Hi RE-Formulated Community!

Today I want to talk about some of the math behind the BRRRR strategy. My wife and I are looking to pull off a house hack in the NYC area and finding deals that you can successfully pull off the refinance portion are slim pickings. After running a bunch of deals through the Bigger Pockets’ rental property and BRRRR calculators, we quickly realized that we needed a simpler screening tool to help analyze a deal before bothering pulling all the inputs for a full cash flow analysis. In this post I’d like to share some observations gleaned from taking a closer look into the numbers.

The goal of this post is to help new investors, especially those looking to do a house hack with an FHA 203k loan, get an idea of what the numbers look like.

Before we dive into a quick overview of the strategy, let me get a few disclaimers out of the way.

  • This is not a substitute for a full cash flow analysis. This analysis should be the first in many steps in analyzing a property.
  • Since this is a quick, back of the envelope style screener, ease of calculation was the top priority. Therefore it does not account for many costs associated with the actual purchase of an investment property. Closing costs, sellers commissions, inspections, etc. are all ignored for the sake of simplicity. Again, this is not a substitute for a full cash flow analysis, just a tool to decide if a full cash flow analysis is worth your time.


BRRR is an acronym coined by BiggerPockets’ own Brandon Turner. It stands for Buy Rehab Rent Refinance Repeat. It’s an incredibly powerful but highly leveraged strategy to buy your first (and potentially 2nd, 3rd, and 4th) investment property. It can be done in many different ways but I am going to focus on the form that most first time house hackers  would use, an FHA or similar type rehab loan.

The first step is to purchase a run down, or outdated, property with an FHA, FNMA Home Ready loan, or other low down payment loan that you can wrap a construction loan into. You can put as little as 3.5%, and even finance the rehab costs through the FHA 203k program. Once you’ve turned your ugly duckling into a beautiful updated property that tenants are banging down the door to live in, you refinance the high rate FHA loan into a conventional 30 year fixed rate, with 20-30% equity. This hopefully drops your rate and allows you to take the money you’ve invested out of the property. Let’s take a look at an example. Let’s assume you find a duplex that costs $250,000 to purchase and requires $50,000 in repairs.





All in Cost


After you have completed the rehab, the property is worth $375,000. This is commonly referred to as ARV or After Repair Value. Assuming your local bank requires a minimum of 20% equity, you can get a loan up to $300,000 upon refinancing the property.



Refi Loan Size (20%)


This will be enough to payoff your original loan, and recoup the construction costs plus any down payment you put down. This is the dream scenario, you now own a cash flowing rental property for 0 money down. If you financed the construction cost and used a 3.5% down payment you would only need to tie up $10,500 (300,000 * 3.5%) for the time that it takes you to buy, rehab the property, rent it out, and refinance it. You now get your $10,500 back and you get to repeat the process! This is totally possible in some areas. Hell, if find a good enough deal, you can even get cash out at the refi step. For every dollar the house appraises for above $375,000, you get to take out $0.80. So if the property appraises for 400,000 you’d get to walk away from the bank with an extra $20k.

Now you’re probably thinking, “wow this is amazing, I want to go do this tomorrow.” Well if you live in a very expensive market, this is much easier said than done.


RE-ality Check

See what I did there? I recently offered on a 3 family for 375,000 that would need about 75,000 in repairs to update. This is what the numbers would look like if I wanted to pull off the dream scenario described above.

Purchase Price 375,000.00
Construction Costs 75,000.00
Down Payment ($) 15,750.00
Total Loan 434,250.00
Down Payment (%) 3.5%
Refi Equity Recoup all Cost ARV
20% 562,500.00
25% 600,000.00
30% 642,857.14
35% 692,307.69

Now here’s the catch. The most a 3 family in that particular town could possibly sell for is approximately $500,000, much lower than the ARV needed to recoup all my costs. When I go to refi this property at $500,000 the largest loan I could get would be $400,000 ($500,000 * 80%). I would then need to put up an additional 34,250 in cash in order to pay off the original FHA loan. Ok take a deep breath and go get a cup of coffee, we can do this. It’s not impossible, just difficult. If it was easy then everyone would be doing it.


