Suppose you purchase 950 shares of stock at $63 per share with an initial cash i

Question

Suppose you purchase 950 shares of stock at $63 per share with an initial cash investment of $20,000. The call money rate is 5 percent and you are charged a 1.5 percent premium over this rate.

Calculate your return on investment one year later if the share price is $71. Suppose instead you had simply purchased $20,000 of stock with no margin. What would your rate of return have been now? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Calculate your return on investment one year later if the share price is $63. Suppose instead you had simply purchased $20,000 of stock with no margin. What would your rate of return have been now? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Calculate your return on investment one year later if the share price is $47. Suppose instead you had simply purchased $20,000 of stock with no margin. What would your rate of return have been now? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Suppose you purchase 950 shares of stock at $63 per share with an initial cash investment of $20,000. The call money rate is 5 percent and you are charged a 1.5 percent premium over this rate.

Explanation / Answer

To calculate the rate of return, we need to find the value of debt used to finance the purchase and interest cost incurred on it. The formula for calculating return of profit in dollar terms would be:

Return/Profit = Sales Value - Purchase Value - Interest Cost on Debt

where Interest Cost on Debt = Value of Debt*(Call Money Rate + Spread)

Value of Debt = Total Value of Shares Purchased - Amount Put Up

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The formula for calculating percentage return is as follows:

Return (Percentage) = Dollar Value of Return or Profit/Purchase Value*100

Without Margin, Rate of Return (Percentage) = (Sales Price - Purchase Price)/Purchase Price*100

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Part a)

Value of Debt = 950*63 - 20,000 = $39,850

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Interest Cost on Debt = 39,850*(5% + 1.5%) = $2,590.25

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Return or Profit in Dollar Terms = 950*71 - 950*63 - 2,590.25 = $5,009.75

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Return or Profit (%) = 5,009.75/(950*63)*100 = 8.37%

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Without Margin, Rate of Return = (71 - 63)/63*100 = 12.70%

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Part b)

Value of Debt = 950*63 - 20,000 = $39,850

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Interest Cost on Debt = 39,850*(5% + 1.5%) = $2,590.25

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Return or Profit in Dollar Terms = 950*63 - 950*63 - 2,590.25 = -$2,590.25

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Return or Profit (%) = -2,590.25/(950*63)*100 = 4.33%

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Without Margin, Rate of Return = (63 - 63)/63*100 = 0

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Part c)

Value of Debt = 950*63 - 20,000 = $39,850

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Interest Cost on Debt = 39,850*(5% + 1.5%) = $2,590.25

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Return or Profit in Dollar Terms = 950*47 - 950*63 - 2,590.25 = -$17,790.25

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Return or Profit (%) = -17,790.25/(950*63)*100 = -29.72%

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Without Margin, Rate of Return = (47 - 63)/63*100 = -25.40%

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