When we wrote our series on how Our $50K Duplex Is Now Worth $97K, some readers were wondering why we weren’t interested in flipping the property and making a quick buck. Well, what it comes down to is that we think the long term cash flows that we’re going to get out of the duplex far outweigh the amount that we would have netted if we tried to sell it shortly after we bought it.

### What Would A Flip Have Looked Like?

Immediately after we bought the duplex for $50K, we put about $8K into it, got it rented, and then it appraised for $76K (an appraisal I thought was a bit of a stretch). So if we had sold it then for, say, $70K, we would have been looking at net consideration to us of $70K minus a 6% realtor fee, so about $65.8K.

- Our costs were about $58K
- Would give an overall profit $7.8K
- But after 28% in taxes (short term capital gains are taxed as ordinary income), that’s only $5.6K

That’s not chump change at an almost 10% profit in about 5 months, but for the number of hours that we put into the duplex (and the number of cuts and electrocutions), we weren’t really ready to sell out for minimum wage (or less).

So instead of looking at it as what we could sell the duplex for in the open market, we tend to look at the duplex as what the cash flows will look to us over the usable life of the duplex. For this, we can use a nifty valuation method called a DCF.

*[In case it's not obvious, this DCF analysis works for any stream of cash flows, so if instead of real estate you own some internet real estate that's bringing in cash - I'm talking to you, other bloggers - this is one way to estimate how much it's worth to you today!]*

### What’s A DCF?

DCF stands for **Discounted Cash Flow**, and the basic idea behind this analysis is that to understand what **future** cash flows are worth **today**, you need to figure out what you would need today to be able to generate that amount of cash at that future date. I know, it sounds a little confusing at first, but hear me out.

Let’s think about first it in terms of what you need **today** to generate a specific dollar amount at some fixed time in the **future**.

For example– Let’s say you want an investment to be worth $5,000 3 years from now. You are reasonably confident that you can generate a safe return of 5% over the next three years. (5% is an example, let’s not get into interest rates on cd’s here…)To find out how much we need to start with, all we need to do is solve for X in the equation:

Thinking back to math class, we can solve this and see that $X = $4,319.19. So if we feel confident that we can get a 5% return over the next 3 years,

we would only need to invest $4,319.19 today to have that $5,000 when we need it.

But the DCF goes the other way around, right? If we know our investment will throw off $5,000 in cash 3 years from now – what is that investment worth to us today?

In reality, this is the same problem that we solved in the example above, except no one has told us what percent return we think we could generate over the next 3 years. The example above, we assumed 5%, but this rate is something that we actually get to think about and choose for ourselves, and it’s called the * discount rate*.

So how did we solve for $X above? We calculated:

which is actually this formula:

But that was only for one year worth of returns three years in the future, so to calculate what ALL of the cash flow is worth over a period of many years, we calculate each year separately and add them up. For short-hand in this formula, = cash flow in year 1, = cash flow in year 2, etc… and = discount rate. So the discounted cash flow, or DCF, is just:

where is however many years forward you’re projecting.

The IRS lets you depreciate an investment property over 27 years, so I tend to take my DCFs out to n=27, and assume the property is “used-up”, with no value at that time. (Not really accurate in real life, but since that’s the way the tax-man looks at it – and it’s an *underestimate* of value – it works for us.)

### DCF Step 1: Calculate Your Yearly Cash Flows

With any investment property, you should have a pretty good idea where your money is coming from and going to. So we have a spreadsheet set up that looks something like this. This table is a version of an Excel table that we used to calculate estimated yearly cash returns – the values are in $ thousands.

Year | Rent Income | Maintenance Costs | Income Taxes | Yearly Cash Flow |
---|---|---|---|---|

1 | $16.5 | $4.6 | $3.3 | $8.6 |

2 | 17.0 | 4.7 | 3.4 | 8.8 |

3 | 17.5 | 4.9 | 3.5 | 9.0 |

… | … | … | … | … |

27 | 35.6 | 11.0 | 6.9 | 17.7 |

Some of the assumptions that go into it include:

- Rent initialized at $1.5K/month with an expected occupancy of 11 months/year.
- Maintenance costs include insurance, RE taxes, repairs, and other maintenance expenses.
- Rent and maintenance costs are currently estimated to rise at about 3%/year due to inflation, RE taxes set at 5% increases.
- Income taxes are calculated at a 28% marginal tax rate.

### DCF Step 2: Determine Your Discount Rate*, r

There are a lot of fancy formulas out there for calculating your discount rate,* r*, that use unnecessarily complicated methods. (I’m talking about WACC, beta, and similar methods.) You should probably ignore all those fancy formulas.

What it really comes down to is what rate of return do you think you would reasonably be assured of earning over that time period if someone handed you a pile of money to invest *now. *We tend to think of it as “If we had this money in our pockets today, where would we invest it and what return do we think we could get there”.