The Cash Neutral Refi

Now that we’ve established the dream scenario, I want to talk about what your minimum goal should be. In order to properly establish a target, we need to set a lower bound. This is what I call the “Cash Neutral Refi”. This is the bare minimum you should be shooting for when evaluating properties. The cash neutral refi is the target ARV in which you do not need to lay out any more cash than you originally put up for the deal. In other words it is the target ARV where your refi loan will be enough to payoff the original loan but you will have to leave your down payment in the property. Here is the same property but computed using the Cash Neutral Refi ARV:

Purchase Price 375,000.00
Construction Costs 75,000.00
Down Payment ($) 15,750.00
Total Loan 434,250.00
Down Payment (%) 3.5%
Refi Equity Cash Neutral Refi ARV
20% 542,812.50
25% 579,000.00
30% 620,357.14
35% 668,076.92

The math behind it looks something like this:

Refi Loan = Purchase Loan


Purchase Loan =  (Purchase Price+Construction Cost) * (1-Down payment(%))

Refi Loan = ARV * (1-Equity Target (%))


ARV * (1-Equity Target (%)) =  (Purchase Price+Construction Cost) * (1-Down payment(%))

By solving for ARV you get:

ARV =  (Purchase Price+Construction Cost) * [(1-Down payment(%)) / (1-Equity Target (%))]


The Value Add Multiplier

If you take a closer look at the formula you will see that the target ARV is a function of your purchase price plus construction costs times a ratio of the leverage you initially used to the target equity percentage. I call this ratio the value add multiplier. It represents a return on investment that you need to achieve in order to obtain a your target ARV.

Value Add Multiplier = [(1-Down payment(%)) / (1-Equity Target (%))]

What does this tell us?

  • The Value Add Multiplier is the minimum value add you need to hit in order to get to your target ARV.
  • The return required to pull off a successful BRRRR is purely a function of the financing strategies you use.
  • Since this is a minimum limit, a higher value add means a higher required return to hit your goal (bad), a lower value add means a lower required return to hit your goal (good).
  • The less you put down up front, the more you need to earn to recoup your costs.
  • The higher the bank’s equity requirement, the higher the return required to hit your target.
  • To compute full cost recovery just assume 0 down payment

Example (Warning more math below):

Down Payment = 3.5%

Target Equity = 20%

Value Add Multiplier(Cash Neutral) = [(1-Down payment(%)) / (1-Equity Target (%))]

Value Add Multiplier(Cash Neutral) = (1-3.5%) / (1-20%)

Value Add Multiplier(Cash Neutral) = 0.965 / 0.800

Value Add Multiplier(Cash Neutral) = 1.206


The first scenario (full cost recovery), can be computed assuming a 0% down payment:

Value Add Multiplier(Full Cost Recovery) = [(1-Down payment(%)) / (1-Equity Target (%))]

Value Add Multiplier(Full Cost Recovery) = (1-0%) / (1-20%)

Value Add Multiplier(Full Cost Recovery) = 1 / .800

Value Add Multiplier(Full Cost Recovery) = 1.250


Side by Side Results:

Value Add Multiplier(Cash Neutral) = 1.206

Value Add Multiplier(Full Cost Recovery) = 1.250

This tells us that the value add required to pull off this strategy with a 3.5% down 203k loan is somewhere between 21%-25%

Below is the full table of returns for initial dow payments ranging from 3.5% – 25% and target equities from 10%-50%. The 0% down payment column represents the full BRRRR, 0 cash in, strategy:

Initial Down Payment

Target Equity 0% 3.5% 5% 10% 15% 20% 25%
10% 11% 7% 6% 0%
20% 25% 21% 19% 13% 6% 0%
30% 43% 38% 36% 29% 21% 14% 7%
40% 67% 61% 58% 50% 42% 33% 25%
50% 100% 93% 90% 80% 70% 60% 50%


We’ve covered a lot of math in this post. You may be bored to tears at this point but understanding the basic concepts that we’ve teased out are important. Don’t worry you don’t need to truly understand the formulas, just the conclusions we’ve drawn. The main point to remember is that the less money you put up originally, the higher the return required to achieve either the full BRRRR or a Cash Neutral Refi. If the properties you’re analyzing don’t hit your target ARVs, then be prepared to bring more cash to the refi table, or make sure your properties cash flow with the higher rate FHA loan INCLUDING PMI. If you are unable to refi out of the FHA loan, you will be unable to execute the Repeat stage of the BRRRR strategy as you can only have one FHA loan at a time.

Bonus Math

Construction Budget:

You can also rearrange this equation to get your rehab budget

Construction Cost = ARV * [(1-Equity Target (%)) / (1-Down payment(%))] – Purchase Price


The term you are multiplying the ARV by is 1 / Value Add Multiplier so for a 3.5% down payment and a 20% equity target, you would simply multiply the ARV by 1 / 0.21

Solve for your max purchase price:

Trying to figure out what you cap on an offer should be? Simply rearrange the construction cost and purchase price in the equation

Purchase Price = ARV * [(1-Equity Target (%)) / (1-Down payment(%))] – Construction Cost

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