Question

1.A property can be purchased for $200,000 subject to an assumable loan at 8.25% (below market reates) with 15 years remaining and a balance of only 120,000 (The original loan was for 165,000). You want to assume the mortgage, but need to finance $150,000 total so you must take out a second mortgage for $30,000 for 15 years at 8.75%. Alternatively, there is a comaprable property for $190,000 for which you can obtain a loan of $150,000 for 15 years at the market rate of 11.00%. What rate of "return" would a borrower earn by assuming the loan and taking out a second mortgage instead of borrowing at the market rate?

2. A property can be purchased for $150,000 subject to an assumable loan at 8.25% (below market rates) with 25 years remaining and a balance of $135,000. A comparable property without special financing costs $145,000 and a loan for $135,000 can be obtained at 8.5% for 25 years. What rate of "return" would a borrower earn by assuming the loan instead of borrowing at the market rate?

Answer 1

1.

Option 1
Assuming the loan and taking out second mortgage
Property value	$200,000
Assumable loan value	$120,000
Interest rate per annum	8.25%
Years remaining	15
Payment per month	$1,164.17	=PMT(8.25%/12,15*12,-$120,000)
Second Mortgage
Loan value	$30,000
Interest rate per annum	8.75%
Years remaining	15
Payment per month	$299.83	=PMT(8.75%/12,15*12,-$30,000)
Total Payment per month	$1,464.00	($1,164.17+$299.83)

Option 2
Borrowing at market rate
Property value	$190,000
Loan value	$150,000
Interest rate per annum	11.00%
Years remaining	15
Payment per month	$1,704.90	=PMT(11%/12,15*12,-$150,000)

Calculation of rate of return theborrower will earn by assuming the loan and taking out a second mortgage instead of borrowing at the market rate:

Monthly saving in payment in Option 1 instead of Option 2	$240.89	($1,704.90-$1,464)
Additional cost of Property in Option 1	$10,000	($200,000-$190,000)
Rate of return per month	2.4%	=rate(15*12,-$240.89,$10,000)

2.

Option 1
Assuming the loan
Property value	$150,000
Assumable loan value	$135,000
Interest rate per annum	8.25%
Years remaining	25
Payment per month	$1,064.41	=PMT(8.25%/12,25*12,-$135,000)

Option 2
Property without special financing costs
Property value	$145,000
Loan value	$135,000
Interest rate per annum	8.50%
Years remaining	25
Payment per month	$1,087.06	=PMT(8.5%/12,25*12,-$135,000)

Rate of "return" would a borrower earn by assuming the loan instead of borrowing at the market rate:

Monthly saving in Option 1 instead of Option2	$22.65	($1,087.06-$1,064.41)
Additional cost of Property in Option 1	$5,000	($150,000-$145,000)
Rate of return per month	0.2%	=rate(25*12,-22.65,$5,000)