CHAPTER 2 VALUE: THE CENTRAL IDEA Examples of alternative value concepts include: market value, investment value, and mortgage value. McGraw-Hill/Irwin

What is Real Estate Valuation? Investors expect cash flow from operations and from the sale of the property. Value is affected by the magnitude, timing, and riskiness of the expected cash flows. McGraw-Hill/Irwin

TIME-VALUE-OF-MONEY TERMS Interest Rate, Discount Rate, Rate of Return Present Value Future Value Lump Sum Annuity Compounding Discounting McGraw-Hill/Irwin

Present Value of a Single Lump Sum Example: Assume Astute Investor has an opportunity that provides $1,610.51 at the end of five years. If Ms. Investor requires a 10 percent annual return, how much can Astute pay today for this future sum? Solution = $1,000.00 McGraw-Hill/Irwin

Sinking Fund Payment Example: Assume Astute Investor wants to accumulate $6,105.10 in five years. Assume Ms. Investor can earn 10 percent, compounded annually. How much must be invested each year to obtain the goal? Solution = $1,000.00 McGraw-Hill/Irwin

Future Value of a Single Lump Sum Example: Assume Astute Investor invests $1,000 today which pays 10 percent, compounded annually. What is the expected future value of that deposit in five years? Solution = $1,610.51 McGraw-Hill/Irwin

Annuities Ordinary Annuity Annuity Due (e.g., mortgage payment) Annuity Due (e.g., a monthly rental payment) McGraw-Hill/Irwin

Present Value of an Annuity Example: Assume Astute Investor has an opportunity that provides $1,610.51 at the end of each year for five years. If Ms. Investor requires a 10 percent annual return, how much can Astute pay today for this future cash flow series? Solution = $6,105.10 McGraw-Hill/Irwin

Future Value of an Annuity Example: Assume Astute Investor invests $1,000 at the end of each year in an investment which pays 10 percent, compounded annually. What is the expected future value of that investment in five years? Solution = $6,105.10 McGraw-Hill/Irwin

Payment to Amortize Mortgage Loan Example: Assume Astute Investor would like a mortgage loan of $100,000 at 10 percent annual interest, paid monthly, amortized over 30 years. What is the required monthly payment of principal and interest? Solution = $877.57 McGraw-Hill/Irwin

Loan Amortization Schedule McGraw-Hill/Irwin

Remaining Loan Balance Calculation Example: Determine the remaining balance of a mortgage loan of $100,000 at 10 percent annual interest, paid monthly, amortized over 30 years at the end of year four. The balance is the PV of the remaining payments discounted at the contract interest rate. Solution = $97,402.22 McGraw-Hill/Irwin

Net Present Value (NPV) The net present value is the present value of a project’s cash inflows, minus the present value of the cash outflows. The cash flows are discounted at the investor’s required rate of return. McGraw-Hill/Irwin

NPV Decision Criteria If NPV>0, the project exceeds the investor’s required rate of return. If NPV<0, the project does not meet the investor’s required rate of return. If NPV=0, the project’s expected return equals the investor’s required rate of return. McGraw-Hill/Irwin

Internal Rate of Return (IRR) The internal rate of return is the discount rate at which NPV = 0, the rate of return at which the present value of the cash inflows equals the present value of the cash outflows. McGraw-Hill/Irwin

IRR Decision Criteria If the IRR is greater than the investor’s required return (the hurdle rate), the investment may be accepted. The IRR decision criterion may be misleading because it assumes that cash inflows can be reinvested at the IRR rate. McGraw-Hill/Irwin

Lender’s Yield and the Effective Cost of Borrowing The lender’s yield is the IRR that equates the loan amount with the present value of the payments to be received. The borrower’s effective cost of borrowing is the mirror image of the lender’s yield. McGraw-Hill/Irwin

Capitalization Rate The overall capitalization rate, Ro, is the ratio between a property’s net operating income and its value. Ro = CFt / SP, where CFt is the expected cash flow in year t, and SP is the selling price of the property. McGraw-Hill/Irwin