Investment analysis exam 1: ch 1-2 short answer problems
Your grandfather invested $1,000 in a stock 50 years ago. Currently, the value of his account is $324,000. What is his geometric return over this period?
Geometric return = ($324,000 / $1,000)^(1/50) − 1 = .1226, or 12.26%
The rates of return on Cherry Jalopies, Inc., stock over the last five years were 17 percent, 11 percent, -2 percent, 3 percent, and 14 percent. What is the geometric return for Cherry Jalopies, Inc.?
Geometric return = [(1 + .17)(1 + .11)(1 − .02)(1 + .03)(1 + .14)]^(1/5) − 1 = .0837, or 8.37%
You decide to buy 1,200 shares of stock at a price of $34 and an initial margin of 55 percent. What is the maximum percentage decline in the stock price before you will receive a margin call if the maintenance margin is 35 percent?
Amount borrowed = (1,200 × $34)(1 − .55) = $18,360 Margin call price = ($18,360 / 1,200) / (1 − .35) = $23.54 Stock price decline = ($23.54 − 34) / $34 = −.3077, or −30.77%
You buy 500 shares of stock at a price of $38 and an initial margin of 60 percent. If the maintenance margin is 30 percent, at what price will you receive a margin call?
Amount borrowed = (500 × $38) − (500 × $38)(.60) = $7,600 Margin call price = ($7,600 / 500) / (1 − .3) = $21.71
A stock has returns of -9 percent, 17 percent, 9 percent, 14 percent, and −4 percent. What are the arithmetic and geometric returns?
Arithmetic = (−.09 + .17 + .09 + .14 − .04) / 5 = .0540, or 5.40% Geometric = [(1 − .09)(1 + .17)(1 + .09)(1 + .14)(1 − .04)]^(1/5) − 1 = .0490, or 4.90%
A stock has had returns of 21 percent, 12 percent, 7 percent, -13 percent, -4 percent, and 26 percent over the last six years. What are the arithmetic and geometric returns for the stock?
Arithmetic return = (.21 + .12 + .07 − .13 − .04 + .26) / 6 = .0817, or 8.17% Geometric return = [(1 + .21)(1 + .12)(1 + .07)(1 − .13)(1 − .04)(1 + .26)]^(1/6) − 1 = .0730, or 7.30%
Stacy purchased 400 shares of stock for $38 a share. She sold those shares six months later for $34 a share. The initial margin requirement is 80% and the maintenance margin is 40%. Ignore margin interest and trading costs. If she purchased the shares for cash, her holding period return would be ________% as compared to ________% if she had used margin.
HPR without margin = ($34 − $38) / $38 = −.1053, or −10.53%. HPR with margin = ($34 − $38) / ($38 × .80) = −.1316, or −13.16%.
A stock was purchased for $45 a share and sold ten months later for $48 a share. If the shares were purchased totally with cash the holding period return would be ________% as compared to ________% if the purchase was made using 70% margin. Ignore trading costs and margin interest.
HPR without margin = ($48 − $45) / $45 = .0667, or 6.67%. HPR with margin = ($48 − $45) / ($45 × .70) = .0952, or 9.52%.
Today, you are purchasing 100 shares of stock on margin. The purchase price per share is $35. The initial margin requirement is 70% and the maintenance margin is 30%. The call money rate is 4.5% and you are charged 1.6% over that rate. What will your rate of return be if you sell your shares one year from now for $37 a share? Ignore dividends.
Initial investment = (100 × $35 × .70) = $2,450 Loan repayment = [100 × $35 × (1 − .70)] × [1 + (.045 + .016)]^(1) = $1,114.05 Rate of return = [(100 × $37) − $1,114.05 − $2,450] / $2,450 = .0555, or 5.55%
Seven months ago, you purchased 400 shares of stock on margin. The initial margin requirement on your account is 60% and the maintenance margin is 30%. The call money rate is 4.8% and you pay 1.85% above that rate. The purchase price was $16 a share. Today, you sold these shares for $18.00 each. What is your annualized rate of return?
Initial investment = 400 × $16 × .60 = $3,840 Loan repayment = [400 × $16 × (1 − .60)] × [1 + (.048 + .0185)]^(7/12) = 2,657.97 HPR = [(400 × $18.00) − $3,840 − $2,657.97] / $3,840 = .1828 EAR = (1 + .1828)^(12/7) − 1 = .3335, or 33.35%
Robin sold 800 shares of a non-dividend paying stock this morning for a total of $29,440. She had purchased these shares on margin nine months ago at a cost per share of $35. The initial margin requirement on this stock is 60% and the maintenance margin is 30%. Robin pays 1.2% over the call money rate of 4.9%. What is her total dollar return on this investment?
