Investor · Member since 2018 · 259 posts · 74 votes
After over a decade of doing this, I still don't understand how the debt terms directly affect the Cash on Cash return of a deal.
For simplicity, define CAP Rate (:= NOI/Purchase Price) and COC (:= Cash Flow/Total Cash Invested).
Assume Cash Flow := NOI - Debt Service, and Purchase Price := Total Cash Invested + Debt Service.
• Say you are considering buying Property A. If you buy Property A WITHOUT debt, then CAP Rate = COC because Debt Service = $0 so Cash Flow = NOI and Purchase Price = Total Cash Invested.
• If you choose to add debt to Property A, then Total Cash Invested goes down (since you're using debt), so the denominator of COC goes down, so COC could potentially go up. HOWEVER, Cash Flow also goes down, because now you have to pay Debt Service, so the numerator of COC also goes down, so your COC could potentially go down as well.
The "math" question is what is an easy way to determine if the COC is going to go up or down, based on the terms of the debt?
For example, if the interest rate for the debt is less than the CAP rate, does that mean the COC will always go up? I don't think so. I think it depends on the LTV and possibly other factors.
After over a decade of doing this, I still don't understand how the debt terms directly affect the Cash on Cash return of a deal.
For simplicity, define CAP Rate (:= NOI/Purchase Price) and COC (:= Cash Flow/Total Cash Invested).
Assume Cash Flow := NOI - Debt Service, and Purchase Price := Total Cash Invested + Debt Service.
• Say you are considering buying Property A. If you buy Property A WITHOUT debt, then CAP Rate = COC because Debt Service = $0 so Cash Flow = NOI and Purchase Price = Total Cash Invested.
• If you choose to add debt to Property A, then Total Cash Invested goes down (since you're using debt), so the denominator of COC goes down, so COC could potentially go up. HOWEVER, Cash Flow also goes down, because now you have to pay Debt Service, so the numerator of COC also goes down, so your COC could potentially go down as well.
The "math" question is what is an easy way to determine if the COC is going to go up or down, based on the terms of the debt?
For example, if the interest rate for the debt is less than the CAP rate, does that mean the COC will always go up? I don't think so. I think it depends on the LTV and possibly other factors.
Is there any simple relationship here
“If you buy Property A WITHOUT debt, then CAP Rate = COC because Debt Service = $0 so Cash Flow = NOI and Purchase Price = Total Cash Invested.”
I agree with your statement above.
But, in theory you could buy a property WITH debt where CAP Rate would still = COC. When you finance a property with loan where 1. Interest Rate is equal to CAP Rate and 2. the loan is interest only loan.
The impact of debt on COC is the net impact of each of the debt terms. It therefore helps to examine each term of the debt and how the terms individually affect a property's Cash Flow (or any business for that matter). Three factors to consider are – Interest Rate, Amortization, and Loan to Cost/Value. Following are several scenarios to help understand the relationship between CAP Rate and COC:
- When debt is used where Interest Rate is equal to CAP Rate, and no amortization (as mentioned above). CAP Rate generally = COC. NOTE: This is true whether LTV is 75% or 25% (i.e. LTV does not matter).
- When debt is used where Interest Rate is less than CAP Rate, and still no amortization. In this case COC will increase and exceed CAP Rate (i.e. this is classic leverage strategy, it's why corporations issue corporate bonds). ALSO NOTE: LTV still does not matter here.
- When debt is used with amortization, then obviously this will reduce COC as you're using Cash to repay the loan. This is also the scenario where LTV finally comes into play – the higher the LTV, the higher the amortization, the lower the COC.
I think calculating Cash on Cash (CoC) returns on cash flow is always monotonically decreasing with increasing debt. CoC return looks better with increasing debt when you are looking at the actual return. The former that you setup is ALMOST like a yield, an annualized number, in my mind.
Basically, you can use statistics to you tell you anything... If you purchased low and sold high, with greater leverage your CoC will be higher... But, if you purchased and sold at the same price, your return, whatever, is basically zero. If start adding in more factors it will adjust. Your CoC on cash flow could be adjusted if you considered amortization, assuming there are principal payments.
Just becareful when making judgements when these various statistics...
For example, if you "max leverage" a rental, your cash flow is zero. But, say in 30years you have a property free and clear. You have gained the amoritzation principal portion and any appreciation. Now calculate your CoC (other on equity or if you sold) comparing with max leverage or if you used all cash.
Real Estate Broker · Tampa Bay/St Petersburg, FL · Member since 2015 · 1k+ posts · 2k+ votes
3y
You just discovered why COC Return is often not the best metric to compare deals, markets, or properties to each other.
I get calls all the time from investors who are targeting a certain cash-on-cash return, and have to explain to them that COC depends on the down payment and debt service, and just because you put very little money down (it it were possible) does not make a property a great deal or a sound investment, even though the COC might be through the roof on paper.
