Real Estate Finance, Spring, 2017 The Return to Equity Real Estate Finance, Spring, 2017

The Leverage Ratio

Using Modigliani-Miller to Understand Leverage Loan Amount (Debt): L Equity: E Underlying Asset Value: V = E + L Leverage Ratio LR = V/E

Leverage Ratio (LR) not equal to Loan-to-Value (LTV)

Effect of Leverage on Risk and Return Purchase price: $10,000 Next Year Outcomes are Risky: Optimistic Scenario, probability 0.5 Cash flow = $900 Sale price = $11,200 Pessimistic Scenario, probability 0.5 Cash flow = $700 Sale price = $9,200

Case 1: All Equity Financed Optimistic Pessimistic Expected Risk Income Ret Apprec. Ret

Case 2: Borrow $6,000 at 8%, Repaid after 1 Year LR = 2.5 with E = $4,000, L = $6,000 and V = $10,000 Interest payment of $480 Optimistic Pessimistic Expected Risk Income Ret Apprec. Ret

Explaining Leverage Math. Start with E = V - L

We can “rework” this last formula WACC, “weighted average cost of capital”

Thinking about WACC Which firm has a higher cost of capital? REIT A Cost of Debt = 6% Cost of Equity = 15% REIT B Cost of Debt = 8% Cost of Equity = 15%

Using WACC Which firm has a higher cost of capital? REIT A Cost of Debt = 6% Cost of Equity = 15% L/V = 0.30 REIT B Cost of Debt = 8% Cost of Equity = 15% L/V = 0.50 REIT A WACC = 6%(0.30) + 15%(0.70) = 12.3% REIT B WACC = 8%(0.50) + 15%(0.50) = 11.5%

Returning to Previous Example Levered Expected Return of 13% In practice it is difficult to observe levered returns We can observe return on loans and returns on property (asset) Given any leverage ratio, can solve for the levered return Typically, leverage boosts both the return and the risk

Deriving income and growth returns to equity Start with

Deriving income and growth returns to equity These are linked with the standard formula yE is the “cash on cash” return or “equity cash yield” Positive vs Negative Leverage Positive leverage: term in parenthesis is positive, adding debt boosts return Negative leverage: term in parenthesis is negative, adding debt reduces return

What are the income and growth returns to debt? Consider: Define the “mortgage constant” as the mortgage payment divided by the initial balance (for a fixed-rate mortgage) Example: 30-year FRM at 5% with annual payments has a mortgage constant of 6.505% In the first year, rD = 5%, yD = 6.505% and gD = -1.505% gD is negative because the mortgage is amortizing and thus declining

Positive Leverage Example Property total return rP = 10% Cap rate yP = 8% Loan interest rate rD = 6% Mortage constant yD = 7% This implies gP = rP – yP = 2% and gD = rD – yD = –1% Suppose A/E = 1. What are rE , yE , gE ?

Positive Leverage Example Property total return rP = 10% Cap rate yP = 8% Loan interest rate rD = 6% Mortage constant yD = 7% Suppose A/E = 3. What are rE , yE , gE ?

Negative Leverage Example Property total return rP = 10% Cap rate yP = 8% Loan interest rate rD = 8% Mortage constant yD = 9% As before: gP = rP – yP = 2% and gD = rD – yD = –1% Suppose A/E = 1. What are rE , yE , gE ?

Negative Leverage Example Property total return rP = 10% Cap rate yP = 8% Loan interest rate rD = 8% Mortage constant yD = 9% Suppose A/E = 3. What are rE , yE , gE ?