Problem 2: Buying on Margin [20 points] An investor decides to purchase shares o
ID: 2816789 • Letter: P
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Problem 2: Buying on Margin [20 points] An investor decides to purchase shares of DWNR on margin. The investor has $175,000 cash in their account to use for the purchase (assume this is the only position in the account). The investor may borrow from their broker at 7% per year and must have an initial margin of at least 50%. The maintenance margin is 30%. The current market price of DWNR is $40.00 and DWR pays quarterly dividends of S0.75 per share (assume the first dividend comes exactly 3 months from today). [4] Assume the investor utilizes their maximum margin potential. How many shares of DWNR can the investor purchase? [4] Below what stock price will the investor receive a margin call? [4] If the investor holds this position for 3 months and then sells the shares and repays the loan, what is the percentage profit (loss) if the market price of DWNR is $47.00 after3 months? [4] If the investor holds this position for 3 months and then sells the shares and repays the loan, what is the percentage profit (loss) if the market price of DWNR is S33.00 after 3 months? [4] Compare your answers in C. and D. to the profit (loss) if the investor did not use the margin account and instead only purchased $175,000 worth of DWNR shares. effect of leverage on returns. a. b. c. d. e. Discuss theExplanation / Answer
.a Current market price per share=$40
Amount available=$175,000
Initial margin requirement=50%=0.5
Amount of shares that can be purchased=175000/0.5= $ 350,000
Number of shares of DWNR can be purchased=(350000/40)=8,750
.b. number of shares purchased=8,750
Margin Loan=$175,000
Account Value=8750*40=$350,000
Account Equity=(350,000-175000)=$175,000
As share price falls, the Account Value and Account equity will decrease.
Margin call will be made when account equity is less than 30% of Account Value
A
B=8750*A
C
D=B-C
E=(30%*B)
F=D-E
Purchase
Account
Margin
Account
Maintenance
Margin
Price
Value
Loan
Equity
Margin
surplus/(shortfall)
$40
$350,000
$175,000
$175,000
$105,000
$70,000
$35
$306,250
$175,000
$131,250
$91,875
$39,375
$30
$262,500
$175,000
$87,500
$78,750
$8,750
$28.57
$249,988
$175,000
$74,988
$74,996
($9)
$25
$218,750
$175,000
$43,750
$65,625
($21,875)
$20
$175,000
$175,000
$0
$52,500
($52,500)
$15
$131,250
$175,000
($43,750)
$39,375
($83,125)
$10
$87,500
$175,000
($87,500)
$26,250
($113,750)
The investor will receive margin call when the share price falls below $28.58
.(c)Amount Received after 3 months:
Dividend=$0.75
Amount from sale of share=$47.00
Total amount received per share =$47.75
Total amount received for 8750shares=47.75*8750= $ 417,812.50
Payment to broker =$175,000
Interest on loan=175000*0.07*(3/12)=$3,063
Total payment to the broker=175000+3063=$178,062.50
Net amount received=(417812.50-178062.50)= $ 239,750.00
Percentage Profit=((239750/175000)-1)*100=0.37*100=37%
(d)
Amount Received after 3 months:
Dividend=$0.75
Amount from sale of share=$33.00
Total amount received per share =$33.75
Total amount received for 8750shares=33.75*8750= $ 295,312.50
Payment to broker =$175,000
Interest on loan=175000*0.07*(3/12)=$3,063
Total payment to the broker=175000+3063=$178,062.50
Net amount received=(295312.50-178062.50)= $ 117,250.00
Percentage Profit=((117250/175000)-1)*100=-0.33*100=-33%
There is a loss of 33%
(e)If the investor did not use the margin account:
Number of shares purchased with $175000=175000/40=4,375
Amount Received is sells at $47=(47.75*4375)= $ 208,906.25
Percentage Profit=((208906.25/175000)-1)*100=19.38%
If share price is $33,
Amount received=33.75*4375= $ 147,656.25
Percentage Loss=((147656.25/175000)-1)*100=15.63%
A
B=8750*A
C
D=B-C
E=(30%*B)
F=D-E
Purchase
Account
Margin
Account
Maintenance
Margin
Price
Value
Loan
Equity
Margin
surplus/(shortfall)
$40
$350,000
$175,000
$175,000
$105,000
$70,000
$35
$306,250
$175,000
$131,250
$91,875
$39,375
$30
$262,500
$175,000
$87,500
$78,750
$8,750
$28.57
$249,988
$175,000
$74,988
$74,996
($9)
$25
$218,750
$175,000
$43,750
$65,625
($21,875)
$20
$175,000
$175,000
$0
$52,500
($52,500)
$15
$131,250
$175,000
($43,750)
$39,375
($83,125)
$10
$87,500
$175,000
($87,500)
$26,250
($113,750)
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