Cash-on Cash is only valuable for an A to B comparison if the terms of the debt service are held constant (so why not just use cap rate in the first place?).
To be clear: COC can be a useful metric, and can be fund to brag about at parties. But it doesn't always tell you whether or not something is a good deal.
If you buy an asset with $10 down and it cash flows $100/yr, that's a super exciting 1000% COC return! But a property that only cash flows $8.33 per month is likely to bankrupt you!
I think calculating Cash on Cash (CoC) returns on cash flow is always monotonically decreasing with increasing debt. CoC return looks better with increasing debt when you are looking at the actual return. The former that you setup is ALMOST like a yield, an annualized number, in my mind.
Basically, you can use statistics to you tell you anything... If you purchased low and sold high, with greater leverage your CoC will be higher... But, if you purchased and sold at the same price, your return, whatever, is basically zero. If start adding in more factors it will adjust. Your CoC on cash flow could be adjusted if you considered amortization, assuming there are principal payments.
Just becareful when making judgements when these various statistics...
For example, if you "max leverage" a rental, your cash flow is zero. But, say in 30years you have a property free and clear. You have gained the amoritzation principal portion and any appreciation. Now calculate your CoC (other on equity or if you sold) comparing with max leverage or if you used all cash.
Make any sense?
Hey @David M., wow did this get me in a rabbit hole! I figured it out. I think I need to explain it in a fresh thread because of my variety of typos above, but here's the basic idea.
It is not actually true that the COC (Cash on Cash) is monotonically decreasing with increasing debt.
The simplest example is an interest only loan.
If you have an interest only loan, and your interest rate is less than the cap rate, then COC is INREASING as a function of debt. In other words, the more debt you take on, the higher your COC.
If your interest rate is higher than your cap rate, then COC is DECREASING as a function of debt. In other words, the more debt you take on, the worse your COC gets.
Lastly, if your interest rate is equal to your cap rate, then your COC is actually equal to your interest rate and your cap rate.
A similar phenomenon is true if it's not an interest only loan, but it's more complicated.
I've written it all out with actual math proofs for myself. I can't believe this doesn't exist anywhere. Can't find it anywhere online. It's incredibly helpful for analyzing an existing portfolio or a new acquisition since you can very quickly understand what adding debt to a property will or will not do to it's COC.
After over a decade of doing this, I still don't understand how the debt terms directly affect the Cash on Cash return of a deal.
For simplicity, define CAP Rate (:= NOI/Purchase Price) and COC (:= Cash Flow/Total Cash Invested).
Assume Cash Flow := NOI - Debt Service, and Purchase Price := Total Cash Invested + Debt Service.
• Say you are considering buying Property A. If you buy Property A WITHOUT debt, then CAP Rate = COC because Debt Service = $0 so Cash Flow = NOI and Purchase Price = Total Cash Invested.
• If you choose to add debt to Property A, then Total Cash Invested goes down (since you're using debt), so the denominator of COC goes down, so COC could potentially go up. HOWEVER, Cash Flow also goes down, because now you have to pay Debt Service, so the numerator of COC also goes down, so your COC could potentially go down as well.
The "math" question is what is an easy way to determine if the COC is going to go up or down, based on the terms of the debt?
For example, if the interest rate for the debt is less than the CAP rate, does that mean the COC will always go up? I don't think so. I think it depends on the LTV and possibly other factors.
Is there any simple relationship here
“If you buy Property A WITHOUT debt, then CAP Rate = COC because Debt Service = $0 so Cash Flow = NOI and Purchase Price = Total Cash Invested.”
I agree with your statement above.
But, in theory you could buy a property WITH debt where CAP Rate would still = COC. When you finance a property with loan where 1. Interest Rate is equal to CAP Rate and 2. the loan is interest only loan.
The impact of debt on COC is the net impact of each of the debt terms. It therefore helps to examine each term of the debt and how the terms individually affect a property's Cash Flow (or any business for that matter). Three factors to consider are – Interest Rate, Amortization, and Loan to Cost/Value. Following are several scenarios to help understand the relationship between CAP Rate and COC:
- When debt is used where Interest Rate is equal to CAP Rate, and no amortization (as mentioned above). CAP Rate generally = COC. NOTE: This is true whether LTV is 75% or 25% (i.e. LTV does not matter).
- When debt is used where Interest Rate is less than CAP Rate, and still no amortization. In this case COC will increase and exceed CAP Rate (i.e. this is classic leverage strategy, it's why corporations issue corporate bonds). ALSO NOTE: LTV still does not matter here.
- When debt is used with amortization, then obviously this will reduce COC as you're using Cash to repay the loan. This is also the scenario where LTV finally comes into play – the higher the LTV, the higher the amortization, the lower the COC.
