Is it possible to create a formula (or is there an existing source) to
determine the monetary advantages of the mortgage/cash decision of
purchasing a home.
I'm not interested in the emotional issues or the security issues, I would
like to be able to use known values and assumed variables to project each of
the options over time.
Thanks
JW

The only way to answer is A better than B is to work out both in
excrutiating detail. Taxes are complicated by the progressive rates
and the AMT.
So let's look at a simple case.
MR = Mortgage rate (e.g. .08)
IR = Investment Rate(e.g. .08)
TR = Tax Rate (e.g. .25)
ATR = After Tax Rate
ATR = MR(1-TR)
ATR = IR(1-TR)
So if the same tax rate applies you can directly compare Mortgage Rate
to Investment Rate.
But if you are clever an put your money in a Roth IRA instead of a
taxable account, then the two Tax Rates are not the same. You get a
mortgage which is tax deductible and put the money in a Roth tax
(earnings) free acount.
Or there is the difference between long term capital gains and
ordinary income (TR could be either).
Other considerations.
Real estate varies widelyby state.
In California Purchase Money Mortgages are tax deductible and usually
non-recourse (to deficiency judgement) loans.
Cash out Refi's and HELOCs are only tax deductible upto 100K (above
original basis) and are usually recourse loans.
Always consult a CPA before making a final decision.
Good Luck!

No emotion. First, you want a downpayment large enough to avoid PMI,
which is expensive compared to the money down which will avoid it.
If you can put 30% down instead of 20%, the question quickly turns to
what other assets you have available, you don't want to deplete all
liquidity. Consider that a mortgage is likely the cheapest money you
will ever come across, so before using cash to increase the downpayment
(or alternately, paying down the mortgage faster than the term), I'd
choose to; pay any/all other debt, credit cards, car loan, etc. Fund the
Roth account for you and the spouse, fund the 401(k) past matching if
the expenses are reasonable. Then, look at your after tax cost of the
loan. In the 28% bracket, a 6% mortgage costs you 4.32%. At 15% cap gain
rate, you need a return of 5.08% to break even.
So long as you are working, and already in itemized deduction land (for
some people, much of their mortgage interest goes to first helping to
cover the standard deduction, so it's not really 100% deductible.) this
last equation should help that decision.
The known values are your interest rate, and current tax bracket,
assumed variable would be the market return in your chosen investment.
The larger unknown is the tax structure any year but 2007. The cap gain
rate may go away, so my equation may go out the window, and 6% may
become the break-even.
JOE

You could also take out a second mortgage to avoid PMI. This can make
sense if the interest rate on the second mortgage is low enough. It can
also make sense to go ahead and pay the PMI depending on the interest
rates involved if you're looking strictly at the numbers (I'm ducking
now...).
-Will

I don't think it can be done. There are several variables that you
simply cannot project, including but not limited to property values,
real estate taxes and investment yields. Sure, you could base them on
past performance, but as we all know, "past performance is not a good
predictor of future success".
That's all there is IMHO.

No need to duck, you're right. It seems to answer OP's question
completely I should have stuck to a decision process comparing the most
expensive part of the mortgage, i.e. either the final amount and its
PMI, or the interest rate on the second mortgage, to the other returns
he might experience. I may have been injecting my own issues of risk
aversion in my response.
JOE

[...]
Totally agree. Your affinity for or aversion to risk (in the broadest
sense) is yours and yours alone. That's ultimately what makes the
financial world go 'round.
Or, try this: can you come up with a quantifiable definition of
"monetary advantage"? No definition, no formula.
-Mark Bole

How about if I have a decision, either X or Y (ignoring the emotional and
risk issues) and if X creates a larger net worth after time T then I should
probably decide X.
I realize that both risk and emotion are important, but the above gives me
the numbers to measure whether taking the added risk (if any) or losing the
sleep (if any) is worth it.
JW

[...]
I appreciate the effort, but I think you have just replaced undefined
"monetary advantage" with undefined "net worth". The problem with net
worth that includes home ownership is, how much is unrealized gain that
may disappear tomorrow (illiquid asset)? How much is subject to future
(unknown) taxes?
The earlier replies contain useful suggestions and items to consider,
and I'm not trying to say there is nothing to take into account besides
emotional issues.
Here's one item I didn't see mentioned, which favors maximizing
loan-to-value: inflation expectations. If you think inflation will be a
major factor in the future, then a long-term loan at a fixed rate is a
great "investment", since you will paying back with cheaper dollars.
-Mark Bole

The problem with the above is that the thought of inflation being a
"major factor in the future" is a risk measurement. *Any* reference to
possible future outcomes is a risk measurement. GJ doesn't want to
discuss risk...

You can't say X creates a larger net worth unless you include the
probability that X will actually create a larger net worth. That's a
risk measurement.

