1. **Problem Statement:** Calculate the annual return on a margin purchase of 600 shares at Tk. 40 each with 55% initial margin, 10% interest on the margin loan, and Tk. 2 dividend per share. 2. **Given Data:** - Shares purchased: 600 - Purchase price per share: Tk. 40 - Initial margin: 55% (meaning 55% of purchase price is investor's own money) - Interest rate on margin loan: 10% - Dividend per share: Tk. 2 3. **Formulas:** - Total cost = Number of shares \times Purchase price - Investor's equity = Initial margin \times Total cost - Loan amount = Total cost - Investor's equity - Interest on loan = Loan amount \times Interest rate - Dividend received = Number of shares \times Dividend per share - Sale proceeds = Number of shares \times Sale price - Annual return on margin = \frac{Sale proceeds + Dividend - Interest - Total cost}{Investor's equity} - Annual return on cash purchase = \frac{Sale proceeds + Dividend - Total cost}{Total cost} --- ### a. Stock sold at Tk. 45 per share 4. Calculate total cost: $$600 \times 40 = 24000$$ 5. Calculate investor's equity: $$0.55 \times 24000 = 13200$$ 6. Calculate loan amount: $$24000 - 13200 = 10800$$ 7. Calculate interest on loan: $$10800 \times 0.10 = 1080$$ 8. Calculate dividend received: $$600 \times 2 = 1200$$ 9. Calculate sale proceeds: $$600 \times 45 = 27000$$ 10. Calculate annual return on margin: $$\frac{27000 + 1200 - 1080 - 24000}{13200} = \frac{27000 + 1200 - 1080 - 24000}{13200} = \frac{3120}{13200} = 0.2364 = 23.64\%$$ --- ### b. Stock sold at Tk. 25 per share 11. Calculate sale proceeds: $$600 \times 25 = 15000$$ 12. Calculate annual return on margin: $$\frac{15000 + 1200 - 1080 - 24000}{13200} = \frac{-6880}{13200} = -0.5212 = -52.12\%$$ --- ### c. Rate of return if purchase made with cash (no margin) 13. For Tk. 45 sale price: $$\frac{27000 + 1200 - 24000}{24000} = \frac{4200}{24000} = 0.175 = 17.5\%$$ 14. For Tk. 25 sale price: $$\frac{15000 + 1200 - 24000}{24000} = \frac{-7800}{24000} = -0.325 = -32.5\%$$ --- **Final answers:** - a) Annual return on margin = 23.64% - b) Annual return on margin = -52.12% - c) Annual return on cash purchase = 17.5% (for Tk. 45 sale), -32.5% (for Tk. 25 sale)