Chapter 14 Time Value of Money Value of a property depends on o Magnitude of expected cash flows o Timing of expected cash flows o Riskiness of expected cash flows Valuation complications 1 Even if the timing of future benefits is known the future benefits of a proposed investment cannot be added up to determine value because the current value of future benefits declines with time in the future 2 Value assessments are based one expected cash flows Risk Probability that actual outcomes will vary from what was expected o Risk averse investors require a higher rate of return for taking on additional risk Time Value of Money Techniques used for quantifying the effects of time and risk on value o If money is received later it isn t worth as much to those receiving it Discounting The adjustment made to find the value of some future value today o Investors who plan to reinvest returns prefer earlier returns because of all of the opportunity to earn interest Terminology Future Value FV Value of money in some period beyond time 0 o Converts cash invested currently into what it will be worth at some future date Present Value PV Value of future cash flows at time 0 o Converts future cash flows into what they are worth today One time receipt or expense occurring in a given period Lump Sum Ordinary Annuity A Annuity Due Compounding Discounting Fixed amount of money to be paid or received at the end of every period Occurs when investor makes or receives payments at the beginning of the period Calculation of future values Calculation of present values Equations for Time Value of Money Adjustments Future Value of a Lump Sum Future Value of Annuity Present Value of a Lump Sum Present Value of Annuity FV 1 r n FVA 1 r n 1 r PV 1 1 r n PVA 1 1 1 r n r Financial Calculator Keystrokes N Number of compounding periods I Periodic interest rate PV Lump sum amount invested at time 0 in real estate the required cash down payment PMT Periodic level payment or receipt a fixed monthly mortgage payment FV Lump sum cash flow or future value of an investment Compounding Operations interest There are two types Compounding means the investor earns interest on the principal plus interest on the accumulated 1 Future Value of a Lump Sum o Investor invests 1 000 today o 5 interest compounded annually o Investor expects to withdraw in 5 years o How much will the investor withdraw 5 years from now N 5 ANSWER FV 1 276 28 I 5 PV 1 000 PMT 0 Note The average amount of annual interest increases as the length of time increases 2 Future Value of Annuity o Investor plans to deposit 1 000 at the end of each year o 5 interest compounded annually o 5 years o How much will these deposits be worth 5 years from now o Now assume the investor makes monthly deposits N 5 ANSWER FV 5 525 63 I 5 PV 0 PMT 1 000 N 12 months 5 years 60 I 5 12 months 0 42 PV 0 PMT 1 000 12 83 33 ANSWER FV 5 666 95 Note The more frequently you compound the greater the FV Discounting Operations Used to convert future cash flow amounts into present values There are two types 1 Present Value of a Lump Sum o Investment expected to provide a 1 276 28 inflow o Occur at the end of 5 years o 5 interest compounded annually discount rate N 5 ANSWER PV 1 000 I 5 PMT 0 FV 1 276 28 Note The 5 discount rate is viewed as an opportunity cost or the return an investor is foregoing on an alternative investment in order to invest in the current opportunity 2 Present Value of Annuity o Receive 1 276 28 at the end of every year o 5 years o Investors require 5 return o What is the maximum you re willing to pay for this annuity N 5 ANSWER PV 5 525 62 I 5 PMT 1 276 28 FV 0 Important Points o PV of future cash flows is inversely related to the discount rate o When the discount rate is lower PV is higher o When the discount rate is higher PV is lower o PV of long term cash flows is more sensitive to changes in the discount rate than securities with shorter term cash flows Expected cash flows from direct investments in commercial property typically come from two Commercial Property things 1 Rental Properties 2 Eventual sale of property Value and Risk The lowest risk level in real estate is investment properties involving financially strong tenants committed to a long term net lease Net Lease Type of lease where occupants of a large building pay their own operating expenses Raw land holds the greatest uncertainty of future income because its value is dependent on future urban growth to create market potential Industrial properties such as warehouses have relatively reliable cash flows Multifamily properties also referred to as normal properties have steady cash flows Office property markets are cyclical creating volatility in rental rate growth Hospitality property holds the greatest uncertainty in terms of cash flows mainly because of the high levels of competition in the market Determining Required Returns Even small changes in the assumed discount rate can significantly affect estimated PV of risky cash flows Discount rates initiate from the capital market where investors buy and sell assets The risk free rate Rf plus the risk premium RP Investors Required Return IRR Rf RP Investment Values vs Acquisition Costs Net Present Value NPV value of cash outflows Compares the costs and benefits of investment opportunities Investment Yield IRR Growth in the invested dollars of an investment Difference between the present value of cash inflows and present o Note If NPV 0 property should be purchased If NPV 0 property should be rejected If NPV 0 investor is indifferent Chapter 7 Valuation Using Sales Comparison Cost Approaches Appraisal Subject Property Appraisal Report Property of interest in an appraisal Document that appraiser submits to their client Unbiased written estimate of the market value of a property o Contains appraisers final estimate of value o Date upon which the estimate is based o Reasoning and calculations used to arrive at the estimate Market Value Investment Value and Transaction Prices Market Value Most probable selling price assuming a normal sale occurs o Value the typical participant would place on a property o It derives from the result of supply demand o In a perfectly competitive market market value transaction price Investment Value Value that a particular investor places on a property o Based on expectations of individual investors not the market itself o Buyer s investment value is the maximum he would be willing to pay o Seller s investment value is the minimum