You can't have it both ways. You can take the emotion out, to a degree,
but even that is just assuming that one has a high risk tollerance.
Risk cannot be ignored. Anticipated returns always come with a measure
of varience or standard deviation. When choosing from one's options, the
shape of the expected return is as important as the mean of that return.
I may choose a fixed, guaranteed, 6% return over an 8% expected return
with a 10% STDEV, not because my 'feelings' tell me to, but perhaps I'm
going to retire, and the numbers show that the higher return offers me a
Monte Carlo result that I will outlive my money with a high probability.
I suppose I could then say "I'll risk it". But at least I need to
acknowledge the numbers.
JOE

We lost sight of my original post. I'm looking for a why to quantify paying
cash for a house or taking out a mortgage.
I need to see the numbers based on my present situation, i.e.
the interest rate of the proposed loan,
where the money is coming from in both cases -- interest rate, retirement
savings, etc.,
my income at present and associated tax and deductions,
and anything else that comes into play.
All of these things are known to me because they exist today. It is my
present situation. I want to take the risk out of the equation. In other
words if all of the rates stay constant what is my net worth in the
following year, 2 years, etc. What I don't know is the "formula" that takes
all of these things into account.
Once I know how the two decisions interplay with my funds, rates, taxes,
etc., I can introduce risk and play what if.
Of course, maybe I'm missing a point -- its been know to happen.
I appreciate all of the responses.
JW

Once I know how the two decisions interplay with my funds, rates, taxes,
What I think you are missing is that there is no formula that takes
everything into account. At least no formula with which everyone
agrees. This explains why "pay off debts or not" is one of the most
debated subjects in personal finance.
Personally - and this always gets me in hot water - I also
think that personal finance is based on common sense, not number
crunching. So my reaction to your question is that if you need a
calculator to see the difference between two choices, there's not
enough difference to matter.
-HW "Skip" Weldon
Columbia, SC

The reason you can't come up with a formula, is because of the "what if."
"What if" interest rates drop. "What if" the stock market crashes. "What if"
the price of housing increases faster than inflation. "What if" we discover
another large pool of oil. Too many "what ifs".
Elizabeth Richardson

We lost sight of my original post. I'm looking for a why to quantify paying
You have the cart before the horse as the saying goes. There is no
"formula" which takes all those thing into account. You
need to run the "what if" scenarios first to determine the bottom line
best action based on sets of assumptions. Then look at the risks of
each scenario to see which one you can tolerate. Take your net worth
statement (I assume you have one) and project it item by item for
each scenario for the number of years you desire to look out into
the future. Of course this involves computing your estimated taxes
for those years based on each scenario and projecting any increase
or decrease in the value of the house.
BeachBum(Jim)

[...]
I'm glad you mentioned this - how true. More than once I've gotten all
excited about creating some complicated computer model, thinking that my
latent quant skills would finally do me some good, only to find that the
bottom line in the end was "within the margin of error" or somesuch.
Likewise on the "common sense" comment -- if it was easy or
straightforward to come up with a formula, someone would have done it by
now.
-Mark Bole

Respectfully, you are missing a point.
There are obvious reasons to not buy a house with cash. As I mentioned
prior, paying any debt that might have a higher rate, all things
considered.
What I feel you are missing is this - a fixed rate mortgage is simple.
It's fixed and you're set for 15-30 years. But the choices for
alternative investments is not fixed. (Of course if you can buy a
government bond yielding more than the rate on your mortgage, that's
good). I take the alternate investment choice to be a stock portfolio,
S&P index fund perhaps. The historical return over any given 15 year
period (since 1871) is 9.2%, but with a standard deviation of 4.1%.
The standard deviation is risk, almost by definition. 1/2 the time the
return will be under 9.2% for even that long a period, and 1/6 the time
it will be less than 5.1%.
(those with a critical eye on my postings please forgive that my reply
assumes that numbers looking forward will somehow reflect the past. not
true. the concept of standard deviation and the variability of returns
is valid, however).
The formula is "can I do better than my mortgage rate investing given my
risk tolerance?"
I can. Only because my after tax cost is 3.4%. But I agree with regular
poster Elizabeth that I need to time my mortgage payoff to my targeted
retirement.
JOE

Maybe this is generally true, but in many cases it is not. It seems to
me that a lot of personal finance is anything but common sense given the
wide array of otherwise intelligent people who are confused by it. Just
this week I built an Excel model for a co-worker to talk him out of
buying a scam software package called MMA (check it out at mmahome.us -
you pay $3500 for software that shows you how to accelerate payments on
a low-interest 30 year fixed mortgage by tapping a high-interest line of
credit and using it for your payments, nothing like paying good money to
nearly double your interest rate on a loan!). This guy is highly
intelligent and mathematically skilled, yet I couldn't use common sense
to talk him out his intended course of action, so I used a spreadsheet
(an expensive calculator). The spreadsheet worked.
-Will

C'mon! This is an easy and straight-forward problem. The OP wants to
make a first-order approximation by holding the variables in his current
situation constant. This is a very common, and wise, approach. Joe
outlined what he needs to do. Then, depending on the outcome, he can
start playing with variables (risk), exactly what he said he wanted to do.
-Will

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