## Description

**Question:**

Suppose you purchase 1,150 shares of stock at $82 per share with an initial cash investment of $47,150. The call money rate is 5 percent and you are charged a 1.5 percent premium over this rate. Ignore dividends.

**a.** Calculate your return on investment one year later if the share price is $90. Suppose instead you had simply purchased $47,150 of stock with no margin. What would your rate of return have been now?

with margin = ?

without margin = ?

**b.** Calculate your return on investment one year later if the share price is $82. Suppose instead you had simply purchased $47,150 of stock with no margin. What would your rate of return have been now?

with margin = ?

without margin = ?

**c.** Calculate your return on investment one year later if the share price is $66. Suppose instead you had simply purchased $47,150 of stock with no margin. What would your rate of return have been now?

with margin = ?

without margin = ?

**Answer:**

a) Loan = 1,150 x 82 – 47,150 = 47,150 at 6.5% rate

Loan repayment after a year = 47,150 x (1 + 6.5%) = $50,214.75

If stock price = $90, value of investment = 1,150 x 90 = $103,500

Value of equity = 103,500 – 50,214.75 = 53,285.25

With margin, Returns = 53,285.25 / 47,150 – 1 = 13.01%

Without margin, Returns = 90 / 82 – 1 = 9.76%

b) If share price is 82, value of equity = 1,150 x 82 – 50,214.75 = $44,085.25

With margin, Returns = 44,085.25 / 47,150 – 1 = -6.50%

Without margin, Returns = 82 / 82 – 1 = 0%

c) If share price is 6, value of equity = 1,150 x 66 – 50,214.75 = $25,685.25

With margin, Returns = 25,685.25 / 47,150 – 1 = -45.52%

Without margin, Returns = 66 / 82 – 1 = -19.51%

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