Hi @Immanuel Sibero and @David M. , I'm excited for more math brains to discuss this with! Let's understand this very simple example first:
Suppose it's an interest only loan. Define the variables: interest rate i, annual debt service DS, loan amount LA, purchase price PP, net operating income NOI, cash on cash COC, and cap rate C.
Since it's an interest only loan,
i x LA = DS (interest rate times loan amount equals annual debt service).
Now suppose the interest rate equals the cap rate: i = C.
Then I claim the COC = i = C. In other words, the COC is equal to both the interest rate and cap rate.
Here's the proof:
Since i = C, DS/LA = NOI/PP.
That's the same as saying NOI/DS = PP/LA. Call this ratio r.
So r = NOI/DS = PP/LA.
Then NOI - DS = r*DS - DS = (r-1) * DS
and PP - LA = r*LA - LA = (r-1)*LA.
So COC = (NOI - DS)/(PP-LA) (by definition)
which is = (r-1)*DS/(r-1)*LA = DS/LA = i = C.
I'm trying to understand this in WORDS though. If the rate of payment (interest rate i) equals the rate of return (cap rate C), then WHY is the return on investment (COC) also equal to these rates? I can understand it mathematically, but not in practice.
Hi @Immanuel Sibero, I'm excited for another math brain to discuss this with. Let's understand this very simple example first:
Suppose it's an interest only loan. Define the variables: interest rate i, annual debt service DS, loan amount LA, purchase price PP, net operating income NOI, cash on cash COC, and cap rate C.
Since it's an interest only loan,
i x LA = DS (interest rate times loan amount equals annual debt service).
Now suppose the interest rate equals the cap rate: i = C.
Then I claim the COC = i = C. In other words, the COC is equal to both the interest rate and cap rate.
Here's the proof:
Since i = C, DS/LA = NOI/PP.
That's the same as saying NOI/DS = PP/LA. Call this ratio r.
So r = NOI/DS = PP/LA.
Then NOI - DS = r*DS - DS = (r-1) * DS
and PP - LA = r*LA - LA = (r-1)*LA.
So COC = (NOI - DS)/(PP-LA) (by definition)
which is = (r-1)*DS/(r-1)*LA = DS/LA = i = C.
I'm trying to understand this in WORDS though. If the rate of payment (interest rate i) equals the rate of return (cap rate C), then WHY is the return on investment (COC) also equal to these rates? I can understand it mathematically, but not in practice.
Okay. I took a quick read at your post and saw the formulas so initially I was going to wait till this afternoon to respond. But then I read your last paragraph with the burning question: Why is the COC also equal these rates? Well I'm going to try to answer without going through the above formulas since I think there may be a quick and simple answer. Hopefully this works:
Say you acquire a property with 10% CAP Rate. If you pay all cash then you get all the 10% CAP Rate (i.e you call this 10% COC). If you use Interest Only debt, it simply means you're sharing the 10% CAP rate with someone else (i.e. a debt holder) in such a way that part of the 10% CAP rate becomes COC (i.e. paid to you) and the other part becomes INTEREST (i.e. paid to the debt holder).
In this scenario, IF the debt holder demands 10% INTEREST can you see that you, as the owner, would also get 10% COC? The reason for this is because the property happens to be paying 10% CAP Rate, so everybody gets 10%!
IF the debt holder only demands 8% INTEREST then you as the owner would get more than 10% COC... this is because the property spits out 10% CAP Rate but the debt holder is happy with 8% INTEREST, so the residual (which would be higher than 10% COC) will go to you, the owner.
I will reread your post in its entirety later and comment further.
Hi @Immanuel Sibero, I'm excited for another math brain to discuss this with. Let's understand this very simple example first:
Suppose it's an interest only loan. Define the variables: interest rate i, annual debt service DS, loan amount LA, purchase price PP, net operating income NOI, cash on cash COC, and cap rate C.
Since it's an interest only loan,
i x LA = DS (interest rate times loan amount equals annual debt service).
Now suppose the interest rate equals the cap rate: i = C.
Then I claim the COC = i = C. In other words, the COC is equal to both the interest rate and cap rate.
Here's the proof:
Since i = C, DS/LA = NOI/PP.
That's the same as saying NOI/DS = PP/LA. Call this ratio r.
So r = NOI/DS = PP/LA.
Then NOI - DS = r*DS - DS = (r-1) * DS
and PP - LA = r*LA - LA = (r-1)*LA.
So COC = (NOI - DS)/(PP-LA) (by definition)
which is = (r-1)*DS/(r-1)*LA = DS/LA = i = C.
I'm trying to understand this in WORDS though. If the rate of payment (interest rate i) equals the rate of return (cap rate C), then WHY is the return on investment (COC) also equal to these rates? I can understand it mathematically, but not in practice.
