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 $25k 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 $3m from the bank in the form of an interest-only loan with an interest rate of 3% pa to buy 4 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 1%, 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. Gear's debt-to-assets ratio one year ago was 75% while Nogear's was zero.

b. Gear's net rent before tax was 100k while Nogear's was 25k.

c. Gear's capital gains before tax were 30k while Nogear's was 10k.

d. Gear's interest expense before tax was 90k while Nogear's was zero.

e. Gear's income and capital gains after tax due to the investment properties (ignoring opportunity costs) was 27.5k while Nogear's was 19.25k.

Answer 1

In the given question option c is incorrect.

Reason is as follow:

Option (a)

Calculation of debt to assets ratio.

Nogear invested his own money of $ 1 million to buy an apartment, therefore his debts are 0 whereas assets are of $ 1m.

Debt to asset ratio = Debt/assets

= 0/1m

= 0

Gear  invested his own money of $ 1 million and borrow $3m from bank to buy 4 apartments worth $ 4m. Therefore his debts are of $3m whereas assets are of $ 4m.

Debt to asset ratio = Debt/assets

= 3000000/4000000

= 75%

This option is correct.

Option (b)

Calculation of net rent before tax

Nogear bought only one apartment and one apartment fetch net rent of $ 25000; Therefore Nogear net rent before tax is $ 25000.

Gear bought 4 apartments and one apartment fetch net rent of $ 25000; Therefore Gear net rent before tax is ($ 25000*4)= $ 100000.

Therefore this option is correct.

Option (c)

Calculation of Capital Gain before tax

Nogear bought only one apartment and price of each aparment increases by 1% before tax.

Therefore his capital gain before tax is (1000000*1%)= $ 10000

Gear bought 4 apartments and price of each aparment increases by 1% before tax; Therefore Gear his capital gain before tax is ($ 1000000*4*1%)= $ 40000.

Therefore this option is incorrect.

Option (d)

Calculation of Interest Expenses before tax

Nogear has no borrowings. Therefore his interest expense is 0.

Gear has borrowings of $ 3m, Therefore interest expenses of Gear is:

=(3000000*3%)= $90000.

Therefore this option is correct.

Option (e)

Calculation of Income and Capital Gain before tax

NOGEAR
Particular	Amt.
Total Rental Income	25000
Total Capital Return (calculated in option c)	10000
Total Return	35000
Tax Rate	45%
Income and Capital Gain after tax                      35000*(1-0.45)	$ 19250

GEAR
Particular	Working	Amt.
Total Rental Income	(25000*4)	100000
Total Capital Return	(1000000*1%*4)	40000
Interest Cost	(3000000*3%)	-90000
Net Return		50000
Tax Rate		45%
Income and Capital Gain after tax	50000*(1-0.45)	$ 27500

Therefore this option is also correct.