Question8 You purchased 750 shares of common stock on margin for $40 per share. The initial margin is 60%, and the stock pays no dividend. What would be your rate of return if you sell the stock at $46 per share? Ignore interest on the margin loan. None of the other options are correct 25.0% 21.7% 13.0% 37.5% ResetMaximum marks: 3 Flag question undefinedSingle choice
A
None of the other options are correct
B
25.0%
C
21.7%
D
13.0%
E
37.5%

Question

Question8 You purchased 750 shares of common stock on margin for $40 per share. The initial margin is 60%, and the stock pays no dividend. What would be your rate of return if you sell the stock at $46 per share? Ignore interest on the margin loan. None of the other options are correct 25.0% 21.7% 13.0% 37.5% ResetMaximum marks: 3 Flag question undefinedSingle choice

A

None of the other options are correct

B

25.0%

C

21.7%

D

13.0%

E

37.5%

BlackTom AI · Accepted Answer

Initial margin of 60% means you fund 60% of the purchase with your own equity and borrow the remaining 40%.

1. Relevant knowledge points and concepts
- Margin purchase: equity = initial margin × purchase price; loan = purchase price − equity.
- Rate of return for a margin purchase = (final equity − initial equity) / initial equity.
- Final equity = sale proceeds − loan. Ignore dividends and interest as stated.

2. Complete reasoning process step by step
- Number of shares = 750. Purchase price = $40/share.
- Total purchase cost = 750 × $40 = $30,000.
- Initial margin (equity) = 60% × $30,000 = $18,000.
- Loan amount = $30,000 − $18,000 = $12,000.
- Sale price = $46/share, so sale proceeds = 750 × $46 = $34,500.
- Final equity after sale = sale proceeds − loan = $34,500 − $12,000 = $22,500.
- Equity gain = final equity − initial equity = $22,500 − $18,000 = $4,500.
- Rate of return = equity gain / initial equity = $4,500 / $18,000 = 0.25 = 25.0%.

3. Intermediate calculation steps shown
- Total cost: 750×40 = 30,000.
- Equity: 0.60×30,000 = 18,000.
- Loan: 30,000 − 18,000 = 12,000.
- Proceeds: 750×46 = 34,500.
- Final equity: 34,500 − 12,000 = 22,500.
- Gain: 22,500 − 18,000 = 4,500.
- Return: 4,500 / 18,000 = 0.25 → 25.0%.

4. Why the correct answer is correct
Because return on a margin investment is measured relative to your equity invested. The $6 per-share price increase produces a $4,500 equity gain on an $18,000 equity stake, which is exactly 25%.

5. Why other options are incorrect
- "None of the other options are correct": incorrect because one option (25.0%) is correct.
- 21.7%: does not match the computed 4,500/18,000 = 25%; likely from a mistaken divisor.
- 13.0% and 37.5%: neither equals the correct 25.0% result; e.g., 13% would correspond to ~$2,340 gain on $18,000, not the actual $4,500.
- Any alternative percentages misapply the definition of return on invested equity or ignore the correct loan/equity split.

6. Conclusion confirming final answer
The correct rate of return is 25.0%, which matches the provided answer.

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