Question

Assume a property can be purchased for $105,000. The existing mortgage has a balance of only $50,000, 15 years remaining and payments are $507.13. You want to assume the mortgage, but need to finance $70,000 total so you must take out a second mortgage for $20,000 for 15 years at 14%. Alternatively you could purchase an equivalent property for $100,000 by obtaining a loan for $70,000 for 15 years at the market rate of 11%.

a.       What is the effective return (or cost) of assuming the loan and taking out a 2^ndmortgage?

b.       Is it better to assume the loan and take out a second mortgage, or should you buy the alternative property and finance the purchase with a new loan at the market rate (answer should be "assume" or "new"?

Answer 1

We need to first calculate the cost of the existing mortgage

by using the PV of ordinary annuity formula,

& plugging-in the known values, as follows:

50000=507.13*(1-(1+r)^-180)/r

Solving the above, we get the

Monthly r= 0.75%

ie.Effective Annual r=

(1.0075)^12-1=

9.38%

Now,

a.the Effective return (or cost) of assuming the loan and taking out a 2ndmortgage=

is the weighted average cost of the 2 separate mortgages

ie.

Weighted average cost of the above 70000 mortgages is:

((50000/70000)*9.38%)+((20000/70000)*14%)=

10.70%

Alternate ,ie purchasing an equivalent property for $100,000 by obtaining a loan for $70,000 for 15 years at the market rate of 11%

b.
Monthly pmt. Under the 2nd mortgage=
20000=X*(1-(1+0.0117)^-180)/0.0117
Mthly. Pmt.,X=266.89
So,
the total mthly .pmt. under the loan assumption option will be 507.13+266.89=774.02
Now, the mthly.pmt. For the new loan will be
70000=X*(1-(1+0.0092)^-180)/0.0092
Mthly. Pmt.,X=797.38

Comparing the alternatives
Alternatives	Down	Mthly.pmt.	Int.
Loan assumption	35000	774.02	10.70%	Wt. av. Cost
New	30000	797.38	11%	Mkt rate
Diff.	5000	-23.36
Now, finding the return for paying $ 5000 more (in loan assumption)
5000=23.36*(1-(1+r)^-180)/r
r works out to -0.19% p.m.
ie.
(1-0.0019)^12-1=
-2.26%
per annum
(Negative return for paying $ 5000 more)

the recommendation will be :

It is better to buy the alternative property and finance the purchase with a new loan at the market rate .

ANSWER: "New"