- If you are very conservative, and would invest in cds, consider using the 10-year cd rate. The best 10-year cd I saw recently was 2.25%.
- If you think you’d likely drop the money into an S&P 500 fund, consider using the historical CAGR of the S&P 500, 7.37%/yr since 1950.
- If you think you’re likely somewhere in between, split the difference and calculate your DCF using r = 5.5%.

Everyone is not going to have the same answer, because we might all do different things with the money. The best answer is what *you* think *you* would do with the money and how much it would earn there. Be realistic. If last year’s return in the stock market was 30% (or a single stock), you’re kidding yourself if you think that any stock (or index) is capable of doing that 27 years in a row. (Eventually the stock would dominate the global economy if that were the case.)*

### DCF Step 3: Plug the Numbers In

Starting from table that we made in Step 1, we can add 3 more columns in Excel in order to compare the Conservative, Risky, and Mixed DCF valuations at the same time.

Year | Yearly Cash Flow | Conservative r = 2.25% |
Risky r = 7.37% |
Balanced r =5.50% |
---|---|---|---|---|

1 | $8.6 | $8.6 | $8.6 | $8.6 |

2 | 8.8 | 8.6 | 8.2 | 8.4 |

3 | 9.0 | 8.7 | 7.9 | 8.2 |

… | … | … | … | … |

27 | 17.7 | 9.9 | 2.8 | 4.4 |

Total |
$341.6 |
$250.1 |
$140.0 |
$169.7 |

So, we can see that we expect our duplex to return $341.6 in after-tax cash flow to our pockets over a 27-year period. But what would someone have to pay us to make it worthwhile to sell the duplex?

- If we know we’re conservative investors, we use r = 2.25% and see that we would have to net $250.1K after taxes to have enough cash to generate the same $341.6 in cash flow that the duplex would return over the 27 years.
- The riskier S&P 500 option with r=7.37% shows that we would have to net $140.0K after taxes in the transaction.
- And the “Balanced” r=5.5% shows that a sale offer would need to net $169.7 in after tax profit to match the cash flows that the duplex will generate.
**Don’t forget!**The taxes that would need to be added back to all these values are two-fold. 1 – the taxes at the time of the sale of the property, 2 – the taxes when you withdraw your investments for income.

* Note – the DCF can be pretty susceptible to the GIGO principle – that is, “garbage in, garbage out”. If you make unrealistic assumptions and then project them forward for almost three decades, the level of surrealism in your model is going to grow exponentially. Pretty soon you’ll start to see melting clocks everywhere… So please don’t do it!

*Have you ever heard of or used a DCF before? What do you think of the concept of trying to figure out how much it would take to “buy” an equivalent stream of cash flows? *

Your maths is far better than mine, that’s for sure!

I do like the idea of having constant cash flow coming in, but I don’t like the idea of having to manage potentially unruly tenants.

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I love “maths” instead of the Americanism “math” =)

Yeah, I geek out with numbers a bit, but the math here is actually easy enough to plug into a spreadsheet.

Plus, Mr. PoP picks some pretty awesome tenants. Right now we have 5 honors students at the university staying in our duplex. No parties, no noise. They are great!

I think you are obviously doing great with your investment!

We also have awesome tenants. I don’t want any of them to ever move!

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Thanks, Holly. Great tenants definitely make the landlording gig way nicer. =)

I have never heard of DCF and your explanation is great. It makes sense to keep your investment instead of selling for a quick profit.

Thanks, Pauline. Glad I shared something new with you today!

I literally just studied these concepts in Managerial Accounting and Corporate Finance classes!! There are nifty formulas in Excel that will solve various components of the DCF formula that you mention above. =PV (solves for “present value”), =FV (solves for “future value”), =PMT (solves for “payment” required each period in order to achieve a known PV or FV), =IPMT (solves for interest), =PPMT (solves for principal), etc… Companies (or individuals) can use these formulas to compare two alternatives. In this case, sell the property now, or hold for 5 years, 10 years, etc.

Yup, Excel formulas can simplify it a bit, BUT… (there’s always a but, right?)

But the formulas generally require your cash flow to be exactly the same over the entire period. If you do it manually (which isn’t too much harder), you can have different cash flows each year, which is a lot more realistic since we have inflation, etc.

I believe the =IRR forumula can be used for varing cash flows, but I am not sure if that formula is available in all versions of Excel.

yay! You may be my new favorite Excel buddy. I love trading excel secrets.

I love all your math(s) here! I’ve never seen DCF applied to real estate.

I have kind of a silly question I guess… How can you feel confident predicting what rent/expenses will be for your house 27 years out? I guess I’m just thinking of how neighborhoods and tastes might change over that time period, and how an older house becomes less attractive to renters.

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I think we used reasonable assumptions that might not be perfect, but at some point you have to assume, right?

We assumed that rent and non-tax expenses are going to increase about with inflation, which has been around 3% long-term. RE-taxes are going to increase more than that in the short term, but then probably level out with inflation long-term when the taxable value meets the market value, which is why we chose 5% increases there.

