investment questions
Tom Jones follows a dollar-cost-averaging approach when purchasing shares of an S&P 500 index fund. Calculate his average cost per share. Year Investment Price per Share 1 $600 $67 2 $600 $72 3 $600 $88 4 $600 $80 5 $600 $89 A) $78.23. B) $79.20. C) $79.77. D) $78.67.
A) $78.23. To calculate the average cost per share, we need to find the total shares purchased and the total amount invested. Year Investment Price per Share Shares Purchased 1 $600 $67 8.96 2 $600 $72 8.33 3 $600 $88 6.82 4 $600 $80 7.50 5 $600 $89 6.74 Total Amount Invested = $600 × 5 = $3,000 Total shares purchased = 38.35 Average cost per share = $3,000 ÷ 38.35 = $78.23
Mike wants to purchase an additional stock for his investment portfolio. He has a required rate of return of 11.5%. Assume the risk-free rate of return is 5% and the expected rate of return of the market portfolio is 12%. What is the expected rate of return for XYZ stock with beta of 1.1? Should Mike invest in the stock? A) 12.7%, yes B) 9.1, no C) 10.8, no D) 12.1%, yes
A) 12.7%, yes The expected rate of return can be found by using the capital asset pricing model (CAPM). ri = rf + (rm − rf)βi = 0.05 + (0.12 − 0.05)1.1 = 0.127, or 12.7% Because the expected rate of return, as determined by CAPM, exceeds Mike's required rate of return, he may elect to purchase XYZ stock for his investment portfolio.
What is the duration of a bond purchased for $948.50 that matures in 5 years and has a coupon rate of 12.5%? (Assume annual coupon payments.) A) 3.977 years. B) 3.919 years. C) 4.006 years. D) 3.948 years.
A) 3.977 years. Step 1: Solve for YTM to determine the appropriate interest rate. Yield to Maturity PV = (948.50) n = 5 PMT = 125 FV = 1,000 i = 14% Step 2: Use the cash flow method to solve for duration. Year CF CF × Year 1 125 125 2 125 250 3 125 375 4 125 500 5 1,125 5,625 CF0 0 CF1 125 CF2 250 CF3 375 CF4 500 CF5 5,625 I/YR = 14 NPV = $3,772.62 Duration = NPV ÷ Bond Price Duration = $3,772.62 ÷ $948.50 = 3.977 years
A $1,000 U.S. Treasury note maturing in 8 years is selling for $938.12. The semiannual coupon payment is $35. What is the yield to maturity for the note? A) 8.06%. B) 4.03%. C) 6.26%. D) 8.33%.
A) 8.06%. Compute the yield to maturity as follows: PV = −938.12 PMT = 35 FV = 1,000 n = 8 × 2 = 16 i = 4.03 × 2 = 8.06%
XYZ mutual fund had the following returns for the past five years: Year Return 1 8.5% 2 −5.3% 3 10.5% 4 6.6% 5 −2.8% Based on a normal distribution of returns, what percent of returns should fall below 10.58%? A) 84% B) 0% C) 16% D) 99%
A) 84% The standard deviation of the returns is 7.08% and the arithmetic mean is 3.5%. One standard deviation to the right of 3.5% is 10.58%. Fifty percent of returns lie below the 3.5% and an additional 34% of returns fall between 3.5% and 10.58% resulting in 84% of returns falling below 10.58%. Calculations: Arithmetic mean (8.5 - 5.3 + 10.5 + 6.6 - 2.8) ÷ 5 = 3.5% Standard deviation (keystrokes are shown for the HP 10BII/10BII+) [■] [C ALL] 8.5 [Σ+] 5.3 [+/-][Σ+] 10.5 [Σ+] 6.6 [Σ+] 2.8 [+/-][Σ+] [■] [Sx, Sy] 7.0841%
Samuel's bond has a current market value of $1,056.78 and Macaulay duration of 7.9. If the bond's yield-to-maturity (YTM) changes from 5.5% to 4.0%, what is the new expected market price of the bond? A) $1,175.46 B) $1,140.27 C) $938.10 D) $1,040.93
B) $1,140.27 The formula for determining the change in the price of the bond: ΔP/P = −D(Δy ÷ (1 + y)) ΔP/P = −7.9[((1+.04) − (1+.055)) ÷ (1+.055)] ΔP/P = -−7.9(−0.0142) = .1123, or 11.23% This means that the bond's price should increase by 11.23% and sell for $1,175.46 in the secondary market.
Hurley wishes to purchase a boat in 20 years when he retires so that he may sail around the world. If the boat presently costs $450,000 and inflation is 4%, how much should he deposit at the beginning of each year to have enough to purchase the boat at the end of 20 years? Assume that Hurley will earn an average compounded return of 12.5% on his investments (round to the nearest dollar). A) $8,573. B) $11,478. C) $5,238. D) $12,912.
