1. Real Estate Finance, Spring, 2018
The Return to Equity
Real Estate Finance, Spring, 2018

2. The Leverage Ratio

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

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

5. 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

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

7. 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

8. Explaining Leverage Math. Start with E = V - L

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

10. 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%

11. 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%

12. 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

13. Deriving income and growth returns to equity
Start with

14. 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

15. 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 = %
gD is negative because the mortgage is amortizing and thus declining

16. 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 ?

17. 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 ?

18. 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 ?

19. 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 ?