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. Gear's debt-to-assets ratio one year ago was 80% while Nogear's was zero.

b. Gear's net rent before tax was 150k while Nogear's was 30k.

c. Gear's capital gains before tax were 200k while Nogear's was 40k.

d. Gear's interest expense before tax was 250k while Nogear's was zero.

e. Gear's income and capital gains after tax due to the investment properties (ignoring opportunity costs) was 82.5k while Nogear's was 38.5k.

Answer 1

Gear total debt in the starting of the year=$4m(as loan) and total asset=$5m(as apartment purchased) and Nongear total asset=$1m (as apartment) and total debt=0(no loan)

a)This statement is correct ,in the starting of the year Gear's debt-asset ratio=4/5=.8 or 80% and Nongear's debt-asset ratio=0/1=0 or 0%

b)Gear's net rent before tax=$30k*5=$150k and Nongear rent before tax=$30k*1=$30k

this statement is correct.

c)Gear's interest expense before tax=5% of $4m pa=.05*$4m=$200k and Nongear has zero interest expense as he has no loan.

THIS STATEMENT IS INCORRECT.

d)Gear's rent income=$30*5=$150k

Gear' income after tax=$150k-.45*$150k=$82.5k

Gear's capital gain=.04*$5m=$200k

Out of this capital gain of $200k he paid the interest of the loan (i.e. .05*$4m=$200k). So he has no capital gain.

Therefore, Gear' income and capital gains after tax=$82.5k

Nongear's income from rent=$30k

Nongear's income after tax=$30k-.45*$30k=$16.5k

Nongear's capital gain after tax =$1m*.04-(.45*.04*$1m)=$22k

So, NONGEAR'S income and capital gain after tax =$16.5k+$22k=$38.5k

THEREFORE THIS STATEMENT IS CORRECT.