Okay. I took a quick read at your post and saw the formulas so initially I was going to wait till this afternoon to respond. But then I read your last paragraph with the burning question: Why is the COC also equal these rates? Well I'm going to try to answer without going through the above formulas since I think there may be a quick and simple answer. Hopefully this works:
Say you acquire a property with 10% CAP Rate. If you pay all cash then you get all the 10% CAP Rate (i.e you call this 10% COC). If you use Interest Only debt, it simply means you're sharing the 10% CAP rate with someone else (i.e. a debt holder) in such a way that part of the 10% CAP rate becomes COC (i.e. paid to you) and the other part becomes INTEREST (i.e. paid to the debt holder).
In this scenario, IF the debt holder demands 10% INTEREST can you see that you, as the owner, would also get 10% COC? The reason for this is because the property happens to be paying 10% CAP Rate, so everybody gets 10%!
IF the debt holder only demands 8% INTEREST then you as the owner would get more than 10% COC... this is because the property spits out 10% CAP Rate but the debt holder is happy with 8% INTEREST, so the residual (which would be higher than 10% COC) will go to you, the owner.
I will reread your post in its entirety later and comment further.
Investor · Member since 2018 · 259 posts · 74 votes
3y
@Immanuel Sibero Awesome! Yes, there are several ways to prove it, but yours I think is the cleanest, great!
Now back to explaining this "in words", I love the direction you were going with that, but when you conclude:
" In this scenario, IF the debt holder demands 10% INTEREST can you see that you, as the owner, would also get 10% COC? The reason for this is because the property happens to be paying 10% CAP Rate, so everybody gets 10%!"
I believe you (of course, since we already proved it's true), but I don't see why if the cap rate is 10% and the debt holder demands 10% in interest, then we get 10% in COC. Does that make sense to you?
@Immanuel Sibero Awesome! Yes, there are several ways to prove it, but yours I think is the cleanest, great!
Now back to explaining this "in words", I love the direction you were going with that, but when you conclude:
" In this scenario, IF the debt holder demands 10% INTEREST can you see that you, as the owner, would also get 10% COC? The reason for this is because the property happens to be paying 10% CAP Rate, so everybody gets 10%!"
I believe you (of course, since we already proved it's true), but I don't see why if the cap rate is 10% and the debt holder demands 10% in interest, then we get 10% in COC. Does that make sense to you?
I'm having trouble answering... lol, how about alternative answers below:
- Based on the formula I laid out, when cap rate is 10% and interest rate is 10% then by definition COC is 10%.
- As owner, your portion of the property's rate of return is residual (whatever is left). Lender's portion of the property's rate of return is contractual (first dib). If the lender's contractual rate of return is higher than the property's rate of return, then the owner's rate of return would be lower than the property's rate of return... and vice versa. By the same logic, if the lender's contractual rate of return is the same as the the property's rate of return, then the owner's rate of return would necessarily have to be the same as the property's rate of return.
- If cap rate is 10% and debt holder demands 10% then COC can NOT be higher than 10% because this would require cap rate to be higher than 10%. In the same way, COC can NOT be lower than 10% because this would require cap rate to be lower than 10%. So COC has no choice but be 10%!
@Immanuel Sibero Awesome! Yes, there are several ways to prove it, but yours I think is the cleanest, great!
Now back to explaining this "in words", I love the direction you were going with that, but when you conclude:
" In this scenario, IF the debt holder demands 10% INTEREST can you see that you, as the owner, would also get 10% COC? The reason for this is because the property happens to be paying 10% CAP Rate, so everybody gets 10%!"
I believe you (of course, since we already proved it's true), but I don't see why if the cap rate is 10% and the debt holder demands 10% in interest, then we get 10% in COC. Does that make sense to you?
I'm having trouble answering... lol, how about alternative answers below:
- Based on the formula I laid out, when cap rate is 10% and interest rate is 10% then by definition COC is 10%.
- As owner, your portion of the property's rate of return is residual (whatever is left). Lender's portion of the property's rate of return is contractual (first dib). If the lender's contractual rate of return is higher than the property's rate of return, then the owner's rate of return would be lower than the property's rate of return... and vice versa. By the same logic, if the lender's contractual rate of return is the same as the the property's rate of return, then the owner's rate of return would necessarily have to be the same as the property's rate of return.
- If cap rate is 10% and debt holder demands 10% then COC can NOT be higher than 10% because this would require cap rate to be higher than 10%. In the same way, COC can NOT be lower than 10% because this would require cap rate to be lower than 10%. So COC has no choice but be 10%!
Which of the above do you like? :-)
Cheers... Immanuel
Hi @Immanuel Sibero! I've been working on applications of this concept all week. I have some good stuff to share but I need to iron out the kinks first.
In terms of your option of explanations "in words"... I'm going to add one to the mix...
It's really just a general rule about ratios and proportionality:
If A/B = C/D then (A-C)/(B-D) = A/B = C/D.
In words:
if A is proportional to B, and C is equally proportional to D then the difference of A and B is equally proportional to the difference of C and D.
