Question

Last year, two friends Gear and Nogear invested in residential apartments. Each invested $1m of their own money (their net wealth). Apartments cost $1m last year and they earned net rents of $30k pa over the last year. Net rents are calculated as rent revenues less the costs of renting such as property maintenance, land tax and council rates. However, interest expense and personal income taxes are not deducted from net rents. Gear and Nogear funded their purchases in different ways: Gear used $1m of her own money and borrowed $4m from the bank in the form of an interest-only loan with an interest rate of 5% pa to buy 5 apartments. Nogear used $1m of his own money to buy one apartment. He has no mortgage loan on his property. Both Gear and Nogear also work in high-paying jobs and are subject personal marginal tax rates of 45%. Assume that capital gains are taxed at the full 45% personal rate when the asset is sold. Over the past year, house prices increased by 4%, before subtracting capital gains tax (CGT). Gear and Nogear both sold their houses and Gear paid back all debt. Which of the below statements about the past year is NOT correct? Note that m stands for million (10^6) and k stands for kilo (10^3). Select one:

a. The net rental return on house assets before tax was 3% and after tax was 1.65% pa.

b. The net capital return on house assets before tax was 4% and after tax was 2.2% pa.

c. The interest rate on debt before tax was 5% and after tax was 2.75% pa.

d. The return on equity for Nogear before tax was 7% and after tax was 3.85% pa. e. The return on equity for Gear before tax was 15% and after tax was 5.5% pa.

Answer 1

Option E is answer because it is incorrect. e. The return on equity for Gear before tax was 15% and after tax was 5.5% pa.

ROE of Gear before tax = (Rental Income from properties + increase in value of property - interest paid) / investment

ROE of Gear before tax = (30000*5 + 5000000*4% - 500000*5%) / 1000000

ROE of Gear before tax = 15%

ROE after tax = ROE before tax * (1 - tax)

ROE after tax = 15% * 0.55

ROE after tax = 8.25%

ROE after tax is not 5.50% it is 8.25%

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