = $34 + $2 – $23 = $13Bond Dollar Return = $980 + $80 – $1,040 = $20Bike Dollar Return = $220 + $0 – $400 = -$1802.Profits. What are the profits on the following investments?InvestmentOriginal Cost or Invested $Selling Price of InvestmentDistributions Received $Dollar ProfitsCD$500.00$525.00$0.00Stock$34.00$26.00$2.00Bond$955.00$1000.00$240.00Car$42,000.00$3,220.00$0.00ANSWERInvestmentOriginal Cost or Invested $Selling Price of InvestmentDistributions Received $Dollar ProfitsCD$500.00$525.00$0.00$25Stock$34.00$26.00$2.00-$6Bond$955.00$1000.00$240.00$285Car$42,000.00$3,220.00$0.00-$38,780CD Dollar Return = $525 + $0 – $500 = $25Stock Dollar Return = $26 + $2 – $34 = -$6Bond Dollar Return = $1,000 + $240 – $955 = $285Car Dollar Return = $3,220 + $0 – $42,000 = -$38,7803.Returns. What are the returns on the following investments?InvestmentOriginal Cost or Invested $Selling Price of InvestmentDistributions Received $Percent ReturnCD$500.00$540.00$0.00Stock$23.00$34.00$2.00Bond$1,040.00$980.00$80.00Bike$400.00$220.00$0.00ANSWERInvestmentOriginal Cost or Invested $Selling Price of InvestmentDistributions Received $Percent ReturnCD$500.00$540.00$0.008.00%Stock$23.00$34.00$2.0056.52%Bond$1,040.00$980.00$80.001.92%Bike$400.00$220.00$0.00-45.00%CD Percent Return = ($540 + $0 – $500) / $500 = 0.0500 or 8.00%Stock Percent Return = ($34 + $2 – $23) / $23 = 0.565217 or 56.52%Bond Percent Return = ($980 + $80 – $1040) / $1040 = 0.01923 or 1.92%Bike Percent Return = ($220 + $0 – $400) / $400 = -0.45 or -45%4.Returns. What are the returns on the following investments?InvestmentOriginal Cost or Invested $Selling Price of InvestmentDistributions Received $Percent ReturnCD$500.00$525.00$0.00Stock$34.00$2600$2.00Bond$955.00$1000.00$240.00Car$42,000.00$3,220.00$0.00ANSWERInvestmentOriginal Cost or Invested $Selling Price of InvestmentDistributions Received $Percent ReturnCD$500.00$525.00$0.005.00%Stock$34.00$2600$2.00-17.65%Bond$955.00$1000.00$240.0029.84%Car$42,000.00$3,220.00$0.00-92.33%CD Percent Return = ($525 + $0 – $500) / $500 = 0.0500 or 5.00%Stock Percent Return = ($26 + $2 – $34) / $34 = -0.1765 or -17.65%Bond Percent Return = ($1,000 + $240 – $955) / $955 = 0.2984 or 29.84%Car Percent Return = ($3,220 + $0 – $42,000) / $42,000 = -0.9233 or -92.33%5.Holding Period and Annual (Investment) Returns. Baker Baseball Cards Incorporated originally purchased the rookie card of Hammerin’ Hank Aaron for $40.00. After holding the card for five years, Baker Baseball Cards auctioned off the card for $200.00. What are the holding period return and the annual return on this investment?ANSWERHolding Period Return ??($200 ??$40)/$40 ??4.00 or 400%Annual Percentage return ??HPR/n ??400%/5 ??80%EAR ??(1 ??4.00)1/5 ??1 ??1.3797 ??1 ??0.3797, or 37.97%6.Holding Period and Annual (Investment) Returns. Bohenick Classic Automobiles restores and rebuilds old classic cars. The company purchased and restored a classic 1957 Thunderbird convertible six years ago for $8,500. Today at auction, the car sold for $50,000. What are the holding period return and the annual return on this investment?ANSWERHolding Period Return = ($50,000 – $8,500) / $8,500 = 4.8824 or 488.24%APR = HPR/n = 488.24%/6 = 81.37%EAR = (1 + 4.8824)1/6 – 1 = 1.3436 – 1 = 0.3436 or 34.36%parison of returns. Looking back at Problems 5 and 6, which investment had the higher holding period return? Which had the higher annual