B) $11,478. Future Cost of Boat PV = 450,000 n = 20 i = 4 PMT = 0 FV = (986,005) Yearly Required Deposit PV = 0 n = 20 i = 12.5 FV = 986,005 PMT = (11,477.74), or $11,477.74
Ten years ago, Leslie purchased 1,000 shares of XYZ stock for $45,000. She is considering selling these shares to help her mother purchase a new condominium in a retirement community. Her mother needs $50,000 to purchase the unit and make upgrades and improvements. The stock is currently trading at $62.50 per share. Leslie and her CFP® professional agree to sell enough shares to fund this goal. Assuming she sells the stock at the current market price, what is the tax consequence? A) $31,000 ordinary income. B) $14,000 long-term capital gain. C) $5,000 short-tem capital gain. D) $12,500 long-term capital gain
B) $14,000 long-term capital gain Leslie will incur a long-term capital gain of $14,000. Basis per share: $45 ($45,000 ÷ 1,000 shares) Number of shares to be sold to meet goal based on a current market price of $62.50: 800 ($50,000 ÷ $62.50) Basis in shares sold: $36,000 (800 shares × $45) Long-term capital gain: $14,000 ($50,000 - $36,000)
Bill bought 100 shares of XYZ stock at $45 per share. He bought a put option on XYZ stock for $1 per share with an exercise price of $48 when the stock was trading at $52. What is his paper profit if the stock drops to $40 per share? A) $300. B) $200. C) $800. D) $700.
B) $200. Bill will have a paper profit of $200, calculated as follows: $4,800 sale price −4,500 initial investment − 100 option premium $ 200 profit
Jeff is interested in BEC stock. BEC's earnings and dividends are expected to grow at a rate of 6% per year for the foreseeable future. If Jeff's required rate of return is 11%, what is the intrinsic value of BEC stock if it is currently paying a dividend of $1.20? A) $10.91 B) $25.44. C) $20.00. D) $24.00.
B) $25.44. Intrinsic value (using the constant growth dividend discount model) = D0(1 + g) ÷ (r − g) = $1.20 (1.06) ÷ (0.11 − 0.06) = $25.44 D0= constant dividend
Harvey, a fundamental stock analyst with a large brokerage firm, is researching ABC stock for one of the firm's clients. The stock has the following characteristics: Beta 2.05 Standard deviation 22.98% Current dividend $1.64 Investor's required rate of return 7.5% Risk-free rate of return 1.75% The current dividend is expected to grow for three years at a rate of 2.25% and then 2.75% thereafter. Based on the information provided, what is the intrinsic value of ABC stock? A) $38.11 B) $35.14 C) $32.95 D) $43.27
B) $35.14 1. Compute the value of each future dividend until the growth rate stabilizes (Years 1-3). D1 = $1.64 × 1.0225 = $1.68 D2 = $1.68 × 1.0225 = $1.72 D3 = $1.72 × 1.0225 = $1.76 2. Use the constant growth dividend discount model to compute the remaining intrinsic value of the stock at the beginning of the year when the dividend growth rate stabilizes (Year 4). D4 = $1.76 × 1.0275 = $1.81 V = $1.81 ÷ (.075 - .0275) = $38.11 3. Use the uneven cash flow method to solve for the net present (intrinsic) value of the stock. CF0 = $0 CF1 = $1.68 CF2 = $1.72 CF3 = $1.76 + $38.11 = $39.87 I/YR = 7.5% Solve for NPV = $35.14 The intrinsic value of the stock is $35.14.
Douglas, a stock analyst, has compiled the following information regarding recent returns for the market and for Stock A. Year Market Stock A 1 15% 12% 2 2% 4% 3 −8% −6% 4 12% 8% 5 6% 3% Stock A has a beta of 1.45 and the rate of return on 90-day US Treasury bills is 1.75%. Which of the following statements are CORRECT? The geometric mean of the market is 5.08%. The geometric mean of Stock A is 4.02%. The expected rate of return for Stock A is 6.83%. Stock A underperformed the market on a risk-adjusted basis. A) 2, 3, and 4. B) 1, 2, and 4. C) 1, 3, and 4. D) 1 and 3.
B) 1, 2, and 4. Market geometric mean: PV = −1; FV = (1 + .15)(1 + .02)(1 − .08)(1 + .12)(1 + .06) = 1.2812; N = 5; Solve for I/YR = 5.0805% Stock A geometric mean: PV = −1; FV = (1 + .12)(1 + .04)(1 − .06)(1 + .08)(1 + .03) = 1.2180; N = 5; Solve for I/YR = 4.0227% Stock A's expected rate of return (using CAPM): ri = 1.75 + (5.08 − 1.75)1.45 = 6.5785% Because the actual return of Stock A was below its expected rate of return, the stock underperformed the market on a risk-adjusted basis.
