Thank you for the question. Many others have offered intelligent and insightful replies.

In my personal opinion, what I believe is trying to be demonstrated here is that investors have different levels of risk-aversion, or fear of losing money. What I hope all readers will ascertain from the example is that:

Scenario 1 = Scenario 2 = Scenario 3

Each asset in scenario 1, 2, and 3 offer a 6% net return on the asset before taxes or paying a mortgage.

Scenario 1

NOI = 240 k

Building = 4 M

cap rate = NOI/Building = 6%

Scenario 2

NOI = 120K

Building = 2 M

cap rate = NOI/Building = 6%

Scenario 3

NOI = 60 k

Building = 1 M

cap rate = NOI/Building = 6%

You can use any amount of leverage on any of the buildings to achieve whatever "ROI" you desire. But what Thomas is cleverly pointing out is that

*debt never changes the productive return of the asset!*

When the question is simply: Which investment is better?

a) 100% ROI

b) 62.5% ROI

c) 42.5% ROI

Mathematical answer:

None of them is better than any other. If you are investing in exactly the same underlying asset, with exactly the same gross return (6%), they are all entirely equivalent assets. (In a universe where we can buy four assets of scenario #3 or two assets of scenario #1 to equal scenario #1)

A bit of interesting (and extremely useful) theory:

Let's ignore final appreciation for a moment because every building here appreciates by the exact same amount. This will allow us to examine the effects of leverage.

Ever wonder how leverage really works?

You have probably heard of "ROI" as "return on investment". ROI is

ROI = (return on asset) * (leverage)

Now what isis equal to:

When the question is simply: Which investment is better?

a) 100% ROI

b) 62.5% ROI

c) 42.5% ROI

Mathematical answer:

None of them is better than any other. If you are investing in exactly the same underlying asset, with exactly the same gross return (6%), they are all entirely equivalent assets. (In a universe where we can buy four assets of scenario #3 or two assets of scenario #1 to equal scenario #1)

A bit of interesting (and extremely useful) theory:

Let's ignore final appreciation for a moment because every building here appreciates by the exact same amount. This will allow us to examine the effects of leverage.

Ever wonder how leverage really works?

You have probably heard of "ROI" as "return on investment". ROI is

ROI = (return on asset) * (leverage)

Now what is

*leverage? Mathematically, we represent leverage as*

Leverage = (building value)/(cash invested)

What is "return on asset"?

Return on Asset = ROA = (cash before tax)

building value today

An easy way to think about return on asset as that it is the cash you have in hand at the end of the day divided by the cost of the house today. On an asset without any debt, return on asset is simply the cap rate ie. net operating income divided by the value of the asset. As more debt is applied, the cash before tax decreases as we now have debt payments.

, our leverageLeverage = (building value)/(cash invested)

What is "return on asset"?

Return on Asset = ROA = (cash before tax)

building value today

An easy way to think about return on asset as that it is the cash you have in hand at the end of the day divided by the cost of the house today. On an asset without any debt, return on asset is simply the cap rate ie. net operating income divided by the value of the asset. As more debt is applied, the cash before tax decreases as we now have debt payments.

**Under scenario 3**Leverage = 1M (building value) = 1

1M (cash invested)

Here, our leverage ratio is 1, or no leverage is used.

Return on Asset = ROA = (cash before tax) = 60K

building value today 1M

ROA = 6%

ong>

*ROI for scenario 3:*

ROI = (return on asset) * (leverage)

ROI = 6% * 1

ROI = 6% / year

ROI (~ 5 year) = 6% * 5 years = 30% ROI

ROI = (return on asset) * (leverage)

ROI = 6% * 1

ROI = 6% / year

ROI (~ 5 year) = 6% * 5 years = 30% ROI

*Now, lets add some leverage for scenario 3:*

50% loan to value. That is we buy the building for $1 million and use a $500k mortgage. Using Thomas' numbers we have 30k mortgage payment and 10k principal pay down so net we lose 20k / year to interest payments.

return on asset = $60K (NOI) - $20K (interest payments)

1 million (building value today)

ROA = 4%

Leverage = 1M (building value) = 2

500 K (cash invested)

ROI = (return on asset) * (leverage)

ROI = 4% * 2

ROI = 8% / year

ROI (~ 5 year) = 8% * 5 years = 40% ROI

The relationship of leverage:50% loan to value. That is we buy the building for $1 million and use a $500k mortgage. Using Thomas' numbers we have 30k mortgage payment and 10k principal pay down so net we lose 20k / year to interest payments.

return on asset = $60K (NOI) - $20K (interest payments)

1 million (building value today)

ROA = 4%

Leverage = 1M (building value) = 2

500 K (cash invested)

ROI = (return on asset) * (leverage)

ROI = 4% * 2

ROI = 8% / year

ROI (~ 5 year) = 8% * 5 years = 40% ROI

The relationship of leverage:

- the higher the leverage applied, the lower

- the return on asset
- Each asset only has the productive capacity of offering a 6% total return on the asset.
- Debt does not "enhance" the productive capacity of an asset. Taking on debt is ultimately an expression of your confidence in that asset.

By the nature of leverage, we can turn a 6% cap rate asset into a 200% ROI or 300% or 4000%. None of these are better than the other, if the higher "ROI" is simply coming from leverage.

As investors, we should search for higher ROA

- .

That's just my two bits. (I have an honours degree in finance and work as a real estate analyst for what it's worth). This is generally how we think about asset valuation.

Thanks for the post, looking forward to more discussion.