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Q2) Xian and Devi are each buying a house for $500,000. Xian puts $200,000 down and gets a mortgage for the other $300,000 at

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Answer #1

Answer A) Down Payment by both is considered as the equity investment by both investors.

Xian Devi
Loan 300000 400000
Down Payment (Equity) 200000 100000
Leverage 1.5 times 4 times

Leverage Ratio is calculated as = Total Debt/Total Equity

Answer B) House Value after 1 year = 500000 + 5%*500000 = 525000

Xian Devi
House Value after 1 year 525000 525000
Purchased Price 500000 500000
Net Profit (without including interest) 25000 25000
Amount Invested 200000 100000
ROI 12.50% 25.00%

ROI = Net Income/Equity (Amount Invested)

Answer C) House Value after 1 year = 500000 + 5%*500000 = 525000

Interest Paid by Xian = 6%*300000 = 18000

Interest Paid by Devi = 6%*400000 = 24000

To calculate ROI for one year, we have assumed that both ill repay their loans after 1 year.

ROI = Net Income/Equity (Amount Invested)

Xian Devi
House Value after 1 year 525000 525000
Interest Paid (after 1 year) 18000 24000
Principal Repaid (after 1 year) 300000 400000
Amount left after the principal repayment 207000 101000
Amount Invested 200000 100000
Net Income 7000 1000
Return on Investment (ROI) 4% 1%

Answer d) From question c), we can conclude, Net profit earned by Xian (after the interest deductions) = 7000

Net profit earned by Devi (after the interest deductions) on 100000 invested in house = 1000

For Devi's ROI to equate with that of Xian, Devi's must earn 6000 interest on the other 100000. Hence, 6% must be the effective annual rate that Devi must earn on the other 100000 to equate her ROI with Xian's.

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