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Q: Reverse Mortgage Calculation ( Answered 4 out of 5 stars,   0 Comments )
Question  
Subject: Reverse Mortgage Calculation
Category: Business and Money > Finance
Asked by: lovebeer84-ga
List Price: $40.00
Posted: 05 Sep 2002 19:31 PDT
Expires: 05 Oct 2002 19:31 PDT
Question ID: 62148
I would like to know the formula(s) for computing a HECM (the most
popular type as far as I know) reverse mortgage.
Given inputs such as: Age of applicant(s), value of home and
(optionally) zip code or location of home - how is the per month (or
year) income calculated?

An example of this is on the following web site/page:
http://www.rmaarp.com/
There is also more information about what reverse mortgages are at
this site.

I already have the formulas for such things as: PV, FV, IRATE,
IPMT.... i.e. the common financial calculations.
Answer  
Subject: Re: Reverse Mortgage Calculation
Answered By: answerguru-ga on 06 Sep 2002 01:09 PDT
Rated:4 out of 5 stars
 
Hi lovebeer84-ga,

Before being able to place dollar value on an MECM, certain
eligibility requirements must first be met:
1. You, and any other owners of your home, must be age 62 or over
2. at least one owner must live in your home as a principal residence
3. your home must be a single-family residence in a 1- to 4-unit
dwelling, or part of a HUD-approved condominium or planned unit
development (PUD)
4. some manufactured housing is eligible, but mobile homes and
cooperatives are not
5. your home must meet HUD's minimum property standards, but you can
use the HECM to pay for any required repairs
6. you must discuss the HECM program with a HUD-approved counseling
agency

http://www.aarp.org/revmort/contents/eligibility.html

Assuming that all of these criteria are met, we know that you are
eligible for an HECM reverse mortgage. The next step is to obtain the
value of the home, which can be done through some sort of certified
appraisal. The critical, and somwhat controversial, part of the
procedure now occurs. each county in the country has a maximum
mortgage limit based on internal data from the FHA for the previous
year for home values in the area (these values are adjusted
annuallly). This maximum ranges from $144,336 to $237,500, with the
higher values being given to counties in the larger metropolitan
areas.

You can find out your county's maximum mortgage limit here:

https://entp.hud.gov/idapp/html/hicostlook.cfm

There are also options that allow the borrower to choose how to
receive the proceeds from an HECM:
(1) a lump sum payment)
(2) fixed monthly payments (for 10 years, or for as long as the
borrower occupies the home)
(3) a line of credit
(4) a combination of monthly payments and a line of credit.

Interest rate is also a factor: "The interest rate charged on a HECM
is adjusted monthly or annually – the borrower chooses. However, these
adjustments don’t alter the monthly payments that borrowers can
receive (if they have chosen the monthly payment option). Instead, the
adjustment affects the total interest that is charged on the loan,
which is added to the loan balance while the loan is outstanding and
is paid when the loan becomes due."

Lastly, "The fee that a lender can charge a borrower for obtaining a
HECM is limited. This origination fee can’t exceed $2,000 or 2 percent
of the maximum claim amount (the FHA loan limit), whichever is
greater." Of course this is also a factor in the final proceeds
received by the borrower.

http://www.reversemortgage.org/hecm.htm


So from the above information, the maximum value of the HECM is the
smaller of the home's value and the maximum mortgage limit. Rather
than an equation that produces a magic number, the determination of an
HECM's value is the result of the conditions (eligibility, county,
home value, lender fees, interest rates) as is described above. Of
course, this could be phrased in terms of some sort of procedural
algorithm that described the process mathematically :)


There have been rumblings about the inequity of using this procedure
the size of the reverse mortgage. An example of this is outline in the
following blurb from President of the Central Pacific Mortgage
Company:

"A HECM can be used by seniors who are "house rich" but "cash poor" to
convert the equity in their home into monthly cash payments. FHA loan
limits for "forward" or traditional mortgages vary by county,
depending upon housing costs in the area. Presently, the maximum loan
limit for an FHA-insured loan in a high cost area is 87 percent of the
Fannie Mae/Freddie Mac conforming limit. In this way, the FHA program
is focused on serving primarily low- and moderate-income families who
would not qualify for conventional financing and private mortgage
insurance. This approach for calculating loan limits, however, does
not make sense for HECMs. Because the county-by-county FHA loan limits
also apply to reverse mortgages, some unintended inequities result.
For example, under current law, a senior living in Des Moines with a
home worth $175,000 can get a reverse mortgage for only $144,336 (the
FHA loan limit in Des Moines) while a senior living in Los Angeles
with a home worth $175,000 can get a reverse mortgage for the full
$175,000 because the loan limit in Los Angeles is $237,500. There
should be no disparate treatment of seniors in this fashion. There is
no rationale for having county-by-county FHA loan limits for reverse
mortgages, because this is a program that serves seniors who already
own their homes and there is only a budding conventional market for
reverse mortgages."

http://www.mbaa.org/industry/docs/02/courson_0424.pdf

Nevertheless, this is the current law and so all are bound by it...