So it's really just about understanding WHY this general statement is true.
I tried to discuss it with ChatGPT, but I swear that guy is not as smart as everyone says he is...I still don't intuitively see it.
But nonetheless, the application is if the cap rate (NOI/PP) is equal to the mortgage constant (DS/LA), then the differences are equally proportional, and that's the cash on cash (NOI-DS)/(PP-LA) by definition.
By the way, the same is true for a regular loan, not just interest only!
Now I'm trying to get a list of relationships like this between the cap rate and interest rate that effect the cash on cash, so that I can easily analyze any property using these simple inputs .... stay tuned ...
It seems your last question is as follows: "I believe you (of course, since we already proved it's true), but I don't see why if the cap rate is 10% and the debt holder demands 10% in interest, then we get 10% in COC. Does that make sense to you?"
Its seems to make plenty of sense to me... Basically, the property generates $10 for every $100. So whether its you, another investor, or a debt holder putting in the money, you get 10%. Your CoC calc is originally identified as based on the total cash invested, which I take to mean the actual amount of cash used.
It would be different If you were looking at the Total amount of cash or cash value as your basis.
Think about it another way, when cap rate > interest rate, isn't that where the benefit of leverage comes in? Isn't this exactly how banks make their money via net interest margin and leveraging that some 10x?
@Immanuel Sibero Awesome! Yes, there are several ways to prove it, but yours I think is the cleanest, great!
Now back to explaining this "in words", I love the direction you were going with that, but when you conclude:
" In this scenario, IF the debt holder demands 10% INTEREST can you see that you, as the owner, would also get 10% COC? The reason for this is because the property happens to be paying 10% CAP Rate, so everybody gets 10%!"
I believe you (of course, since we already proved it's true), but I don't see why if the cap rate is 10% and the debt holder demands 10% in interest, then we get 10% in COC. Does that make sense to you?
I'm having trouble answering... lol, how about alternative answers below:
- Based on the formula I laid out, when cap rate is 10% and interest rate is 10% then by definition COC is 10%.
- As owner, your portion of the property's rate of return is residual (whatever is left). Lender's portion of the property's rate of return is contractual (first dib). If the lender's contractual rate of return is higher than the property's rate of return, then the owner's rate of return would be lower than the property's rate of return... and vice versa. By the same logic, if the lender's contractual rate of return is the same as the the property's rate of return, then the owner's rate of return would necessarily have to be the same as the property's rate of return.
- If cap rate is 10% and debt holder demands 10% then COC can NOT be higher than 10% because this would require cap rate to be higher than 10%. In the same way, COC can NOT be lower than 10% because this would require cap rate to be lower than 10%. So COC has no choice but be 10%!
Which of the above do you like? :-)
Cheers... Immanuel
Hi @Immanuel Sibero! I've been working on applications of this concept all week. I have some good stuff to share but I need to iron out the kinks first.
In terms of your option of explanations "in words"... I'm going to add one to the mix...
It's really just a general rule about ratios and proportionality:
If A/B = C/D then (A-C)/(B-D) = A/B = C/D.
In words:
if A is proportional to B, and C is equally proportional to D then the difference of A and B is equally proportional to the difference of C and D.
So it's really just about understanding WHY this general statement is true.
I tried to discuss it with ChatGPT, but I swear that guy is not as smart as everyone says he is...I still don't intuitively see it.
But nonetheless, the application is if the cap rate (NOI/PP) is equal to the mortgage constant (DS/LA), then the differences are equally proportional, and that's the cash on cash (NOI-DS)/(PP-LA) by definition.
By the way, the same is true for a regular loan, not just interest only!
Now I'm trying to get a list of relationships like this between the cap rate and interest rate that effect the cash on cash, so that I can easily analyze any property using these simple inputs .... stay tuned ...
But nonetheless, the application is if the cap rate (NOI/PP) is equal to the mortgage constant (DS/LA), then the differences are equally proportional, and that's the cash on cash (NOI-DS)/(PP-LA) by definition.
I was not a math major, maybe that's why I'm having trouble answering your question. But I feel like I'm going in circle. As normally defined, COC = CF/DP where CF is Cashflow and DP is down payment. I can restate your statement above with substitutions in bold font... and it would also be true:
But nonetheless, the application is if the cap rate (NOI/PP) is equal to the COC (CF/DP), then the differences are equally proportional, and that's the Interest (NOI-CF)/(PP-DP) by definition.
Are you NOT interested in the “why” for this proportional equality?
By the way, the same is true for a regular loan, not just interest only!
Interest Only has been a necessary assumption in all my responses, so I don't agree with this statement. If you were to amortize the loan by 1 dollar, COC would go out of synch (i.e. no longer equal to interest rate or cap rate). But since you made the claim, you have the burden of proof... lol. So how would you show that with an amortizing loan, when i = C, then COC also = C?? I just don't see it possible.
