My Math Forum How to calculate return on investment if the money is borrowed?

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 August 18th, 2017, 01:48 PM #1 Newbie   Joined: Sep 2016 From: Florida Posts: 15 Thanks: 0 How to calculate return on investment if the money is borrowed? So I'm trying to do some business math. It is easy to calculate return on investment (ROI) if I am paying cash. Let's say that I spend 202,750.26 in cash to flip a house (this is for the initial purchase, labor, etc.) and I end up profiting 38,341.89. This is easy. I take the final amount (202750.26 + 38341.89 = 241,092.15) and divide that by the initial amount of cash I put into the project (202,750.26). This gives me appr. 1.189. I then subtract 1 and multiply by the amount of time that it took. If it took 4 months, then I multiply by 12/4 = 3. This gives me a ROI of appr. .567 or 56.7%. Now things get confusing if I am borrowing money to do this. Let's say that I borrowed the initial 202,750.26. Now, I have zero of my cash in. So does this give me a "divide-by-zero" error when trying to calculate ROI because I didn't actually invest anything other than other people's money? Is this just something really obvious that I'm overthinking?
 August 18th, 2017, 02:46 PM #2 Member   Joined: Jan 2017 From: California Posts: 80 Thanks: 8 Your return would be infinite since you did not invest any of your own money. Pretty much what Wall Street punks do. Last edited by skipjack; August 18th, 2017 at 04:31 PM.
 August 18th, 2017, 04:25 PM #3 Senior Member   Joined: May 2016 From: USA Posts: 785 Thanks: 312 An economist would say that your return is 56.7% annualized. The reason is that you invested 202,750.26 of your capacity to invest. Whether you do so by investing cash or reducing your borrowing capacity makes no difference: that is the amount of your net worth at risk.
August 18th, 2017, 04:54 PM   #4
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 Originally Posted by dthiaw Your return would be infinite since you did not invest any of your own money. Pretty much what Wall Street punks do.
Yes, this is the conclusion that I came to.

But is there any way to analyze these infinities mathematically? I am aware of the fact that not all infinities equal each other.

It would obviously make business sense to take out money at 8% rather than 18%. In both cases, my ROI would be infinity.

Or perhaps I should be measuring in terms of earnings/year instead of ROI?

 August 18th, 2017, 05:22 PM #5 Global Moderator   Joined: Dec 2006 Posts: 17,919 Thanks: 1386 How do you borrow \$202,750.26 without having to pay interest on that loan? August 18th, 2017, 05:54 PM #6 Newbie Joined: Sep 2016 From: Florida Posts: 15 Thanks: 0 Quote:  Originally Posted by skipjack How do you borrow \$202,750.26 without having to pay interest on that loan?
I borrow more to cover the loan payments.

August 18th, 2017, 06:05 PM   #7
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 Originally Posted by farmerjohn1324 I borrow more to cover the loan payments.
That is not the point. In terms of opportunity cost, whatever you borrow is a reduction in your aggregate capacity to borrow and so in your aggregate capacity to invest. Your capacity to invest is reduced whether you use cash or whether you use a credit line from a bank.

You are mixing up the profitability of the investment with the financing of the investment.

August 18th, 2017, 06:24 PM   #8
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 Originally Posted by JeffM1 That is not the point. In terms of opportunity cost, whatever you borrow is a reduction in your aggregate capacity to borrow and so in your aggregate capacity to invest. Your capacity to invest is reduced whether you use cash or whether you use a credit line from a bank. You are mixing up the profitability of the investment with the financing of the investment.
There are theoretically infinite number of houses that I could flip. If I had access to infinite amount of money to borrow, I could flip all of them.

The profitability is easy to measure. That is in terms of dollars and how long it took me to get those dollars.

I am just wondering if there is any way to measure ROI as a percentage if the money is borrowed. But I guess this is kind of pointless since it is money I'm trying to make, not % signs.

In other words, I'm not going to go to the bank and deposit a % sign.

August 18th, 2017, 09:32 PM   #9
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 Originally Posted by JeffM1 That is not the point. In terms of opportunity cost, whatever you borrow is a reduction in your aggregate capacity to borrow and so in your aggregate capacity to invest. Your capacity to invest is reduced whether you use cash or whether you use a credit line from a bank. You are mixing up the profitability of the investment with the financing of the investment.
Okay after reading again, I see what you're saying.

So first I need to quantify how much I can borrow.

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