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You are given the following data: The risk-free rate is 5 percent. The required return on the market is 8 percent. The expected growth rate for the firm is 4 percent. The last dividend paid was $0.80 per share. Beta is 1.3. Now assume the following changes occur: The inflation premium drops by 1 percent. An increased degree of risk aversion causes the required return on the market to rise to 10 percent after adjusting for the changed inflation premium. The expected growth rate increases to 6 percent. Beta rises to 1.5. What will be the change in price per equilibrium before the changes occurred? a. b. c. d. e. share, assuming the stock was in +$12.11 -$ 4.87 +$ 6.28 -$16.97 +$ 2.78 65. Equilibrium stock price Before: ks = 5% + (8% - 5%)1.3 = 8.9%. $0.80(1.04) 0.089 - 0.04 P0 = = $16.98. After: ks = 4% + (10% - 4%)1.5 = 13%. $0.80(1.06) 0.130 - 0.06 P0 = = $12.11. Answer: b Diff: M Hence, we have $12.11 - $16.98 = -$4.87. Constant growth stock i . a. b. c. d. e. 66. Answer: d Diff: M A stock that currently trades for $40 per share is expected to pay a year-end dividend of $2 per share. The dividend is expected to grow at a constant rate over time. The stock has a beta of 1.2, the risk-free rate is 5 percent, and the market risk premium is 5 percent. What is the stock’s expected price seven years from today? $ 56.26 $ 58.01 $ 83.05 $ 60.15 $551.00 Constant growth stock Answer: d Diff: M To find the stock price seven years from today, we need to find the growth rate. Nonconstant growth stock iii Answer: a Diff: M .$40g = $2. $ 7.53 69. Step 2: Calculate the growth rate using the constant growth formula: P0 = D1/(ks . What is the current stock price? a.89 d.e.00 g = 0. and the market risk premium is 5 percent.62 c.Step 1: Calculate the required rate of return: ks = kRF + (kM . The most recent .06 = 6%. the current price is given by discounting the future price in Year 4 to the present at the required rate of return: $16. $ 8.36 b.40/$40.15. Nonconstant growth stock Answer: d Diff: M The required return on the stock is given by: ks = kRF + RPM(b) ks = 5% + (5%)1.05 = = $16.00). $11. $10. Thus.2. the company anticipates that it will establish a dividend of $1. D5 = $1. A stock is not expected to pay a dividend over the next four years. Five years from now. E. Once the dividend is established.06)7 = $60.2 = 11%.00 g = $2.g) $4. Step 3: Determine the expected stock price seven years from today: = $40. Lee recently took his company public through an initial public offering.0. The required rate of return on the company’s stock is expected to remain constant.00 (1.00 0.R.kRF)b = 5% + (5%)1.1452 $60.11)4 P0 = = $10.98 e. The stock price is given by: D5 ˆ k P4 s g = $1.40 .2 = 11%.11 .00/(0. $ 9. The risk-free rate is 5 percent. the company’s beta is 1.11 .98. the market expects that the dividend will grow at a constant rate of 5 percent per year forever.00 per share (i. He is expanding the business quickly to take advantage of an otherwise unexploited market..667.g) $40 = $2. Nonconstant growth stock Answer: d Diff: M ii .667 (1. Growth for his company is expected to be 40 percent for the first three years and then he expects it to slow down to a constant 15 percent. 