Initial investment = 800 × $35 × .60 = $16,800 Loan repayment = [800 × $35 × (1 − .60)] × [1 + (.012 + .049)]^(9/12) = $11,708.59 Holding period dollar return = ($29,440 − $11,708.59 − $16,800) = $931.41
You short sold 600 shares of a stock at $52 a share. The initial margin requirement is 75% and the maintenance margin is 35%. What is the amount of your total liability for this transaction as initially shown on your account balance sheet?
Liability = 600 × $52 = $31,200
Sarah purchased 700 shares of Detroit Motors stock at a price of $55 a share. The initial margin requirement is 60% and the maintenance margin is 35%. The effective interest rate on the margin loan is 4.5%. How much margin interest will she pay if she repays the loan in four months?
Margin interest = [(1 + .045)^(4/12) − 1] × [700 × $55 × (1 − .60)] = $227.62
You purchase 500 shares of stock on margin at a cost per share of $22. The initial margin requirement is 60%. The effective interest rate on the margin loan is 6.4%. How much interest will you pay if you repay the loan in four months?
Margin interest = [(1 + .064)^(4/12) − 1] × [500 × $22 × (1 − .60)] = $91.93
You recently purchased 200 shares of stock at a cost per share of $23.50. The initial margin requirement on this stock is 75% and the maintenance margin is 50%. The stock is currently valued at $25.00 a share. What is your current margin position? Ignore margin interest.
Margin loan = 200 × $23.50 × (1 − .75) = $1,175 Current stock value = 200 × $25.00 = $5,000 Current equity = $5,000 − $1,175= $ 3,825 Current margin = $3,825 / $5,000 = .7650, or 76.50%
Last week, you sold 800 shares of Ace stock for $24,000. The sale was a short sale with an initial margin requirement of 70%. The maintenance margin is 40%. Some positive news concerning the company was released last night and the stock price jumped this morning to $35 a share. What is your current margin position in this stock?
Proceeds from sale = $24,000 Initial margin deposit = $24,000 × .70 = $16,800 Short position = 800 × $35 = $28,000 Account equity = $24,000 + $16,800 − $28,000 = $12,800 Margin position = $12,800 / $28,000 = .4571, or 45.71%
The stock of Flop Industries is trading at $48. You feel the stock price will decline, so you short 1,000 shares at an initial margin of 60 percent. If the maintenance margin is 30 percent, at what share price will you receive a margin call?
Proceeds from short sale = 1,000 × $48 = $48,000 Initial deposit = $48,000(.60) = $28,800 Account value = $48,000 + 28,800 = $76,800 Margin call price = $76,800 / [1,000 + (.30 × 1,000)] = $59.08
Whitney just purchased 100 shares of Disney (DIS) stock for $135.00 a share. Her broker required a cash payment of $10,125, not including trading costs, for the purchase. What is her initial margin requirement for this stock?
Purchase cost = 100 × $135.00 = $13,500 Initial margin percentage = $10,125 / $13,500 = .75, or 75%
Maddie recently short sold 400 shares of common stock for $25 a share. Her initial margin requirement was 70% and the maintenance margin is 35%. The stock is currently trading at $22.22 a share. What is her current short position in this stock?
Short position = 400 × $22.22 = $8,888
Today, you short sold 1,100 shares of Jasper Industrial stock at $48 a share. The initial margin is 60% and the maintenance margin is 30%. Which one of the following is correct concerning your account balance sheet for this transaction?
Total assets = (1,100 × $48) + (1,100 × $48 × .60) = $84,480
Suppose you bought 100 shares of stock at an initial price of $37 per share. The stock paid a dividend of $.28 per share during the following year, and the share price at the end of the year was $41. Compute your total dollar return on this investment.
Total dollar return = 100($41 − 37 + .28) = $428
Elizabeth short sold 500 shares of stock at $25 a share. One month later, she covered the short at a price of $22. What was her total dollar return on this investment?
