The Effects of Risk As we know, the cap rate relation is given by: R = NOI/V This relation is also the total return relation when an investor buys an income property for cash (V=AP) and holds it in perpetuity: y = NOI/AP Economy, market (regional), and property specific risk factors affect the NOI of a property One approach to modeling the impact of risks on NOI is by treating NOI as a stochastic variable

NOI Under Uncertainty Let NOI  (NOI + , where  is “white noise” with E(  )=0 and E(   )=  2 (NOI). Then, R = (NOI +  /v and, in the previous example, y = (NOI +  /AP The variance on returns is:  2 (R) = (1/V 2 )  2 (NOI) = (1/AP 2 )  2 (NOI) =  2 (y)

Risks With Debt Financing V > AP, when an investor borrows to finance the purchase of an income producing property In exchange, the investors assume new market and economic (financial) risks Relevant cash flows now must account for debt service

Risks With Financing: Leverage BTCF = (NOI – DS) + , where  is “white noise” Assuming loan terms may be extended in perpetuity (infinite refinancing at the same terms), the risk of a debt financing purchase are higher than that of a cash purchase:  2 (BTCF) = (1/V 2 )  2 (NOI) < (1/AP 2 )  2 (NOI) =  2 (y)

Risks With Financing: Debt Service BTCF = (NOI +  ) – (DS +  ), where e and v are uncorrelated white noise, with E(  )=0, E(   )=  2 (NOI), E(  )=0, E(   )=  2 (DS), and E(  ) = 0 Then, the variance of the total returns changes to:  2 (BTCF) = (1/V 2 )  2 (joint) < (1/AP 2 )  2 (joint) =  2 (y) Where:  2 (joint) = (  2 (NOI) +  2 (DS) ) >  2 (NOI)

Managing Debt Service Risks BTCF = (NOI +  ) – (DS +  ), where  and  are negatively correlated white noise, with E(  )=0, E(   )=  2 (NOI), E(  )=0, E(   )=  2 (DS). And E(  ) < 0 Then, the variance of the total returns changes to:  2 (BTCF) = (1/V 2 )  2 (joint) < (1/AP 2 )  2 (joint) =  2 (y) Where:  2 (joint) =  2 (NOI) +  2 (DS) + 2E(  ), which is lower than the joint risk under the assumption of zero correlation

Managing Debt Service Risks Participation loans, convertible mortgages, interest only and accrual loans are examples of financing tools that can accomplish the above “negative correlation between debt service uncertainties and income uncertainties. Risks do not disappear, they are shared – to the extent lenders and borrowers have incentives (return) that affect their risk taking decision

Summary Debt financing augments risks of investing in income properties by reducing the expected cash flows before taxes Debt financing augments risks of investing in income properties by introducing financing risks that are usually partly correlated with cash flow risks The net effect of debt financing is to enhance the expected return from an income generating property, at the expense of increasing the assumed risks from investing in debt financed real estate

Summary Debt financing may be used to accomplish the same risk reduction/sharing that is accomplished by investors choosing alternative ownership structures (partnerships, incorporations, etc.) to spread risks of investing in real estate. The major difference between decisions about risk versus decisions about ownership structure is that before-tax returns are not augmented by the choice of ownership structure, as they are by the choice of financing terms

Summary Loan terms (loan amount, amortization schedule, loan term, refinancing terms, nature of interest rate and interest payments, lender participation in cash flows, convertibility of debt instrument, etc.) Are used by the lender and the investor to manage or allocate the financing risks of the income producing property