Mathematical Connection Between Debt Terms & Cash on Cash Return

[Kim Hopkins]

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? 

[Immanuel Sibero]

Quote from @Kim Hopkins:

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.

Cheers... Immanuel