Total dollar return = 500 × ($25 − $22) = $1,500
Suppose you bought 100 shares of stock at an initial price of $37 per share. The stock paid a dividend of $.28 per share during the following year, and the share price at the end of the year was $41. a. What is the capital gains yield? b. What is the dividend yield? c. What is the total rate of return on the investment?
a. Capital gains yield = ($41 − 37) / $37 = .1081, or 10.81% b. Dividend yield = $.28 / $37 = .0076, or .76% c. Total rate of return = 10.81% + .76% = 11.57%
Suppose you bought 500 shares of stock at an initial price of $37 per share. The stock paid a dividend of $.28 per share during the following year, and the share price at the end of the year was $34. a. Compute your total dollar return on this investment. (A negative value should be indicated by a minus sign.) b. What is the capital gains yield? c. What is the dividend yield? d. What is the total rate of return on the investment?
a. Dollar return = 500 x ($34 − 37 + .28) = −$1,360 b. Capital gains yield = ($34 − 37) / $37 = −.0811, or −8.11% c. Dividend yield = $.28 / $37 = .0076, or .76% d. Total rate of return = −8.11% + .76% = −7.35%
You purchase 275 shares of 2nd Chance Co. stock on margin at a price of $53. Your broker requires you to deposit $8,000. a. What is your margin loan amount? b. What is the initial margin requirement?
a. Margin loan = ($53 × 275) − $8,000 = $6,575 b. Margin requirement = $8,000 / ($53 × 275) = .5489, or 54.89%
You've just opened a margin account with $20,000 at your local brokerage firm. You instruct your broker to purchase 500 shares of Landon Golf stock, which currently sells for $60 per share. a. What is your initial margin? b. Construct the equity account balance sheet for this position.
a. Total purchase = 500 shares × $60 per share = $30,000 Initial margin = $20,000 / $30,000 = .6667, or 66.67%
A particular stock has a dividend yield of 1.2 percent. Last year, the stock price fell from $65 to $59. What was the return for the year?
Capital gains yield = ($59 − 65) / $65 = −.0923, or −9.23% Total return = Capital gains yield + Dividend yield Total return = −9.23% + 1.2% = −8.03%
The rates of return on Cherry Jalopies, Inc., stock over the last five years were 17 percent, 11 percent, -2 percent, 3 percent, and 14 percent. Over the same period, the returns on Straw Construction Company's stock were 16 percent, 18 percent, -6 percent, 1 percent, and 22 percent. What was the arithmetic average return on each stock over this period?
Cherry average return = (17% + 11% − 2% + 3% + 14%) / 5 = 8.6% Straw average return = (16% + 18% − 6% + 1% + 22%) / 5 = 10.2%
The rates of return on Cherry Jalopies, Inc., stock over the last five years were 17 percent, 11 percent, -2 percent, 3 percent, and 14 percent. Over the same period, the returns on Straw Construction Company's stock were 16 percent, 18 percent, -6 percent, 1 percent, and 22 percent. Calculate the variances and the standard deviations for Cherry and Straw.
Cherry: Cherry average return = (17% + 11% − 2% + 3% + 14%) / 5 = 8.6% Var = (1/4)[(.17 − .086)^2 + (.11 − .086)^2 + (−.02 − .086)^2 + (.03 − .086)^2 + (.14 − .086)^2] = .00623 Standard deviation = (.00623)^(1/2) = .0789, or 7.89% Straw: Straw average return = (16% + 18% − 6% + 1% + 22%) / 5 = 10.2% Var = 1/4[(.16 − .102)^2 + (.18 − .102)^2 + (−.06 − .102)^2 + (.01 − .102)^2 + (.22 − .102)^2] = .01452 Standard deviation = (.01452)^(1/2) = .1205, or 12.05%
Louis purchased 300 shares of stock on margin for $22.15 a share and sold the shares eleven months later for $24.50 a share. The initial margin requirement was 75% and the maintenance margin was 30%. The interest rate on the margin loan was 8.5%. He received no dividend income. What was his holding period return?
Initial investment = 300 × $22.15 × .75 = $4,983.75 Loan repayment = [300 × $22.15 × (1 − .75)] × (1.085)^(11/12) = $1,790.24 HPR = [(300 × $24.50) − $1,790.24 − $4,983.75] / $4,983.75 = .1156, or 11.56%.
Yvette recently purchased 500 shares of stock at a cost per share of $34.50. The initial margin requirement on this stock is 75% and the maintenance margin is 40%. The stock is currently valued at $36.75 a share. What is her current margin position? Ignore margin interest.
Margin loan = 500 × $34.50 × (1 − .75) = $4,312.50 Current stock value = 500 × $36.75 = $18,375 Current equity = $18,375 − $4,312.50 = $14,062.50 Current margin = $14,062.50 / $18,375 = .7653, or 76.53%
Carson Corporation stock sells for $17 per share, and you've decided to purchase as many shares as you possibly can. You have $31,000 available to invest. What is the maximum number of shares you can buy if the initial margin is 60 percent?