50. Calculate D as $3.17 )2 P0 = + = $77.00. D4.75(1. $50. D3. The risk-free rate is 8 percent and the market risk premium is 6 percent.15) = $118.41. $73.11 .0.15.25 $3. and D3 = $2.14.41 c.88 e. .00 for the subsequent 2 years (D4 and D5). D4 and D5P 6 1.058.17 $1.dividend (D0) was $0.11) (1.25 $2. $67. $2.g = $2.50 d. Nonconstant growth stock Answer: a Diff: M Answer: b Diff: M ks = kRF + RPM(b) = 8% + 6%(1.335 (1. $2.25 $2.17 .47 (1.11) (1. ˆ5 P The stock price today represents the sum of the present values of D 1. $0. and .McPherson Enterprises is planning to pay a dividend of $2. What is the current price of Lee’s stock? a. $0. The stock price at t = 5 is = $3. $32.4)2 = $1.75. If the required return on the company’s common stock is 11 percent per year.00 $52. The company is planning to pay the same dividend each of the following 2 years and will then increase the dividend to $3.14 b.11) (1.94 74.058 + $118.05 = $3.15/(0. Nonconstant growth stock Answer: b Diff: M ˆ5= $3. Based on the most recent returns.4)3 = $2.75(1. D2. $77. D5.47. $0.75(1.15) = $2. $1. = D4/ks . $52.3667/(0.3667.05) = $52.17 )3 + Nonconstant growth stock iv .00 $3.00 We’re given D1. After that time the dividends will grow at a constant rate of 5 percent per year.25 per share at the end of the year (D1 = $2.5) = 17%.05 1.05.20 71.51 d.0.25).50 2 3 4 1.5. $93.25. D2. what is its current stock price? a.75(1. $40.11)5 P0 = = $40.335.50 b. his company’s beta is approximately 1.11 (1. $37.00 e. $75.4)3(1.4) = $1. D1 D2 D3 D4 = = = = $0.17 c. The stock has a required rate of return of 13 percent (k s = 0.87 c.00. $83.25 = $4. What is the expected price of the stock two years from today? (Calculate the price assuming that D2 has already been paid. D3 = $2.56 d. $67.00. and then solve for NPV = $69.00 1. D3 = $2. D6 = $4. the dividend will grow forever at a constant rate of 7 percent a year. The dividend is expected to grow 25 percent a year for the following four years.00 (1. After this time period.56. (D5 = $2. Due to a new product.076823.25 = $2.63 e. CF1 = 3.13 + $3.00 per-share dividend at the end of the year (D 1). Financial calculator solution: Step 1: Calculate the dividends each year: D1 = $2.125/1.96 77.90625. ABC expects to achieve a dramatic increase in its .g) = $5.07 = $5. Step 2: Find the stock’s value at Year 5: = D6/(ks .Whitesell Technology has just paid a dividend (D 0) and is expected to pay a $2.07) = $87.7655 + $3.) a.5573 $69.00 1. $69.125.25 = $3.125.25)4 = $4.13)2 + ($4.90625 1.8828).25 = $2. D6 = $4. CF2 = 3.07) = $87.00. $91. and it just paid a dividend of D 0 = $3.97 b.125 1.25 = $4.076823.0.90625.Nonconstant growth stock Answer: c Diff: M v .224609375. D5 = $3.90625.50.224609375/(0.125 1.224609375/(0.8828125.55729 ≈ $69.076823)/(1.8828125 1.076823.8828125 + 87.13). Step 2: Find the stock’s value at Year 5: = D6/(ks .ABC Company has been growing at a 10 percent rate.125. Step 3: Now find the value of the stock in Year 2: Enter the following inputs in the calculator: CF0 = 0.07 = $5. $95. D2 = $2.8828125. D4 = $3. Step 3: Now = = = find the value of the stock in Year 2: $3.25 = $3.g) = $5.0. I = 13.90625/(1.50 1.50 1. D2 = $2. Supernormal growth stock vi Answer: b Diff: M .25 = $3.0592 + $63.7326 $69. Nonconstant growth stock Answer: c Diff: M Step 1: Calculate the dividends each year: D1 = $2. CF3 = 4.90625 1.224609375.13 .8828125 + $87.25 = $3.13)3 $2.8828125 1.50. D4 = $3. D5 = $3.13 .56. 18 e. After this time. and the risk-free rate is 7 percent.60% c.752 0. the required return on an average stock is 11 percent.26.0. growth is expected to return to the long-run constant rate of 10 percent. 3.26.60%.60 2 | gs = 20% gn = 10% 4.90 2 | 1.15 (1.60.26 = 0.23 c. $28. $20. What will be the price of the company’s stock three years from now? a.805 3 | 1. Declining growth stock Answer: d vii Diff: M .32 ˆ2 = 95.11 . The company’s analysts predict that earnings (and dividends) will decline at a rate of 5 percent annually forever. 10. 