Last comment for today... here's another quote from your earlier post: I've written it all out with actual math proofs for myself. I can't believe this doesn't exist anywhere. Can't find it anywhere online. It's incredibly helpful for analyzing an existing portfolio or a new acquisition since you can very quickly understand what adding debt to a property will or will not do to it's COC.
So, property analysis seems to be your bottom line (i.e. not necessarily the math connections between debt and COC). Well I made a post quite sometime ago that covers exactly this, that is, the impact of debt terms on COC... So YES, it does exist and it's been written before :-) Here is the excerpt:
I was evaluating a property with the following metrics:
Cap Rate: 6%
Interest Rate: 4%
LTV: 75%
Since the spread between cap rate and interest rate was slim (2%), I knew COC would be low. Since low COC means running the risk of negative cash flow which means risk of not paying the loan, I wanted to know how the various loan terms affect COC. For example, how sensitive was COC to the Cap and Int spread. This can easily be done using sensitivity tables in Excel. Based on the financial data of the property, following are two sensitivity tables:
As you can see, my Cap rate - Int rate spread is 2% and from the first table it puts my COC at 2.39% which is concerning. Note that this table shows how sensitive COC is against the spread.
Second table shows how sensitive COC is against LTV. It shows that 75% debt is about the most I should borrow. Anything higher can put me in negative cashflow. HTH
@Kim Hopkins This sort of thing was going through my mind when I first responded. usally when you run a series of calcs the CoC isn't constant...
You trying to analyze this stuff in your head? Just wondering why you need these sort of relationships. I would think that normally a spreadsheet or other computer system would calculate anything you'd want with these basic inputs.
@Immanuel Sibero Awesome! Yes, there are several ways to prove it, but yours I think is the cleanest, great!
Now back to explaining this "in words", I love the direction you were going with that, but when you conclude:
" In this scenario, IF the debt holder demands 10% INTEREST can you see that you, as the owner, would also get 10% COC? The reason for this is because the property happens to be paying 10% CAP Rate, so everybody gets 10%!"
I believe you (of course, since we already proved it's true), but I don't see why if the cap rate is 10% and the debt holder demands 10% in interest, then we get 10% in COC. Does that make sense to you?
I'm having trouble answering... lol, how about alternative answers below:
- Based on the formula I laid out, when cap rate is 10% and interest rate is 10% then by definition COC is 10%.
- As owner, your portion of the property's rate of return is residual (whatever is left). Lender's portion of the property's rate of return is contractual (first dib). If the lender's contractual rate of return is higher than the property's rate of return, then the owner's rate of return would be lower than the property's rate of return... and vice versa. By the same logic, if the lender's contractual rate of return is the same as the the property's rate of return, then the owner's rate of return would necessarily have to be the same as the property's rate of return.
- If cap rate is 10% and debt holder demands 10% then COC can NOT be higher than 10% because this would require cap rate to be higher than 10%. In the same way, COC can NOT be lower than 10% because this would require cap rate to be lower than 10%. So COC has no choice but be 10%!
Which of the above do you like? :-)
Cheers... Immanuel
Hi @Immanuel Sibero! I've been working on applications of this concept all week. I have some good stuff to share but I need to iron out the kinks first.
In terms of your option of explanations "in words"... I'm going to add one to the mix...
It's really just a general rule about ratios and proportionality:
If A/B = C/D then (A-C)/(B-D) = A/B = C/D.
In words:
if A is proportional to B, and C is equally proportional to D then the difference of A and B is equally proportional to the difference of C and D.
So it's really just about understanding WHY this general statement is true.
I tried to discuss it with ChatGPT, but I swear that guy is not as smart as everyone says he is...I still don't intuitively see it.
But nonetheless, the application is if the cap rate (NOI/PP) is equal to the mortgage constant (DS/LA), then the differences are equally proportional, and that's the cash on cash (NOI-DS)/(PP-LA) by definition.
By the way, the same is true for a regular loan, not just interest only!
Now I'm trying to get a list of relationships like this between the cap rate and interest rate that effect the cash on cash, so that I can easily analyze any property using these simple inputs .... stay tuned ...
But nonetheless, the application is if the cap rate (NOI/PP) is equal to the mortgage constant (DS/LA), then the differences are equally proportional, and that's the cash on cash (NOI-DS)/(PP-LA) by definition.
I was not a math major, maybe that's why I'm having trouble answering your question. But I feel like I'm going in circle. As normally defined, COC = CF/DP where CF is Cashflow and DP is down payment. I can restate your statement above with substitutions in bold font... and it would also be true:
But nonetheless, the application is if the cap rate (NOI/PP) is equal to the COC (CF/DP), then the differences are equally proportional, and that's the Interest (NOI-CF)/(PP-DP) by definition.
Are you NOT interested in the “why” for this proportional equality?
By the way, the same is true for a regular loan, not just interest only!