Maximum investment = $31,000 / .60 = $51,667 Number of shares = $51,667 / $17 per share = 3,039 shares
You have $22,000 and decide to invest on margin. If the initial margin requirement is 55 percent, what is the maximum dollar purchase you can make?
Maximum purchase = $22,000 / .55 = $40,000
Neshoba Industries stock is selling for $33 a share. You would like to purchase as many shares of this stock as you can. Your margin account currently has available cash of $7,000 and the initial margin requirement is 65%. What is the maximum number of shares you can buy?
Maximum purchase = $7,000 / .65 = $10,769.23 Maximum number of shares = $10,769.23 / $33 = 326 shares, rounded down to the last full share
Jennifer believes that Northern Wine stock is going to decline in value so she is short selling 1,000 shares at $22 a share. Her initial margin requirement is 70% and the maintenance margin is 30%. What is the highest the stock price can go before she receives a margin call?
P* = {[(1,000 × $22) + (1,000 × $22 × .70)] / 1,000} / (1 + .30) = $28.77
You short sold 500 shares of Jasper stock at $41 a share at an initial margin of 60%. What is the highest the stock price can go before you receive a margin call if the maintenance margin is 40%.?
P* = {[(500 × $41) + (500 × $41 × .60)] / 500} / (1 + .40) = $46.86
Suppose you purchase 500 shares of stock at $48 per share with an initial cash investment of $8,000. If your broker requires a maintenance margin of 30 percent, at what share price will you be subject to a margin call?
Total purchase = 500 shares × $48 = $24,000 Margin loan = $24,000 − 8,000 = $16,000 Margin call price = $16,000 / [500 − (.30 × 500)] = $45.71
You purchased 800 shares of stock for $49.20 a share. The initial margin requirement is 65% and the maintenance margin is 35%. What is the lowest the stock price can go before you receive a margin call?
P* = {[800 × $49.20 × (1 − .65)] / 800} / (1 − .35) = $26.49
Aaron purchased 200 shares of a technology stock for $13.30 a share. The initial margin requirement on this stock is 75% and the maintenance margin is 50%. What is the lowest the stock price can go before he receives a margin call?
P* = {[200 × $13.30 × (1 − .75)] / 200} / (1 − .50) = $6.65
Nelson purchased 1,600 shares of stock for $18.75 a share. The initial margin requirement is 70% and the maintenance margin is 40%. What is the maximum percent by which the stock price can decline before he receives a margin call?
P* = {[1,600 × $18.75 × (1 − .70)] / 1,600} / (1 − .40) = $9.375 Maximum percentage decline = 1 − ($9.375 / $18.75) = .50, or 50%
Marcia purchased 100 shares of Hyde Foods stock on margin at a price of $35 a share. The initial margin requirement is 65% and the maintenance margin is 35%. What is the lowest the stock price can go before Marcia receives a margin call?
P* = {[100 × $35 × (1 − .65)] / 100} / (1 − .35) = $18.85
Mary purchased 100 shares of Best Foods stock on margin at a price of $37 a share. The initial margin requirement is 60% and the maintenance margin is 35%. What is the lowest the stock price can go before Mary receives a margin call?
P* = {[100 × $37 × (1 − .60)] / 100} / (1 − .35) = $22.77
You sold short 1,000 shares of stock at a price of $36 and an initial margin of 55 percent. If the maintenance margin is 35 percent, at what share price will you receive a margin call? What is your account equity at this stock price?
Proceeds from short sale = 1,000($36) = $36,000 Initial deposit = $36,000(.55) = $19,800 Account value = $36,000 + 19,800 = $55,800 Margin call price = $55,800 / [1,000 + (.35 × 1,000)] = $41.33 Account equity = $55,800 − (1,000 × $41.33) = $14,466.67
You purchase 275 shares of 2nd Chance Co. stock on margin at a price of $53. Your broker requires you to deposit $8,000. a. Suppose you sell the stock at a price of $62. What is your return? What would your return have been had you purchased the stock without margin? b. What is your return if the stock price is $46 when you sell the stock? What would your return have been had you purchased the stock without margin?
a. Terminal price = $62 With margin = {($62 × 275) − ($53 × 275)} / $8,000 = .3094, or 30.94% Without margin = ($62 − 53) / $53 = .1698, or 16.98% b. Terminal price = $46 With margin = {($46 × 275) − ($53 × 275)} / $8,000 = −.2406, or −24.06% Without margin = ($46 − 53) / $53 = −.1321, or −13.21%
