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

In the given question option e is wrong, reason is as under:

Option a: Net Rental Income p.a. is $ 30000 per apartment and apartment cost is $ 1000000

Therefore net rental return = ( Net Rental Income/ Apartmental Income)*100

=(30000/1000000)*100

=3%

As both Gear and Nogear is in tax rate of 45%: net rental return

= Rental return*(1-tax rate)

= 3*(1-0.45)

=1.65% p.a.

(This option is correct)

Option b: Net capital return is the return by which price of apartment is increased. In the given case, apartment price increased by 4% after one year, Therefore net capital return is 4%

As capital gain is in tax rate of 45%: net capital return on house assets

= Net Capital return*(1-tax rate)

= 4*(1-0.45)

=2.20% p.a.

(This option is correct)

Option c: As it is clearly given that interest rate is 5% p.a. in case of bank borrowing, and both Gear and Nogear is in tax rate of 45%

Interest rate on debt before tax is 5% p.a.

and after tax is : Interest Rate before tax*(1-tax rate)

5(1-0.45) = 2.75% p.a.

(This option is correct)

Option d:

Net Rental Return	3%
Net Capital Return	4%
Total Return before tax	7%

or

Particular	Amt.
Total Rental Income	30000
Total Capital Return	40000
Total Return (a)	70000
Equity Investment (b)	1000000
Return on equity (a/b) before tax	7%

After Tax Return Will be : 7*(1-0.45) = 3.85% p.a.

This option is correct.

Option e:

Particular	Working	Amt.
Total Rental Income	30000*5	150000
Total Capital Return	(1000000*4%*5)	200000
Interest Cost	(4000000*5)	-200000
Net Return (a)		150000
Equity Investment (b)		1000000
Return on equity (a/b) before tax		15%

Return after Tax: 15(1-0.45) = 8.25% p.a.

Therefore this option is incorrect.