Kris buys one share of stock for $55. One year later the price of the stock has risen to $60, at which time she buys another share. At the end of the second and third years, the stock is priced at $65 and $68, respectively. Each year the stock pays $1 in dividends. Kris sells the stock at the end of year three. Cash outflow/inflow Dividends Received Net Cash Flow Initial Investment -$55 -$55 End of year 1 -$60 $1 -$59 End of year 2 $2 $2 End of year 3 +$136 $2 +$138 The arithmetic mean rate of return of the stock is: A) 10%. B) 9.02%. C) 8.64%. D) 11.34%.
B) 9.02% To calculate the arithmetic mean rate of return of the stock, calculate each individual holding period return, then take a simple average. First period return = ((60 − 55) + 1) ÷ 55 = 10.91% Second period return = ((65 − 60) + 1) ÷ 60 = 10% Third period return = ((68 − 65) + 1) ÷ 65 = 6.15% The arithmetic mean rate of return = (10.91% + 10% + 6.15%) ÷ 3 = 9.02%
Bob Jones invested $10,000 in the stock of Thai Bank when the rate of Thailand baht was $1 = 28 baht and the Thai Bank's stock was selling at 140 bahts. After one year, Bob sells the stock for 168 baht per share and converts the proceeds into dollars at the rate of 54 bahts per dollar. Which of the following statements is NOT correct? A) Bob earned a -37.78% return on his investment. B) Thai baht appreciated by about 93% during this period. C) Thai Bank had a 20% return in the local currency. D) Bob's investment was worth 336,000 bahts when he sold his shares.
B) Thai baht appreciated by about 93% during this period. The baht depreciated by about 48% during the period. Value of one baht in the beginning = 1/28 = $0.0357 Value of one baht in the end = 1/54 = $0.0185 Percent change in the baht's value = (0.0185 − 0.0357) ÷ 0.0357 = −0.4818 = −48.18% Bob was able to get 280,000 bahts (28 × 1,000) for $10,000. He used this to buy 2,000 shares (280,000 ÷ 140) of Thai Bank. He sold the shares for 336,000 bahts (2000 × 168) for an increase of 20%. However, upon conversion, he received only $6,222.22 (336,000 ÷ 54), therefore, his return was: ($6,222.22 − $10,000) ÷ $10,000 = −0.3778, or −37.78%.
Mary Anne is considering the purchase of Davidson stock. The stock has a market price of $35 and is currently paying a dividend of $1.75 per share. The company's dividend is expected to grow 4% annually. If Mary Anne requires a 9% rate of return, should she purchase the stock? A) Yes, the stock is overvalued by $1.40 per share. B) Yes, the stock is undervalued by $1.40 per share. C) Yes, the dividend is expected to grow at a rate that outpaces inflation. D) No, the stock is overvalued by $1.40.
B) Yes, the stock is undervalued by $1.40 per share. Use the constant growth dividend discount model to solve for the intrinsic value of the stock. [$1.75(1.04)] ÷ [0.09 − 0.04] = $36.40 According to the constant growth dividend discount model, the intrinsic value of Davidson stock is $36.40. Because the current market price is lower, a purchase of the stock may be warranted.
Harvey, an astute real estate investor, is considering the purchase of an apartment complex. He has obtained the following information regarding the property. Gross rental receipts = $1,000,000 Other income = $33,000 Average vacancy rate = 5% of potential gross income Operating expenses = $315,000 Mortgage payments = $452,500 Depreciation expense = $163,750 Capitalization rate = 15% What is the value of the property? (Hint: use the NOI capitalization approach) A) $6,542,933. B) $4,786,667. C) $4,442,333. D) $766,302.50.
C) $4,442,333. The value of the property using the NOI capitalization approach is calculated as V = NOI ÷ Capitalization rate or $666,350 ÷ 0.15 = $4,442,333. NOI = $1,000,000 + $33,000 - (5% x $1,033,000) - $315,000 = $666,350.
