FNCE 333 Lecture 7

1. FNCE 333Lecture 7 Before-Tax Mortgage-Equity Valuation Professor C. F. Sirmans

2. Review • Valuation using Rules of Thumb/Ratios • Office Building Development Case • Strip Shopping Center Case – Review Cash Flow Forecast

3. Readings • Brueggeman and Fisher, Chapter 13 • Readings 16 and 17 • Problem Set 7

4. Mortgage-Equity Valuation • The basic idea: View the total value of a real estate investment as the value of the debt (mortgage) plus the value of the equity. • Value of debt is the present value of the cash flows to the debt position. • Value of the equity is the present value of the cash flows (before-tax) to the equity. • Equity treated as the “residual” claim.

5. Mortgage-Equity Valuation • What is the maximum price that could be bid such that the NPV of both the debt and equity claims are exactly equal to zero? • What are inputs? Forecast of NOI and NSP, required rates of return on debt and equity, and how to allocate cash flows to each position (mortgage maturity, equity holding period, loan-to-value ratio).

6. Mortgage-Equity Valuation

7. Mortgage-Equity ValuationAn alternative version where reversion selling price is written as a growth rate (g) in property values

8. Some Definitions • V = Value of investment • L/V = Loan-to-Value Ratio • BTCF = Before-tax Cash Flow • BTER = Before-tax Equity Reversion • NOI = Net Operating Income • DS = Annual Debt Service • NSP = Net Sale Price • UM = Unpaid Mortgage Balance

9. Some Definitions • MC = Mortgage Constant (Annualized) • Rn = Going-out “Cap” Rate • SE = Percentage Selling Expenses • PO = Proportion of Mortgage Outstanding • y = Required Before-tax yield on Equity

10. All Equity Financed Example A real estate investment has the following assumptions: (see Problem Set 7, #2) NOI = $10,000 per year (constant) Holding Period = 10 years Reversion = Selling price equal to today’s value (no change in price) All equity financed (no mortgage) Required Equity Yield = 9.75% How much would the investor bid?

11. All Equity Example The Value is

12. All Equity Example • Proof: If the investor pays $102, 565, what is the (expected) internal rate of return to the equity investor? Answer: 9.75%

13. Mortgage-Equity Valuation:Some Basic Questions • What is the level and pattern of the expected NOI? • What is the expected NSP? • What are the characteristics of the Mortgage? Loan-to-Value Ratio, Interest Rate, Amortization term, frequency of compounding • What is the required yield (before-tax) on equity?

14. Mortgage-Equity Valuation • What is the pattern of the NOI? A. Constant (annuity) B. Growing at a constant rate C. Variable each year

15. Mortgage-Equity Valuation • How to forecast reversion cash flow? SP = NOI/Rn or SP = V(1 + g)n g = % growth rate per year in value NSP = SP(1 – SE) SE = % selling expenses

16. Mortgage-Equity Valuation • Characteristics of the mortgage? A. Amount Borrowed as a $ Amount or B. Amount borrowed in relation to Value, i.e., (L/V)(V)

17. Before-Tax Mortgage Equity:Basic Equations Value = Mortgage Value + Equity Value BTCF = NOI - DS DS = Amt. Borrowed (Mortgage Constant) DS = L/V(V)(MC) BTER = NSP – UM UM = (L/V)(V)(Proportion Outstanding)

18. Mortgage-Equity Valuation

19. Mortgage-Equity ValuationAn alternative version where reversion selling price is written as a growth rate (g) in property values

20. Mortgage-Equity Valuation:Interest-Only Mortgage • Suppose the investment is financed as follows: (see Problem Set 7, #2) 75% loan-to-value 9% interest rate (interest-only) Balloon payment in 10 years 12% equity yield

21. Mortgage-Equity Example:Interest-Only Mortgage The value of the investment is:

22. Mortgage-Equity Valuation:Amortized Mortgage • Mortgage maturity of 15 years, with monthly payments. All other mortgage terms the same. • Annual Mortgage Constant = (.010143)12 = .12171 • Proportion Outstanding at end of year 10 = .48861

23. Mortgage-Equity Valuation:Amortized Mortgage

24. Mortgage-Equity Valuation:Amortized Mortgage

25. Mortgage-Equity Valuation:Proof • Value = $100,355 • Mortgage = $100,355(.75) = $75,266 • Equity = $25,089 • DS = $75,266(.1217) = $9,160 • BTCF = $10,000 - $9,160 = $840 • Unpaid Mortgage at end of year 10 = $75,266(.48861) = $36,775 • BTER = $100,355 - $36,775 = $63,580 • Calculated IRR on Equity = 12%; NPV = 0

26. Before-Tax Mortgage Equity: Another Amortized Debt Example See Problem Set 7, #3 NOI = $45,000 (constant) Reversion: g = 4% per year SE = 6% N = 5 years Debt: L/V = 75% i = 12% Maturity = 20 years (monthly) Equity: y = 15%

27. Mortgage-Equity Valuation: Another Amortized Mortgage Example

28. Additional Concepts • How to solve the mortgage-equity equations when NOI is not constant? • When DS is not constant? Or if more than one mortgage? • How to account for Acquisition Costs, Financing Costs and Prepayment Penality

29. Mortgage-Equity Valuation: Office Building Development Case • See Office Building Development Case beginning with question #28, slides 78, 79 • Comparison of mortgage-equity value with NPV analysis in Office Building Case • Correction of Mortgage-Equity value for financing and acquisition costs and prepayment penality. Question #29, slide 80

30. Office Building Development Case Calculating the mortgage-equity value using the spreadsheet. Solving for the Value where NPV of BTCFs is equal to Zero

31. Summary • Basic premise of mortgage-equity valuation: What is the maximum price that could be bid for an investment, given the expected income and the required rates of return on the debt and equity claims? What price makes the NPV of both claims exactly equal to zero?