4.93% b.60 4. P0 $78.0460 = 4.00 1 | 1.36 ks = 0. Numerical solution: $3.60%. I = 15. Supernormal growth stock Answer: b Diff: M Time line: 0 ks | g s 1 | = 15% = 20% 3.10 99.short-run growth rate.54% e.00.752 4.60 3 | Years 4.The Textbook Production Company has been hit hard due to increased competition.15)2 P0 = = $78.07)2. $27.36 1.0 = 0.00% d. Output: NPV = $78. to 20 percent annually for the next 2 years.0. D1 $3. $10.15 0.50 d. Declining growth stock Answer: d Diff: M Time line: ks = 11% 0 gn = -5% | 2.07 + (0. 7. CF2 = 99.63 91.15 = 15%. Dividend yield = $3.36.00 P0 = ? 3. The company’s beta is 2.60 $99. What should be the dividend yield (D1/P0) today? a. $ 6. Assume that ks = 11 percent and D0 = $2.26 Dividend yield = Financial calculator solution: Inputs: CF0 = 0.60/$78.6290125 .17 b.71475 4 Years | 1.33% 87. CF1 = 3. 2.04 = P CFt 0 3. 00 b. Step 2: Calculate the P/E ratio one year from today: P/E = $87/$2.11 . 36.You have been given the following projections for Cali Corporation for the coming year.00.Lamonica Motors just reported earnings per share of $2.138 g $40 = $5. 5. 44. and it will pay its first dividend of $1.80% d. so the stock’s current price is $80 per share.18. Analysts expect that one year from now the company will have an EPS of $2.40. Stock price x EPS = $2.00.40. P 0 = $80.$80)/$80 8 = $1 + P1 .95)3 = $10. constant growth model. The stock has a price earnings ratio of 40.90 0. we can solve for the growth rate as follows: $2(1 g) 0. EPS1 = Answer: d Diff: M .P0)/P0 0. Stock growth rate Answer: e Diff: M The required rate of return on the stock is 9% + (6%)0.875. 4. the market risk premium is 6 percent. The previous dividend was $2 (D0 = $2) and dividends are expected to grow at a constant rate.6797. Step 1: Calculate the price of the stock one year from today: ks = D1/P0 + (P1 . D1 = $1. P/E = 40×. 13.$1.25×.8. and the risk-free rate is 9 percent. ks = 10%.8%.52 g = 8. The stock has a required return of 10 percent.05) ˆ0 P $1.38%.38% 93. 40.10 = $1/$80 + (P1 . .40 = 36.$40g = $2 + $2g $42g = $3.52 .17 d.00 e. What is the stock’s growth rate? a.00. 5.00 per share. The company’s beta is 0. Stock growth rate Answer: e Diff: M viii .Grant Corporation’s stock is selling for $40 in the market. 8.00% c. Expected return and P/E ratio Answer: b Using the Diff: M ix . 36.16 = = = $11.52% b. = $11. Expected return and P/E ratio Answer: b Diff: M Data given: $2.875(0.$80 $87 = P1.90 0.(-0.8 = 13.80% e.25 c. What price earnings ratio must the stock have one year from now so that investors realize their expected return? a. 8. a.000 units.55 $53. b. Calculate the current price per share for Cali Corporation. kRF = 5%.4. e. Tax rate = 40%.72 $59. $35.27 $48.000. Growth rate = 8%.000. Bonds outstanding = $15. kM = 9%. Sales price per unit = $10. kd on outstanding bonds = 8%. Sales = 10.76 . Dividend payout ratio = 60%. c. Beta = 1. Shares of common stock outstanding = 10.22 $46. Variable cost per unit = $5.000 shares. Fixed costs = $10. d. 05% and Stock X has a beta of 2.00 b.000 = $1.05% + (9.106 .000 $5 10.05(12%) = 9.30 9 0.0.The probability distribution for kM for the coming year is as follows: Probability kM 0. calculate the total amount of dividends.3968/(0. an expected constant growth rate of 7 percent.09 .30 8 0.6 = $13.30(10%) + 0. Stock price Step 1: Answer: d Set up an income Sales Variable costs Fixed costs EBIT Interest EBT Taxes NI Diff: M statement to find net income: $100.3968.05%.08 $15.280 Then.40 $38.000 1.30(8%) + 0. what market price gives the investor a return consistent with the stock’s risk? a. $42.800 15.30(9%) + 0.08) = $53.6. $37.38 e. Step 2: Use the CAPM equation to find the required return on the stock: kS = kRF + (kM . Calculate expected equilibrium stock price: .05 7% 0.000 $ 38.000 $10 10.800 $ 23.99.05)1. Dividends/Share = Total dividend/# of shares outstanding = $13.6%.05(7%) + 0.05%. Risk and stock value Answer: d Diff: M Calculate required return on market and stock: kM = 0.72.280 0. or the dividend for the coming year.kRF)b = 0.968/10.05 + (0.30 10 0.0.000 10.106 = 10.4 = 0.72 d. $25.94 101. Div = Net income Payout = $23. Note: Because these projections are for the coming year.968.05%)2.520 0. Step 3: Calculate stock price: P0 = D1/(kS .50 c. this dividend is D1.05% . Risk and stock value xi Answer: d Diff: M . ks = 6.g) = $1.0.05 12 If kRF = 6.000 (Given) $ 40.200 0. and D0 = $2. $21. $56.000 50.0 = 12. 2) = 0.g).D1/P0 = g .49 e. The stock’s dividend is expected to grow at a constant rate of 5 percent a year. the market risk premium is 5 percent.05) = $60. $72.63 d. kRF.58 c. The stock currently sells for $20.49 d. $25.Kirkland Motors expects to pay a $2. What is the expected stock price five years from now? a. $56. Future stock price--constant growth Answer: b Diff: M First. $72.12 . $36.00 per share dividend on its common stock at the end of the year (D1 = $2.25 e.2. $22. Future stock price--constant growth Answer: b Diff: M xiii .00(1. $60.00 a share (D1 = $3.00/ ˆ5 ˆ5 P (0.07)5 = $2.11 e.00 a share.8051/(0.8051. The stock has a beta of 0. Future stock price--constant growth xiv Answer: b Diff: M . = $60(1. The required rate of return on the company’s stock is 12 percent (k s = 0.8. P0 = $3.08 c.96 102.ˆ0 P $2(1. Finally. compound this at the 5% growth rate for 5 years to find . What is the stock’s expected price five years from now? a. Then. that is. find ks = 6% + 5%(0.12.07) $42.10 c. The risk-free rate.10 – P 0. $35.43 b.12). What is the expected ˆ5 P stock price five years from now.00).00 b. $76.00 a share (D1 = $2.05)5 = $76.00). $21.54 104. (kM – kRF).Newburn Entertainment’s stock is expected to pay a year-end dividend of $3.07 Future stock price--constant growth Answer: b Diff: M xii . The dividend is expected to grow at a constant rate of 7 percent a year. and the company’s beta equals 1. find P 0 = D1/(ks . is 5 percent. find D6 = $2.06 + 0. The risk-free rate is 6 percent. $52. It follows that: P5 = $2. calculate ks = 0. Future stock price--constant growth Answer: b Diff: M First. $63. The dividend is expected to grow at some constant rate over time.58.8) = 10%.78 105.10.Graham Enterprises anticipates that its dividend at the end of the year will be $2.38. $68.07) = $56. Future stock price--constant growth Answer: b Diff: M To find the growth rate: ks = D1/P0 + g Therefore ks . what is ? a. 0.1205 0.00). $96. $70.65 b.05(1. Then.64 d. is 6 percent and the market risk premium.0. g).208. -$ 7. Supernormal growth stock xvi Answer: c Diff: T .60. Last year’s earnings . Change in stock price = $22.696 ˆ P0 0.33 b.208/0.00 d.02. It is expected that the firm will experience (beginning now) an unusually high growth rate (20 percent) during the period (3 years) it has exclusive rights to the property where the raw material used to make this kitty litter is found.1348 0.33.73.12 .5) = 1.095. E0.$30.00 = -$7. Calculate the new expected equilibrium stock price: $1. and from that time on the firm will achieve a normal growth rate of 8 percent annually.