Owen purchased 100 shares of ABC stock for $32 per share from his stockbroker and CFP® professional, Lucas. One year later, the stock paid a dividend of $1.50, and he purchased an additional 100 shares for $35 per share. At the end of the second year, he contacted Lucas to sell all of the stock for $31 per share using a limit order. The order was filled and the stock sold at $31 per share. The stock did not pay a dividend at the end of the second year. What was the dollar-weighted return to Owen over the two-year holding period? A) -6.61% B) 1.05% C) -3.63% D) -5.14%
C) -3.63% Owen earned a −3.63% dollar-weighted rate of return on ABC stock over the two-year period, calculated as follows: CF0 = $32 × 100 = −$3,200 CF1 = ($1.50 × 100) − ($35 × 100) = −$3,350 CF2 = $31 × 200 = $6,200 Solve for the internal rate of return (IRR) = −3.6331% (rounded to −3.63%)
A 15-year bond has a yield-to-maturity of 12% and a modified duration of 7.24 years. If the market yield changes by 50 basis points, the bond's expected price change is: A) 3.75%. B) 6.65%. C) 3.62%. D) 5.00%.
C) 3.62%. The correct answer is 3.62%. Modified duration reflects a bond's expected price change based on a 100 point basis (1%) change in the market yield. A 50 basis (.5%) point change would be expected to result in a 7.24 ÷ 2 = 3.62% change in bond price.
Security A has a standard deviation of 23% and the market has a standard deviation of 18%. The correlation coefficient between Security A and the market is 0.80. What percent of the change in Security A's price can be explained by changes in the market? A) 36%. B) 80%. C) 64%. D) 50%.
C) 64%. Because the correlation coefficient is 0.80, the coefficient of determination (R squared) is 0.64. Therefore, only 64% of investment returns can be explained by changes in the market (i.e., systematic risk represents 64%).
Kevin, a portfolio analyst, has compiled the following information regarding three large-cap growth portfolios. 5-year average return ßp Portfolio A 12% 2.1 Portfolio B 8% 1.6 Portfolio C 6% 1.2 The 90-day T-bill rate is 0.95%. Which of these portfolios has the best risk-adjusted performance? A) Portfolio C. B) Cannot be determined. C) Portfolio A. D) Portfolio B.
C) Portfolio A. Because only beta was provided, Treynor's ratio should be used to determine each portfolio's risk-adjusted performance. Portfolio A: (.12 − .0095) ÷ 2.1 = .05262 Portfolio B: (.08 − .0095) ÷ 1.6 = .04406 Portfolio C: (.06 − .0095) ÷ 1.2 = .04208 Portfolio A has the highest Treynor ratio; therefore, this portfolio has outperformed the others on a risk-adjusted basis.
A portfolio had an IRR for a 3-year period of 5.57%. During this 3-year period the following dividends were paid, and the current FMV of this portfolio is $40. Dividend year 1 (end): $4.80 Dividend year 2 (end): $5.90 Dividend year 3 (end): $7.25 What was the portfolio worth when it was purchased 3 years ago? A) $34. B) $30. C) $37. D) $50.
D) $50. CF0 = 0 CF1 = 4.80 CF2 = 5.90 CF3 = (7.25 + 40) = 47.25 i = 5.57 NPV = $49.99
William purchases a 20-year AA rated corporate subordinated debenture for $1,025. This bond features a 5.75% coupon rate and may be called in 10 years for 105% of par. All of the following statements are correct EXCEPT A) William purchased the bond at a premium. B) The yield to call on the bond is 5.79%. C) If the coupon rate on comparable new bonds is 5.25% in 5 years, the new market price of the bond should be $1,051.46. D) The yield to maturity on the bond is 5.68%
D) The yield to maturity on the bond is 5.68% With a market price of $1,025, William purchased the bond at a premium. YTM: PV = −1,025; FV = 1,000; N = 40; PMT = 28.75; Solve for I/YR = 2.7708 × 2 = 5.5416% YTC: PV = −1,025; FV = 1,050; N = 20; PMT = 28.75; Solve for I/YR = 2.8966 × 2 = 5.7932% Assuming the coupon rate on comparable new bonds is 5.25% in 5 years: FV = 1,000; N = 30; PMT = 28.75; I/YR = 2.6250%; Solve for PV = 1,051.46, or $1,051.46
Ron is considering the purchase of XYZ stock. XYZ recently paid a dividend of $2.00 per share. He expects to sell this stock at the end of one year for $32.00, and also expects to receive a dividend of $2.50 at the end of the year. If his required rate of return is 12% for XYZ, what is the most he would be willing to pay for this stock? A) $30.58. B) $34.50. C) $30.80. D) $32.81
The present value of the cash flows associated with owning the stock is the most Ron would be willing to pay for the stock. If he purchases the stock he will not get the recently paid dividend of $2.00. The only relevant cash flows are the $32.00 and $2.50 that will be received at the end of the first period. Value of the stock = (expected sales price at year end + expected dividend) ÷ (1 + required rate of return) = ($32.00 + $2.50) ÷ (1 + 0.12) = $30.80.