return?ANSWERHolding Period Return for Trading Card = ($180 – $35) / $35 = 4.1429 or 414.29%Holding Period Return for Classic Car = ($50,000 – $8,500) / $8,500 = 4.8824 or 488.24%Trading Card HPR< Classic Car HPRTrading Card APR= HPR/n = 414.29%/5 = 82.86%Classic Car APR= HPR/n = 488.24%/6 = 81.37%Trading Card APR> Classic Car APR82.86%>81.37%Trading Card EAR= (1 + 4.1429)1/5 – 1 = 1.3875 – 1 = 0.3875 or 38.75%Classic Car Annual Return= (1 + 4.8824)1/6 – 1 = 1.3436 – 1 = 0.3436 or 34.36%Trading Card EAR> Classic Car EAR.parison of returns. WG Investors are looking at three different investment opportunities. Investment One is a five-year investment with a cost of $125 and a promised payout of $250 at maturity. Investment Two is a seven-year investment with a cost of $125 and a promised payout of $350. Investment Three is a ten-year investment with a cost of $125 and a promised payout of $550. WG Investors can only take on one of the three investments. Assuming all three investment opportunities have the same level of risk, calculate the annual return for each investment and select the best investment choice.ANSWERHolding Period Return for Investment One = ($250 – $125) / $125 = 1.00 or 100.00%EAR-- Investment One = (1 + 1.00)1/5 – 1 = 1.1487 – 1 = 0.1487 or 14.87%Holding Period Return for Investment Two = ($350 – $125) / $125 = 1.80 or 180.00%EAR-- Investment Two = (1 + 1.80)1/7 – 1 = 1.1585 – 1 = 0.1585 or 15.85%Holding Period Return for Investment Three= ($550 – $125) / $125 = 3.40 or 340.00%EAR-- Investment Three = (1 + 3.40)1/10 – 1 = 1.15969 – 1 = 0.15967 or 15.97%Investment Three has the highest annual return rate of the three choices. If all choices have the same level of risk, choose Investment Three.9.Historical returns. Calculate the average return of the U.S. Treasury bills, long-term government bonds, and large company stocks for 1990–1998 from Table 8.1. Which had the highest and which had the lowest return?ANSWERAverage Return U.S. Treasury Bill for 90s: 5.02%Average Return U.S. Long-Term Government Bonds for 90s: 9.23%Average Return U.S. Large Company Stocks for 90s: 18.99%Highest was Large Company Stocks, Lowest was 3 Month T-Bills10.Historical returns. Calculate the average return of the U.S. Treasury bills, long-term government bonds, and large company stocks for the 1950 to 1959, 1960 to 1969, 1970 to 1979, and 1980 to 1989 from Table 8.1. Which had the highest return? Which had the lowest return?ANSWERAnswer from data is:Average Return U.S. Treasury Bill for 50s: 1.87%Average Return U.S. Long-Term Government Bonds for 50s: 0.35%Average Return U.S. Large Company Stocks for 50s: 20.94%Answer from data is:Average Return U.S. Treasury Bill for 60s: 3.90%Average Return U.S. Long-Term Government Bonds for 60s: 1.31%Average Return U.S. Large Company Stocks for 60s: 8.74%Answer from data is:Average Return U.S. Treasury Bill for 70s: 6.31%Average Return U.S. Long-Term Government Bonds for 70s: 6.80%Average Return U.S. Large Company Stocks for 70s: 7.55%Answer from data is:Average Return U.S. Treasury Bill for 80s: 9.04%Average Return U.S. Long-Term Government Bonds for 80s: 11.99%Average Return U.S. Large Company Stocks for 80s: 18.24%Highest Return was 20.94% in the 50s for Large Company Stocks and the lowest return was 0.35% for Long-Term Government Bonds in the 50s. ................
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