Question

Bob buys a property with an 80% LTV interest only mortgage at an annual rate of 6%, with annual compounding and annual payments. Bob’s annual cap rate for the first year is 8%.

Which of the following is true about Bob’s Return on Equity (ROE) for the first year?

	A.	ROE is higher than if he didn’t use leverage
	B.	ROE is lower than if he didn't use leverage
	C.	There is not enough information to answer this question
	D.	ROE is the same as it would have been if he didn't use leverage

Answer 1

Answer:

LTV = 80%

Interest only mortgage = 6%

Annual cap rate for the first year is 8%.

Lets assume value of the property = $ 1 Million

Option 1: Taking the mortgage loan (leveraged)

LTV = 80%

Loan amount = $ 1 million * 80% = $800,000

Down payment (own funds) = $200,000 ($1,000,000-$800,000)

Cap rate = Net Operating Income (NOI) / Property Value

8% = NOI / $1 million , thus NOI = $80,000

Interest payment = $800,000*6% = $48,000

Net Income = $80,000-$48,000 = $32,000

Return on equity = Net Income / equity (own funds) = 32,000/200,000 = 16%

Option 2 : Not taking the mortgage loan (unleveraged)

Net Operating Income as above = $80,000

Equity (property value) = $ 1 million

Return on equity = Net Income / equity (own funds) = 80,000/1,000,000 = 8%

Thus, Return on equity if leveraged is used is higher than if leveraged is not used. Hence the answer is A. ROE is higher than if he didn’t use leverage.