Calculating the Max Affordability Purchase Price

[hdjc]

Dear all,

Im trying to calculate the Max purchase a customer can afford.
where (cash) downpayment +(tax 1) +(tax 2) = 1,809,000
where purchase price - loan = downpayment (cash + tax 1 + tax2 + fix processing fee ) = 1,809,000

In this case i assume tax 2 =0%

1) Max Purchase Price: *I can't figure out*
2) Loan: Using Loan Available (Assuming $3,741,275)
3) Deposit= Using Cash Available (Assuming $1,809,000)
4) Tax 1: 4% of Purchase Price (with the condition as below)
5) Tax 2: 0% of Purchase Price*
6) Processing Fee: Fix at $4,000

Is there a solution to:
Loan (2) + Deposit/ Cash(3) + tax 1(4) + tax 2(5) + Processing Fee(6) = Max Purchase Price(1)
Finding out my maximum possible Purchase price based on my Available Cash and LOAN
Tax 1 and Tax 2 is depending on Purchase Price

For tax 1, there is some conditions:*
If Purchase Price = $0, Tax 1 is 0%*
If Purchase Price <= $180,000, Tax 1 is 1%*
If Purchase Price <= $360,000, Tax 1 is 2%*
If Purchase Price <= $1,000,000, Tax 1 is 3%
Else 4%

If tax 1 is 3%, tax 1 will be 3%-$5400
If tax 1 is 4%, tax 1 will be 4%-$15400

Please take the answer from the reference.

 

[tkhunny]

Looks like you have this:
Purchase Price - 30% Purchase Price = (1-0.3)* Purchase Price = Max Loan
Or, More Succinctly
ML = 0.70*PP

I see this:
Down Payment = Cash + Tax1 + Tax2 + Fixed Fee
Or, More Succinctly
DP = C + T1 + T2 + FF
Or
DP = C + T1%*PP + T2%*PP + FF
Or
DP = C + T1%*(ML/0.70) + T2%*(ML/0.70) + FF
Or
DP = C + (ML/0.70)*(T1% + T2%) + FF

I'm Guessing:
Amortized Loan Amount = Max Loan - Down Payment
Or, More Succinctly
ALA = ML - DP
Or
ALA = ML - (C + (ML/0.70)*(T1% + T2%) + FF)
Or
ALA = ML(1-(T1%+T2%)/0.70) - (C + FF)
Or
ALA = (ML/0.70)(0.70-(T1%+T2%)) - (C + FF)
Or
ML = [(ALA + C + FF)/(0.70-T1%-T2%)]* 0.70

You also have the Term and Interest Rate of the Amortization to consider, but these will only get you back and forth between ALA and the Monthly Payment Amount, so having ALA may be enough information to get to the Purchase Price. it's hard to tell without very specific terms. Since you included the payment for only year #1, perhaps you're considering a variable interest rate? That might be an interesting complication.

I will have to suggest one thing, namely, that these things do not always have simple solutions. Iterative techniques may be required. Still, it's just algebra. You do have to pay attention. Decide what it is you have and what it is you need and solve away.

Example: I have $52,000 Cash and can manage $18,000 monthly for 150 months. Interest is at 6% / year.

[Math]ALA = 18,000\cdot\dfrac{1-v^{151}}{1-v} = 1,912,956[/Math], where [Math]v = \left(\dfrac{1}{1.06}\right)^{1/12}[/Math]
Okay! Now, you can start backing into the rest of the values. Fill in the ones you know and solve for the rest. Again, there may be no direct solution in some scenarios. You WILL need iterative techniques in some cases.

Let's see where you are on this.

 

[hdjc]

Hi tkhunny,

wow, this is definitely interesting! Thanks for replying!

Now there is a concern, as I am a product provider. The loan amount is determined by the loan provider which I will not be involve how long the loan term is. Thus I am tasked to focus on what the customer can afford given the loan amount they are entitled and what are the cash available to determine their maximum purchasing power.

(which also means I will have to ignore the loan term, loan interest, % of purchase price)

I will try to summarize in the simplest form to seek more clarity from all of you.

