1. A stock sells for $10 a share. you purchase 100 shares for $1000 and after a
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Question
1. A stock sells for $10 a share. you purchase 100 shares for $1000 and after a year, the prices rises to $17.50. What will be the percentage of return on your investment if you bought the stock on margin and the margin requirement was 25%, 50%, and 75%? ( ignore commissions, dividends and interest expense)
2. Repeat problem 1 to determine the percentage return on your investment but in this case suppose the price of stock falls to $7.50 per share.
3.What generalization can be inferred from the answers to problems 1 and 2?
4.Ms. Gandi has decided that the stock of SmallCap inc is overvalued at $4 a share and wants to sell it short. Since the price is relatively low, short sales cannot be executed on margin so Ms Gandi must put up the entire value of the stock when it is sold short.
a) what is the percentage loss if the price of the stock rises to $8?
b)what is the percentage loss if the price of the stock rises to $10?
c) What is the percentage gain if the company goes bankrupt and is dissolved?
d) What are the maximum percentage gain the short seller can earn and the largest percentage loss the seller can sustain?
e)From the short sellers perspective, what are the best and worst case scenarios?
Explanation / Answer
Given,
Price of each stock = $10
Number of stocks purchaesd = 100
Therefore, total investment = 100 x $10 = $1,000
Case I - 25% margin requirement
This means that you need to pay only 25% of the total investment. Hence the amount you invested here is 25% of $1000 = $250. Hence, you borrow $750 from your borker ($1000 - $250)
After a year, when the stock appericiates to $17.50 a piece, the value of your total investments become = Value of each stock x Number of stocks
= $17.50 x 100 = $1750
Of this price, you return the broker the borrowed amount, which was $750. So, your earnings become $1750 - $750/
Your return on investments is = Total amount earned - Total amount invested
= $1000 - $250 = $750 (Ans)
Case II Margin = 50%
In this case, you pay $500 on your own and borrow another $500 from your broker.
When the stock appericiates, you pay your broker $500. So the amount you earned becomes $1750 - $500 = $1250.
Return on investment in this case becomes = $1250 - $500 = $750 (Ans)
Case III Margin = 75%
In this case, you pay $750 yourself and borrow $250 from your broker.
After the price appericiates, you return the broker his amount leaving you with = $1750 - $250 = $1500. Of this, return on investment becomes = $1500 - $750 = $750 (Ans)
Question 2
When price drops to $7.50 a piece.
Your present value of investments = $7.50 x 100 = $750.
Case I (25% margin).
In this case, as done in question 1, you borrowed $750 from the broker. After you return him all the borrowed amount, you are lft with exactly $750 - $750 = $0. Add to this, the $250 you invested yourself, you return on investment is a loss of $250.
Case II (50 % margin)
In this case, you borrowed $500 from your broker. After the depreciation of the sotcks, you return him his $500 and are left with $250. Your investments were $500, so when you take that out, at the end of the day, your return on investment becomes a loss of $250.
Case III (75% margin)
In this case, you put up $750 from your own account and borrow the remaining $250 from your broker. After the depreciation, you are left with $750. You return the broker his amount and are now left with $500. You subtract the amount you put up in the first place and are now left with a loss of $250.
Question 3
It is evident from questions 1 and 2 that when you borrow on margin, the amount you stand to make or loose is more than what have you invested. However also, from the successive calculations, it can be established that for the given parameters, the profit or the loss, as is the case remains the same irrespective of margin.
Question 4
Ms Gandi here short sells the stock for $4. Short selling basically means that you sell something that you don't actually own in the hope that the prices of that security will fall and in which case you stand to make a profit. However, as the case here is, when the value of security appericiates, the short seller makes a loss.
Assume for the sake of simplicity that Ms Gandi purchased 100 shares (this assumption will make calculating percentages very easy!!).
The value at which she short sells = $4 x 100 = $400
After the appericiation, the value of stocks become = $800. Hence her losses are 100%. This happens as she looses $400, the exact amount she invested in the first place.
When the stock overshoots to $10 a piece, she will have to payback $600. This makes her loss come to be 150%.
When a company oges bankrupt, the shareholders practically get nothing. There is some provision for the common shareholders to get a pie of the left over value of assets, but theoretically, the value of shares becomes zero. This is the best case for the short seller. In this case, Ms Gandi has to pay back nothing and the entire $400 becomes her profit. This is a 100% profit.
The best amount that the short seller can earn is the value of stock x number of stocks purchased. This happens only in the case when the company goes bankrupt.
In short selling, as you may infer from the above discussions, there is no limit to the amount of loss that could be incurred. As the value of stocks keeps on appericiating, the losses for the short seller keeps on mounting.
So, coming to the last question, the best possible case for the sohrt seller is when the company goes bankrupt and the wost case is when the company starts making huge profits which results in an exponential increase the value of its stocks.
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