Q3- Suppose you purchase 300 shares of stock at $75 per share with an initial ca

Question

Q3- Suppose you purchase 300 shares of stock at $75 per share with an initial cash investment of $10000 it your broker requires 25% maintenance margin, at what share price will you be subject to a margin call? Suppose that t call money rate is 4% and you are charged 2% premium over this rate. Calculate your return on investment for eat' of the following share prices one year later. What would your rate of return be in each case if you purchased $1000 of stock with no margin? Assume that there are no dividends .

Explanation / Answer

Answer:

As it is given in the question 300 shares at$75 each are purchased.

So the total worth of investment at the time of purchase = 300 * $75 = $22500

The amount invested by himself = $10000 (This is the equity)

therefore borrowing made by the investor = $22500 - $10000 =$12500

Now given that 25% is the margin requirement by the broker. It means at any point of time if the value of investment in 300 shares goes down to this 25% of value of investment than margin call would be made by the broker.

Here in this case margin requirement = 25% * Value of investment = 25% * $22500 = $5625

It means if the equity of investor goes beyond this value he/she would be subject to a margin call by the broker.

In this case the value of equity = Value of investment - borrowing = $22500 - $12500 = $10000

As the value of equity $10000, is more than $5625, so in this cas ethere will be no margin call.

Now to find out the price of share to get a margin call we have to assume stock price as x.

So the value of investment = 300*x = 300x

Margin requirement = 25% * 300x = 75x

Now we know that the borrowing in this case is $12500

so the value of equity = 300x - 12500

To get a margin call this value of equity = margin requirement

therefore,

300x - 12500 = 75x

solving for x we get,

x = $55.55

So this is the value of share to get a margin call from the broker.

Case-1 When share price = $85

In this case the cost of borrowing = 4% + 2% = 6%

Total borrowing = $12500

So cost of borrowing = $750

Now initial price of share was $75 which rose to $85 getting $10 of profit per share

Hence total profit = $10 * 300 = $3000

Cost = $750

therefore net profit = $3000 - $750 = $2250

So, return on investment = $2250/$10000 * 100 % = 22.5%

Case-2 When share price = $65

In this case the cost of borrowing = 4% + 2% = 6%

Total borrowing = $12500

So cost of borrowing = $750

Now initial price of share was $75 which fell to $65 getting $10 of loss per share

Hence total loss = $10 * 300 = $3000

Cost = $750

therefore net loss = $3000 + $750 = $3750

So, return on investment = $3750/$10000 * 100 % = 22.5% = 37.5%

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