The number I have is

1) Loan Amount (Assuming $3,741,275.00)
2) Cash Available (Assuming $1,809,000), This cash portion will be used for the downpayment, Tax 1, Processing fee of $4000 where the customer will not fork out any additional cash and at the same time fully utilise the cash of $1,809,000)
3) Tax Tier table below depending on Purchase Price
4) Fix processing fee of $4000


For tax 1, there is some conditions:*
If Purchase Price = $0, Tax 1 is 0%*
If Purchase Price <= $180,000, Tax 1 is 1%*
If Purchase Price <= $360,000, Tax 1 is 2%*
If Purchase Price <= $1,000,000, Tax 1 is 3%
Else 4%

If tax 1 is 3%, tax 1 will be 3%-$5400
If tax 1 is 4%, tax 1 will be 4%-$15400

 

[JeffM]

Your attachment does not agree with your explanation. Taxes, at least taxes at levels that you are talking about, do not seem to play any role in your attachment.

The attachment itself seems to be calculating the maximum purchase price based on the amount the lender is willing to lend assuming an approximate loan-to-value ratio of 70%. Then it seems to calculate the cash required by subtracting the loan amount from the maximum purchase price. However, the arithmetic does not work out exactly. I presume that the differences can be explained by fees and taxes, but what that explanation is is not given in the attachment.

 

[hdjc]

Dear Jeff, thank you! You might be right. The attachment is a reference calculator I found it somewhere in the web.

I am also wondering how they are able to compute the loan to value as 70% ($3,741,275.00) . Where the other 30% ($1,809,000) includes the downpayment, processing fee and taxes.

This value of $1,809,000 was also the number I key in the field prior to the calculation results. This is where I start to get very curious how did the system calculate based on just 2 inputs 1) Loan Amount ($3,741,275.00) and 2) Cash Available ($1,809,000).

I do know how the Tax Calculation works this way:
If Purchase Price = $0, Tax 1 is 0%*
If Purchase Price <= $180,000, Tax 1 is 1%*
If Purchase Price <= $360,000, Tax 1 is 2%*
If Purchase Price <= $1,000,000, Tax 1 is 3%
If Purchase Price > $1,000,000, Tax 1 is 4%

If tax 1 is 3%, tax 1 will be 3%-$5400
If tax 1 is 4%, tax 1 will be 4%-$15400

Fix Processing Fee of $4000

 

[tkhunny]

I will try to summarize in the simplest form to seek more clarity from all of you.

Never a good idea. Communication requires enough information.

 

[JeffM]

Dear Jeff, thank you! You might be right. The attachment is a reference calculator I found it somewhere in the web.

I am also wondering how they are able to compute the loan to value as 70% ($3,741,275.00) . Where the other 30% ($1,809,000) includes the downpayment, processing fee and taxes.

This value of $1,809,000 was also the number I key in the field prior to the calculation results. This is where I start to get very curious how did the system calculate based on just 2 inputs 1) Loan Amount ($3,741,275.00) and 2) Cash Available ($1,809,000).

I do know how the Tax Calculation works this way:
If Purchase Price = $0, Tax 1 is 0%*
If Purchase Price <= $180,000, Tax 1 is 1%*
If Purchase Price <= $360,000, Tax 1 is 2%*
If Purchase Price <= $1,000,000, Tax 1 is 3%
If Purchase Price > $1,000,000, Tax 1 is 4%

If tax 1 is 3%, tax 1 will be 3%-$5400
If tax 1 is 4%, tax 1 will be 4%-$15400

Fix Processing Fee of $4000

Banks have different standards about loan-to-value ratios. The one I am on the board of treats, for example, as exceptions commercial real estate loans with a loan-to-value ratio in excess of 70%. This does not mean that such loans are not made; it means that there must be compensating factors that mitigate the risk of making an under-collaterlized loan. Moreover, loan-to-value ratios alone do not determine loan amounts; other factors may play a role, such as debt-to-income ratios or, for personal loans, credit scores.

The most practical way to estimate maximum purchase price is to go to a bank (presumably one where you are a long-time customer), ask about your credit availability and standard maximal loan-to-value ratios on various forms of collateral. If you qualify for 1 million in credit, you are shopping for a house for your personal residence, and their maximum standard loan-to-value is 85% on owner-occupied housing, then a rough estimate of maximum purchase price is

[MATH]\dfrac{1,000,000}{0.85} \approx 1,176,000[/MATH]
if you have roughly 76,000 in cash for a downpayment. If you do not like the answer, talk to other banks.

But there are so many variables involved, taxes, fees, whether fees can be financed, additional available collateral, credit scores, etc. that any exact computation will require access to the specific underwriting criteria of a specific bank. Moreover, the rate a bank charges (and thus the monthly payment due) may well vary depending on where you fit into its underwriting criteria.

In short, you can make a crude estimate. If you have a good relationship with a bank, you may be able to get that estimate confirmed but not guaranteed. Anything more exact is probably mere speculation.