# How much of a mortgage with a 4% yield, can 'self service'

#### Timmy_Rangi

##### New member
I have an exercise where I am trying to calculate a fictional property investors 'borrowing power' from the bank.

Essentially the bank calculates their income, subtracts their expenses which gives them a UMI (uncommitted monthly income).

This amount, for example, $5,000, is then tested against a 'test interest rate' of 7.3%, using a 25-year Principal & Interest Loan. Which says they can afford to borrow$688,675.54. In my spreadsheet looks like this PV((0.073/12),(25*12),5000)

But. If they are purchasing an investment property, their future rental income can contribute to their UMI.
The rental income is treated specially by the bank, the bank removes 25% of it. ie If you receive $20,000 of rent, you can only use$15,000.

In addition to that, there is a limit to how much they can borrow set by their deposit and equity. I calculate this first. So for this example, let's say their equity says they can borrow $1,500,000. But obviously, they can't afford to service that much. I want to know how to find out the maximum amount that they can service. I am assuming a 4% yield on their property investment. In my mind there seems to be two calculations to run: 1. the$688,675.54 * 4% yield * 75% bank discounting = $20,660.27 2. then there is an amount of the equity limit of$1,500,000 that will self service?
3. then the $20,660.27 means you can borrow some more, which means you can service some more. Does that make sense to you? Because it is breaking my brain!!! Thanks so much, Timmy. #### JeffM ##### Elite Member I am having trouble following your question. You say they have 1.5 million in equity. Equity in what? Their residences? They get no cash income from a residence; they get a non-cash service. They have 1.5 million in earning assets? Then the income from that is already counted (at least in part) in their base income. They have 1.5 million in marketable securities? The bank may let them borrow 80% of the appraised value of the house regardless of the relationship between their income and debt service provided that they also put up the securities as collateral. (As a practical matter, getting possession of and liquidating marketable securities is a whole lot faster and a whole lot cheaper than doing the same thing with real estate. Usually, the bank takes constructive possession of securities when it makes the loan.) The investment property to be financed has an appraised value of 1.5 million? It will be a rare bank that will not modify its debt service to income limits if the borrower can fund the entire purchase without debt. My bank would lend 0.5 million secured by the property with little concern for anything other than how the property's projected cash flow relates to the contractual debt service unless the Dodd-Frank regulations throw up a roadblock. Last edited: #### Timmy_Rangi ##### New member Thanks so much for helping me out!! Let me clarify. In New Zealand to calculate borrowing power. You calculate two different things: One, what your equity/deposit will let you afford. We have a loan to value ratio limit imposed by the central bank. So to buy an investment property you are not allowed to borrow more than 70%. ie an investment property worth a Million dollars, could only have a mortgage of$700,000.
But if you have a house worth $800,000 with no mortgage - you can use the 'equity here' as a 'deposit' for your investment. So, in this case, you could use a million dollar loan for the investment. This is easy for me to calculate. So we can assume that because of other properties they are 'allowed' to borrow up to$1,500,000.

Two, how much can they afford to borrow according to their servicing. Which is calculated using the UMI.

Then, they just take the lowest number. So you are always limited by either equity or servicing. In our example, the servicing is the limiting factor.

Does that help?

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#### Denis

##### Senior Member
I'm more confused than Jeff!
Is this a classroom problem?

Edit: does "service it" mean "ability to make the monthly payment"?

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#### Timmy_Rangi

##### New member
Not a classroom - it is my problem I am trying to make a spreadsheet, that calculates how much I can borrow to buy an investment property.

At least everyone else is confused. I am definitely a little perplexed.

1. calculate how much someone can afford to borrow according to their LVR (equity + debt) = $1,500,000. 2. calculate how much someone can afford to borrow according to their income ((income-expenses) * mortgage payments) =$688,000
3. calculate how much more they can afford to borrow because by buying an investment it increases their income* = ???
Whatever they buy increases their income using 3% (4% yield * 75% shading), ie a $688,000 investment will contribute$20,640 of annual income, so $1,720 of UMI. Which means we can then borrow more, which will contribute more... Which means we can then borrow more, which will contribute more... ... Which means we can then borrow more, which will contribute more... ... ... #### tkhunny ##### Moderator Staff member Not a classroom - it is my problem I am trying to make a spreadsheet, that calculates how much I can borrow to buy an investment property. At least everyone else is confused. I am definitely a little perplexed. 1. calculate how much someone can afford to borrow according to their LVR (equity + debt) =$1,500,000.
2. calculate how much someone can afford to borrow according to their income ((income-expenses) * mortgage payments) = $688,000 3. calculate how much more they can afford to borrow because by buying an investment it increases their income* = ??? Whatever they buy increases their income using 3% (4% yield * 75% shading), ie a$688,000 investment will contribute $20,640 of annual income, so$1,720 of UMI.

Which means we can then borrow more, which will contribute more...
Which means we can then borrow more, which will contribute more... ...
Which means we can then borrow more, which will contribute more... ... ...

"Mortgage Payments" is fixed, M.
"Expenses" is fixed, E
"Income" is a moving target, C.

(C-E) * M = 688000
[(C-E) * M] + [(C-E) * M]*0.03 = 688000 + 20640
[(C-E) * M] + [(C-E) * M]0.03 + [(C-E) * M]0.03^2 = 688000 + 20640 + 619.2
etc.

[(C-E) * M] + [(C-E) * M]0.03 + [(C-E) * M]0.03^2 + ... = [(C-E) * M]*(1 + 0.03 + 0.03^2 + 0.03^3 + ...)

Can you add an infinite geometric sequence?

#### Timmy_Rangi

##### New member
I have never heard of infinite geometric sequences, so have done a quick read. And am trying to calculate it manually first so I at least slightly grasp it before getting a formula to do the work.

Is this the manual version of what you are talking about, and essentially we keep adding lines until New Monthly UMI = close to 0?

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#### tkhunny

##### Moderator
Staff member
Well, it's not infinite if you cut it off.

1 + r + r^2 + r^3 + ... = 1/(1-r)

#### Timmy_Rangi

##### New member
lol. I do get that, but my brain doesn't cope well with infinity. I am just checking that we are talking about the same thing.

Do you know how to express that as a formula?

#### tkhunny

##### Moderator
Staff member
See above. [(C-E) * M]/(1-0.03)