If you have nay problems understanding the above information please
feel free to post a clarification and I will respond in a timely
manner.

Cheers!

answerguru-ga

Request for Answer Clarification by lovebeer84-ga on 06 Sep 2002 15:45 PDT
I understand that there are several variables in this problem. Lets
say that I have already asked my 'client' what the home is worth, and
I knew the maximum mortgage limit for where they live - lets say its
90% of home value.

How is the per month income calculated? Again lets assume that the
'client' has requested a fixed amount per month (vs a line of credit).
Now given that we can't predict what interest rates will do in the
future, we can use a constant interest rate for our calculations.

So, how would I compute the income per month on:
A $200,000 home where the owner can take up to 90% (FHA loan limit) of
the home value and the interest rate is 4%. Lets ignore any fees being
charged to get the reverse mortgage.

In other words is it:
incomePerMonth = FV((200000 *.9),    // beginning balance
                    0.04,            // interest rate
                    yearsLeftToLive) // life expectancy 85 - current
age 65 = 20
                    div (yearsLeftToLive div 12);//cause we want per
month inc.

This is the kind of information I'm looking for.

Thanks

Clarification of Answer by answerguru-ga on 06 Sep 2002 16:19 PDT
Hi again,

As a result of the modifications you'vemade with your clarification,
yes it is possible to now determine the per month income.

Restating the values given:

Face value of mortgage = $180,000
Interest rate = 4%

But from [ http://www.reversemortgage.org/hecm.htm ] we know that "The
interest rate charged on a HECM is adjusted monthly or annually – the
borrower chooses. However, these adjustments don’t alter the monthly
payments that borrowers can receive (if they have chosen the monthly
payment option). Instead, the adjustment affects the total interest
that is charged on the loan, which is added to the loan balance while
the loan is outstanding and is paid when the loan becomes due."

So the per month income is determined by ONLY the interest rate at the
time when the reverse mortgage is granted...any other adjustments are
treated as described above. (No future value calculations)

In terms of a formula, monthly payments are calculated as follows:

incomePerMonth = (($180,000)*((1.04)^(yearsLeftToLive)))/(yearsLeftToLive*12)

Thanks for your question.

answerguru-ga

Request for Answer Clarification by lovebeer84-ga on 11 Sep 2002 05:16 PDT
I much as I've tried, I haven't been able to get the numbers from the
formula you've provided to match the results from www.rmaarp.com.
Via other websites, I've been able to determine things like: bank fees
and closing costs, loanable amount (limit) for an area of the country
and the loanable percentage given the age of the applicant. I know
that the www.rmaarp.com web site uses all of these inputs and as I've
said, I am unable to repeat there results.

Clarification of Answer by answerguru-ga on 11 Sep 2002 09:19 PDT
Hi again,

I agree that you are not likely to get the same values, because in
your previous clarifications you asked that the following
simplifications be made to the formula:

1. Do not consider the fees being charged for the reverse mortgage
2. Constant interest rate

Its quite likely that a definitive answer to this question is not
possible for a couple key reasons:
1. It is not explicitly available to the public
2. You don't know which interest rate is being used (it may not be the
current prime rate but actually a certain amount above or below it)
3. You don't know the fee being charged to being obtained the reverse
mortgage

From a mathematical standpoint, you would need a system of two
equations to find these two variables described in 2 and 3, but of
course we are only talking about one formula here!

I did a little digging regarding legal obligation to make these types
of calculations public knowledge, but came up empty. It might be worth
posting another question to our pool of talanted researchers along
these lines to see if you can force them to provide you with the
calculation :)

Thanks for using Google Answers :)

answerguru-ga
lovebeer84-ga rated this answer:4 out of 5 stars
I received the basic formula for what I was after. Unfortunatly
turning that into a real world application will take a bit more work.

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