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?