$2/$20 = 0.48%.22 e. -$15.12 . Risk and stock price Answer: a Diff: T Calculate the required rate of return: D0 = E0(Payout ratio) = $4. Calculate the new beta: bNew = 0. Calculate the new required rate of return: ks = 8% + (5%)1. Therefore = D6/ks .0.02)5 = $2.02) = $22.67. During the rapid growth period.) a. How-ever. and the dividend payout ratio is 40 percent.06) ˆ D0 (1 + g) k s P0 $30 + g = + 0.00(0. +$ 7.73(1.60(1. $1. Last year’s earnings per share.095 = 13. Risk and stock price Answer: a Diff: T xv .06 = = $22.08. the decrease in growth in the fourth year will be accompanied by an increase in the dividend payout to 50 percent. the firm’s dividend payout ratio will be relatively low (20 percent) in order to conserve funds for reinvestment.00. +$22.67 . by how much will the stock price change? (Hint: Use four decimal places in your calculations. We therefore need D6. were $4.63 114. and the market risk premium is 5 percent.Hard Hat Construction’s stock is currently selling at an equilibrium price of $30 per share. and all other factors remain constant. -$15.14 c. To find we can use the following formula: = D6/ks .g) = $2. However. The firm has been experiencing a 6 percent annual growth rate.0. D6 = D1(1 + g)5 = $2(1. If market risk (beta) increases by 50 percent.65%.The Hart Mountain Company has recently discovered a new type of kitty litter that is extremely absorbent.475% 13. The risk-free rate is 8 percent. beginning with the fourth year the firm’s competition will have access to the material. b = 0.06 = 11.65% = 8% + (5%)b.40) = $1. Calculate beta: 11. 2 1. $17.. 20 percent next year. and the firm’s required return is 10 percent.88 E3 = 3. $87.00 per share.73248 P0 = ? D1 = 0.003. Calculate the dividend and price stream (once the stock becomes a constant growth stock): .576 $94. After three years the dividend is expected to grow at a constant rate of 7 percent a year. a new high-growth company.15 = 15%.08 0.54.0625 + (0.456 E4 = 3.53 d.4) = $1. $18. CF3 = 94.10) (1. CF1 = 0.50 b. $93.25 e. The company has a 40 percent payout ratio.50.6912 D4 = 1.75) = 0.31 0.50)(0.54 d.48 $0.86624 1.576 ˆ3 P CFt 0 0. $19. and that Fast Start’s beta is 1.003 P0 $71.86624 = 93. $19.54.48 D3 = 0.33 c. CF2 = 0. Calculate dividend per share: D0 = (EPS0)(Payout ratio) = ($2.A financial analyst has been following Fast Start Inc. $71. She estimates that the current risk-free rate is 6.48.10 (1.576. the market risk premium is 5 percent.were E0 = $2.89 119 Nonconstant growth stock Answer: c Diff: T Use the SML equation to solve for ks: ks = 0.51 b.05)(1. The analyst estimates that the company’s dividend will grow at a rate of 25 percent this year.10)3 Financial calculator solution: Inputs: CF0 = 0.25 percent. I = 10.96 c. The current earnings per share (EPS0) are $2. The analyst believes that the stock is fairly priced. $61.00 E1 = 2. $16.54.75.00. What is the current stock price? a. What should be the current price of the common stock? a.10 0.576 94. Nonconstant growth stock Answer: c Diff: T xvii .50 116 Supernormal growth stock Answer: c Diff: T Time line: ks = 10% 0 1 2 3 4 Years gs = 20% gs = 20% gs = 20% gn = 8% | | | | | E0 = 2. Output: NPV = $71.48 D2 = 0.78 e. The company is expected to maintain its current payout ratio. P0 = $71. and 15 percent the following year.40 E2 = 2. $66.003 Numerical solution: $0. 6.50.10)3 + Years .07 Put all the cash flows on a time line: Time line: 0 ks = 15% 1 2 3 | gs = 25% | | gs = 20% gs = 15% | gn = 1.15 0. After t = 4. After this payment. Stock growth rate xviii Answer: b Diff: T .00 1.953125. D3 = $1. CF2 = 1. 6.50.20 = $1.10)2 + $1.15 = $1.5625 (1.84575.5625 1.5625/(1.725. g4+ = ? Step 1: Draw the time line: 0 ks = 10% | g = 25% s P0 = 50 1 2 3 4 | g = 25% | g = 25% | g = 25% | g = ? s s s n 1. what is X? a.87% c.796875 4 Years | 1. D1 = $1. D2 = $1.D0 = $1. CF1 = 1.725 1.25 (1.5000 1.53.071875 = CFt 0 1.071875.25 1.07 = $1.00.00/1. the dividend is expected to grow at a constant rate of X percent per year forever.50 1.47% b.25 = $1.7250 P0 = ? 