Interest Only has been a necessary assumption in all my responses, so I don't agree with this statement. If you were to amortize the loan by 1 dollar, COC would go out of synch (i.e. no longer equal to interest rate or cap rate). But since you made the claim, you have the burden of proof... lol. So how would you show that with an amortizing loan, when i = C, then COC also = C?? I just don't see it possible.
Last comment for today... here's another quote from your earlier post: I've written it all out with actual math proofs for myself. I can't believe this doesn't exist anywhere. Can't find it anywhere online. It's incredibly helpful for analyzing an existing portfolio or a new acquisition since you can very quickly understand what adding debt to a property will or will not do to it's COC.
So, property analysis seems to be your bottom line (i.e. not necessarily the math connections between debt and COC). Well I made a post quite sometime ago that covers exactly this, that is, the impact of debt terms on COC... So YES, it does exist and it's been written before :-) Here is the excerpt:
I was evaluating a property with the following metrics:
Cap Rate: 6%
Interest Rate: 4%
LTV: 75%
Since the spread between cap rate and interest rate was slim (2%), I knew COC would be low. Since low COC means running the risk of negative cash flow which means risk of not paying the loan, I wanted to know how the various loan terms affect COC. For example, how sensitive was COC to the Cap and Int spread. This can easily be done using sensitivity tables in Excel. Based on the financial data of the property, following are two sensitivity tables:
As you can see, my Cap rate - Int rate spread is 2% and from the first table it puts my COC at 2.39% which is concerning. Note that this table shows how sensitive COC is against the spread.
Second table shows how sensitive COC is against LTV. It shows that 75% debt is about the most I should borrow. Anything higher can put me in negative cashflow. HTH
I'm writing this from my phone so I can definitely clarify more later from the computer if needed, but this is getting exciting so I wanted to respond now!
First, I am very interested into WHY the proportionality holds in the interest only example. That's why I keep asking you to say it 10 different ways, but none of them have exactly clicked yet for me :-)
Now moving on to the example of a normal loan that is not interest only.
In this case, there is something called the mortgage constant M, AKA mortgage capitalization rate, which is defined as the debt service divided by the loan amount, DS/LA. By definition M*LA = DS. If you look at the formula for this,
M = i/(1-(1+i/12)^(-12Y) where i is the interest rate, and Y is the amortization years. You can see clearly that this number is independent of the amount of the loan LA, or the LTV.
Fix an amortization rate Y. And write the notation for M as M(i) to indicate that it is a function of the interest rate i.
Then here is the analog for a regular loan of what we have been discussing for an interest only loan:
Suppose you have a property with cap rate C.
Then there is one unique interest rate, I, so that the mortgage capitalization rate M(I) equals the cap rate C.
M(I) = C.
Then for any interest rates i with i< I, your cash on cash will increase as a function of loan amount. In other words the more loan you take out, the better your cash on cash.
Conversely, for any interest rate i bigger than I, your cash on cash will decrease as a function of the loan amount. So in particular, your cap rate for that property is going to be bigger than any cash on cash return with any amount of debt. In other words, the property will perform better without debt than with debt, regardless of the loan amount.
So in the example you did with the sensitivity analysis, you could just calculate I, and then you know instantly that any interest rates less than I will give you cash on cash better than your cap rate, and any interest rates greater than I will give you cash on cash less than your cap rate and will decrease with the more loan you take out.
@Kim Hopkins This sort of thing was going through my mind when I first responded. usally when you run a series of calcs the CoC isn't constant...
You trying to analyze this stuff in your head? Just wondering why you need these sort of relationships. I would think that normally a spreadsheet or other computer system would calculate anything you'd want with these basic inputs.
I'm trying to be able to analyze properties in my portfolio for a keep or trade analysis.
some of the properties are debt-free, and so I need to also look at whether adding debt to the property improves the return. (And even for properties with debt, the same analysis is helpful to know if refinancing improves returns.)
I want to be able to analyze this keep or trade decision as simply as possible, having to analyze as few possibilities as possible.
So for example, based on what I wrote above, I can solve for "I" above with a very simple spreadsheet calc, using my property's current cap rate.
Then I can take the current market interest rate for a typical loan for my asset class, and compare it to I.
This will tell me immediately if adding debt to this property could possibly improve the returns over the current return.
as another cute little application, it turns out that if the cap rate of my current property is less than 1/Y where Y is the years of amortization for a loan, then any interest rate and any loan amount will give a cash on cash less than the cap rate of the property without debt. So for example if you take Y to be 25 years which is the typical amortization for my asset class, then 1/Y is 4%. I have some older properties with undermarket rent where the cap rate is less than 4%. I now know immediately that adding debt to these properties will not improve their return no matter what the loan amount is OR the interest rate! No calculations at all needed!