As for the rent and neighborhood changing greatly, I don’t think this is going to be a big issue as this neighborhood isn’t brand spanking new to begin with and it’s in an area that is still growing and is expected to continue to grow in the future with more students. So we’re not too worried long-term on the demand side.

But you’re totally right, that at some point, you’ve just got to make some good estimates and go forward. That’s the risk part of any investment, right?

Ahhhh, I’m having flashbacks to my college accounting & finance classes!

I really like this post though, I think you did a great job explaining DCF and how it can be applied.

Thanks! Though sorry for the flashbacks – hopefully they weren’t painful ones.

Sometimes I wonder why they save stuff like the DCF for college finance classes. The algebra behind it isn’t all that complicated, and this is totally the kind of applications that I would have been fascinated to learn about in high school.

On you cash flow sheet, dont forget that you should add in depreciation costs if it was an asset bought with cash, or the monthly payments if it was an asset bought on credit.

You’re definitely right – I didn’t include it in our numbers here, but we would depreciate most of the $50K (since we can’t depreciate the land) over the 27 year period, probably using straight-line depreciation. So that would lessen the taxes in each year – increasing the cash thrown off.

But a traditionally financed purchase would have the financing costs as a cash flow cost for the DCF, and as a pay-off costs for a “sell-now” cost.

Love that you’re showing everyone how to really do the math to figure it out ! This all reminds me of one of my last university courses. I actually enjoy figuring it all out.

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Glad to provide the trip down memory lane.

I wrote this thinking that a lot of the times people think of “Finance” (like big bank stuff) as so different from “personal finance” – but there are a lot of lessons from “Finance” that we can use in our “personal finances”, too! =)

Very good analysis, Mrs. PoP. I am certainly not that detailed but those are some good details to learn. I would think most real estate investments would do better over the long term, but it would depend on your ability to maintain and keep tenants there as well.

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Thanks, Kim! It definitely involves more work to keep good tenants than it does to leave investments in an account, but we think it’s worth it =)

I always hated doing those calculations in my management accounting class. However, it’s very useful to use if you want to know what your money is worth now compared to the future.

Another great time to use it is when you’re deciding to take a lump sum and invest it over a lifetime payment at a certain amount. Which is similar to selling the duplex v.s. renting it out.

Absolutely. Lottery winners should be doing these kinds of calculations when they’re faced with taking the lump sum or getting payments over a number of years!

I agree what you said above in the comments…great tenants make landlording easier…we have had great tenants in the past 3 years we have owned a duplex…so far so good…i love the example you give and constant cash flows are nice…

Christopher @ This that and the MBA recently posted..Using Online Tools to Manage a Household Budget

Thanks, Christopher!

Thanks for sharing those calculations.

It’s always interesting to see the long term value of holding a property instead of selling it.

In general, I think the benefits of holding onto a rental property far outweigh the costs, even if it requires learning to find and manage tenants.

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And the thing about finding and managing good tenants is that it gets easier with time! Good tenants know good landlords, and recommend the place to their friends when they want to move. And even when that doesn’t happen, we learn which methods of advertising tend to get the highest quality referrals.

Mmm, delicious math!

At your duplex’s current appreciation rate, you may very well hit your numbers!

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Haha, anything’s possible, but only if RE values get completely bonkers again here. We expect the appreciation to level off soon and then hit a slow and steady pace in that neighborhood. But you’re right – anything’s possible!

It’s funny….I would have never thought to do otherwise. How do you know the upside of something without walking through the numbers and finding your crossover point? Sweet post.

AT first the 28% threw me because I was thinking about all of your income and deductions. But of course, this money would lay on top of your other income streams, so calculating it at your tax bracket (assumed) rather than overall tax rate makes sense. Still, if you’re deducting expenses against income, wouldn’t your tax rate be significantly less?

That said, even if I’m correct, that you DO pay tax at a lower effective rate, I like how conservative you are here. If the math works with these numbers, you’ll be ecstatic in real life!

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Joe – I would think out of anyone, you would know how many people never do both calculations to figure out where they maximize value.

The 28% in the table is taken as 28%*(Rent – Expenses), but as another reader pointed out, I didn’t include the non-cash expense of depreciation, so you’re right that by the time you depreciate a little less than $2K per year on the property, the tax rate is going to be a bit less than 28%, with the depreciation providing a bigger boost in the early years than in the later years.

If (when?) we leave our jobs, the duplex income won’t sit on top of $150K that we’re earning at our day jobs, so the tax rate will go down then, too. But until that happens, I don’t want to plan on it.

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Yup, DCF analysis works for any investment that produces good cash flows. I use it on equities, and it can be used on property as well.

For a discount rate, I generally just use the desired rate of return, rather than weighted averaged cost of capital (WACC) or the treasury rate.

But the desired rate of return can depend on the subjective risk assessment of the investment, as well as what other options are available.

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Couldn’t agree more.

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