7% 23.00 per share.Mulroney Motors’ stock has a required return of 10 percent. Stock growth rate Answer: b Diff: T ks = 10%.25) = $1. use the cash flow register to calculate PV: CF0 = 0. What is the stock’s expected constant growth rate after t = 4? In other words. That is.98% d.5000 24. ˆ3 $1.84575 0.725(1.00(1.953125 5 | Step 2: Calculate the dividends: g2-4 = 25%.25/(1. The year-end dividend. D2 = $1 (1.00 1.25.25 1. D4 = $1.796875. D3 = $1.5625.00. D4 = $1.2500 1. CF3 = 24. is expected to be $1.25.07 Finally. P0 = $50.00% e.2500 1.10 + $1. 5.15 0.00 1.25) = $1. 8.25)3 = $1.953125. Step 3: Calculate the present value of these dividends: PVdiv = $1. P 0.25. I = 15%. The stock currently trades at $50 per share. D1 = $1. the dividend is expected to grow by 25 percent per year for the next three years. D1 = $1.84575 1. D4 = $1. 8.00.27% 120. D 1. and then solve for NPV = $18.25) = $1.07) $23. 10 – g) $6.953125 = $68.1739 + $1. FV = $45. However.704.25 121 Preferred stock value Answer: d Diff: T Time line: 0 EAR = 6. Amount needed to buy 100 shares: $50(100) = $5.953125g $6.64288g $4. it has a required annual rate of return of 12 percent.87% = g. Step 5: Determine the constant growth rate: = D5/(ks .g) = [D4(1 + g)]/(ks . In fact. Because the preferred stock is riskier.PVdiv PVdiv Step 4: $1.4501 $4. This is the price at t = 4. but where interest is compounded daily (assume a 365-day year).6898 = [$1. Preferred stock value Answer: d Diff: T xix .18.291.953125 + $1.66898 – $66.6898.23 c.183% 1 | | PV = ? 2 | umerical solution: $6 0. Determine the stock’s price at t = 4: The PV of the stock at t = 4 must be the future value of the difference between today’s price and the PV of the dividends through t = 4.12 Pp = = $50. $3. (Assume that this rate will remain constant over the next 5 years.953125(1 + g)]/(0. $2.704.55. 3 | 4 | 5 Years | FV = 5. the best that you can do now is to invest your money in a bank account earning a simple interest rate of 6 percent.18 e.66898 – $1. $4.$4.Assume that you would like to purchase 100 shares of preferred stock that pays an annual dividend of $6 per share.45.953125/(1. $4.00 . PV = $50. so you cannot afford the purchase price.3498) PV = $3.985.3340 = $4.g) $66.000 = PV(1.000 N .138.6898g = $1.10)4 = $66. you have limited resources now.) For you to be able to purchase this stock at the end of 5 years.10)4 = $0.0331 + $1.45 = $45.00 b.64288 = g 6.000. $5. at t = 0? a.831.52 d.06/365)5(365) $5. how much must you deposit in your bank account today.000 = PV(1 + 0. $3.7158/$68.9091 + $1.55(1. 18.704.18313%. FV = 5000. I = 6. Output: EFF% = EAR = 6. Calculate PV of deposit required today: Inputs: N = 5. Deposit $3.704. .Financial calculator solution: Convert the nominal interest rate to an EAR: Inputs: P/YR = 365.704.18. Output: PV = -$3. NOM% = 6.182 -$3. PMT = 0. Note: If the financial calculator derived EAR is expressed to five decimal places it yields a PV = -$3.18313.704.18. kRF)b = 5% + (5%)1. Step 1: Calculate the required rate of return: ks = kRF + (kM .g) $4. Step 3: Determine the expected stock price seven years from today: = $40.00 g = $2.g) $40 = $2.00 g = 0.2 = 11%. we need to find the growth rate.2 = 11%.1452 $60.40 .06)7 = $60. Step 2: Calculate the growth rate using the constant growth formula: P0 = D1/(ks .00 (1.Nonconstant growth stock The required return on the stock is given by: ks = kRF + RPM(b) ks = 5% + (5%)1.Constant growth stock Answer: d Diff: MTo find the stock price seven years from today.15.00/(0.40/$40.i.$40g = $2. iii iv v vi vii viii ix x xi xii xiii xiv xv xvi xvii Answer: d Diff: M . ii.11 .06 = 6%. xviii xix .