Investor · Member since 2022 · 3k+ posts · 3k+ votes
3y
Leverage is always going to almost always show you a better look, but if you think investing is strictly numerate you're going to learn the hard way. It's every bit behavioral too, you really sit in the leverage area for as much as you can tolerate. And most really, really sophisticated investors don't go out there and leverage things even like real estate. Tolerance levels the past dozen years + was great with debt service never creeping up, but go check the bal-decade interest payments vs the last 6-7 years. It's just going to be an incredibly difficult time to think being cute with debt is as fun.
Leverage is always going to almost always show you a better look, but if you think investing is strictly numerate you're going to learn the hard way. It's every bit behavioral too, you really sit in the leverage area for as much as you can tolerate. And most really, really sophisticated investors don't go out there and leverage things even like real estate. Tolerance levels the past dozen years + was great with debt service never creeping up, but go check the bal-decade interest payments vs the last 6-7 years. It's just going to be an incredibly difficult time to think being cute with debt is as fun.
Hi @V.G Jason,
No, leverage is NOT going to almost always show you a better return. That's the entire point of what I've shown above, and you echo the same point at the end of your comment where you say: "It's just going to be an incredibly difficult time to think being cute with debt is as fun."
The reason this is true is what I've said above.
There's a specific interest rate, I, so that the mortgage constant, M(I) is equal to the cap rate.
If the interest rate you can get for your property, i, is LESS than I, then it is TRUE that cash on cash INCREASES as a function of loan amount. So what you said is true in this case.
However, if the interest rate you can get for your property, i, is GREATER than I, then cash on cash DECREASES as a function of loan amount. So the more debt you take on, the worse your property performs. This is what makes your last point true - that you cannot be "cute" with debt right now. To say it another way, the interest rates right now make it IMPOSSIBLE to increase the return of your property using leverage.
Furthermore the mortgage constant, M(i) is always greater than the interest rate i itself, and M is an increasing function of i, so the interest rates have to be MUCH less than the cap rate (i << M(i) < M(I) = cap rate) in order to get a cash on cash return that beats no-leverage.
So we need to come a LONG way down in interest rates for leverage to be cute again.
Leverage is always going to almost always show you a better look, but if you think investing is strictly numerate you're going to learn the hard way. It's every bit behavioral too, you really sit in the leverage area for as much as you can tolerate. And most really, really sophisticated investors don't go out there and leverage things even like real estate. Tolerance levels the past dozen years + was great with debt service never creeping up, but go check the bal-decade interest payments vs the last 6-7 years. It's just going to be an incredibly difficult time to think being cute with debt is as fun.
Hi @V.G Jason,
No, leverage is NOT going to almost always show you a better return. That's the entire point of what I've shown above, and you echo the same point at the end of your comment where you say: "It's just going to be an incredibly difficult time to think being cute with debt is as fun."
The reason this is true is what I've said above.
There's a specific interest rate, I, so that the mortgage constant, M(I) is equal to the cap rate.
If the interest rate you can get for your property, i, is LESS than I, then it is TRUE that cash on cash INCREASES as a function of loan amount. So what you said is true in this case.
However, if the interest rate you can get for your property, i, is GREATER than I, then cash on cash DECREASES as a function of loan amount. So the more debt you take on, the worse your property performs. This is what makes your last point true - that you cannot be "cute" with debt right now. To say it another way, the interest rates right now make it IMPOSSIBLE to increase the return of your property using leverage.
Furthermore the mortgage constant, M(i) is always greater than the interest rate i itself, and M is an increasing function of i, so the interest rates have to be MUCH less than the cap rate (i << M(i) < M(I) = cap rate) in order to get a cash on cash return that beats no-leverage.
So we need to come a LONG way down in interest rates for leverage to be cute again.
When interest rates come down, what do you think the underlying asset does? Don't think simply math, think economics and behavior.
Leverage will almost always be the best tool. Yes, almost. Even at these rates, they let you scale appropriately and if you're buying in good areas(the test results come in 10-20 years), it would be proven to be a better method than cash and no scale. All retrospectively. And cash on cash return is just one metric, it's not the metric to evaluate real estate. There's no metric.
Buy in good areas, keep the house in good condition, keep entities for it to be under, hire a good team to manage it. And hope for the best with this risk. Getting mathematical on a physical piece of real estate that has too many variables is just a waste of time, with all due respect.
Investor · Member since 2018 · 259 posts · 74 votes
3y
Well, in case anyone is curious. I FINALLY figured out all the mathematical connections between cap rate, interest rate, and what I call the "break even interest rate" that determines when your return will increase or decrease with debt.
I created a portfolio wide analysis where I use all the "math" on our existing portfolio to assess property performance and analyze whether to:
1. Do Nothing
2. Refi and Reinvest (i.e. keep property and buy another) or
3. Sell and Reinvest.
Here is a 6 minute video that walks through the process in case anyone is curious or would like to try to apply this to their own portfolio.
