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Chapter 14 - 2011

Course: FINANCE 370, Spring 2012
School: Western Kentucky...
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Effects Chapter14 The of Time and Risk on Value McGrawHill/Irwin Copyright2010byTheMcGrawHillCompanies,Inc.Allrightsreserved. Value:TheCentralIdea Investment Value: Maximum price an investor is willing to pay for ownership interest in real property or mortgages. Real estate valuation: Estimate all future net cash flows Convert into estimate of present value How are investment decisions made? By comparing estimate of present value to acquisition cost 14-2 ValueDependson? Value of a property or mortgage thus depends on: magnitude of expected cash flows timing of expected cash flows riskiness of expected cash flows 14-3 EffectofTimingonValue? Why cant we simply add up the future cash flows to find their value? 14-4 EffectofRiskonValue For which investment would you pay the most? Why? 60,000 B A 50,000 0 0 3 Outcome = $50,000 with certainty. 0 3 40,000 3 Outcome = $60,000 or $40,000 with even chance. 14-5 ValuationRequirestheUseofTimeValue ofMoneyOperations Compounding Operations Future value of a lump sum Future value of an annuity Discounting Operations Present value of a lump sum Present value of an annuity 14-6 HowMoneyWorks: RemembertheCompoundingProcess 0 1 2 3 4 Year Beginning Amount Interest (10%) Ending Amount 1 100 10.00 110.00 2 110 11.00 121.00 3 121 12.10 133.10 4 133.10 13.31 146.41 14-7 WhyDoesTimeAffectValue? $100 $100 A B 0 1 2 3 4 Why is cash flow A worth more than cash flow B? If cash flow A can be invested to yield 10% per year, how much is cash flow B worth? 14-8 WhyDoesTimeAffectValue? $100 $100 A C 0 1 2 3 4 If cash flow A can be invested to yield 10% per year during years 1 & 2, how much is cash flow C worth at time 0? 14-9 DiscountingBringsFutureValuesBack DowntheCompoundingCurve Compounding Discounting A Year 0 C 1 2 3 4 14-10 TerminologyofTimeValue Present Value (PV): An amount at time point 0 Future Value (FV): A single cash flow at any future time point Payment (PMT): A repeating amount of cash flow normally begins at time point 1, sometimes at time point 0 Ordinary annuity (A): Earlier name for Pmt Lump sum: Any future cash inflow or outflow occurring only once 14-11 TheMathofCompounding Year 1 2 3 4 5 $1.00 x (1.05) = $1.05 $1.05 x (1.05) = $1.1025 $1.1025 x (1.05) = $1.1577 $1.1577 x (1.05) = $1.2155 $1.2155 x (1.05) = $1.27628 or (1.05)5 = $1.27628 14-12 TheKeystrokes 5 5 1,000 0 nn ii PV PV Pmt Pmt FV FV $1,276.28 14-13 CompoundingExample:5Yearsat10%per Year Initial Deposit (PV): $1,000 Compounding Process per $ Starting Ending Year Amount Interest Amount 1 $1.00 + $0.10 = $1.10 2 $1.10 + $0.11 = $1.21 3 $1.21 + $0.121 = $1.331 4 $1.331 + $0.1331 = $1.4641 5 $1.4641 + $0.1464 = $1.6105 Ending amount (FV): $1,000 x 1.6105 = $1,610.50 14-14 TheKeystrokes 5 10 1,000 0 nn ii PV PV Pmt Pmt FV FV $1,610.50 14-15 AccumulatedValueofaSeriesofDeposits (withCompounding) Deposits: $1,000 at the end of each year Interest rate: 5% Deposit Year 1 1 2 3 4 5 $1,000 $1,050 $1,102.50 $1,157.63 $1,215.51 2 3 4 5 Sum $1,000.00 End of 1,000 $2,050.00 Year 1,050 1,000 Amount $3,152.50 1,102.50 1,050 1,000 $4,310.13 1,157.63 1,102.50 1,050 1,000 $5,525.63 14-16 TheKeystrokes 5 5 0 1,000 nn ii PV PV Pmt Pmt FV FV $5,525.63 How would you find the accumulated value of a monthly deposit of 83.33 ($1,000/12) for 5 years, compounding monthly at 5%? 60 nn 5/12 ii 0 PV PV 83.33 Pmt Pmt FV FV $5,666.95 14-17 AccumulatedValueofanAnnuityDue Deposits: $1,000 at the beginning of each year Interest rate: 5% Deposit Year 1 1 2 3 4 5 $1,050 $1,102.50 $1,157.63 $1,215.51 $1,276.28 2 3 4 5 Sum End of $1,050.00 1,050 $2,152.50 Year Amount $3,310.13 1,102.50 1,050 1,157.63 1,102.50 1,050 $4,310.13 1,215.51 1,157.63 1,102.50 1,050 $5,801.91 14-18 RepeatKeystrokes,withCalculatorinBegin Mode 5 5 0 1,000 nn ii PV PV Pmt Pmt FV FV $5,801.91 Begin Mode 14-19 WhatWillBetheFutureValueofYour 401(k)? Deposit $1,000 per year beginning at age 25 Future Value It Could Really Happen, at 8% , But Don't Forget About Inflation! $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 14-20 TheKeystrokes n 8 0 nn ii PV PV -1,000 Pmt Pmt FV FV ? 14-21 WhatWillBetheFutureValueofYour 401(k)? Deposit $1,000 per year beginning at age 25 This Could Happen, at 10% , But Remember Inflation! F u tu re Valu e $500,000 $400,000 $300,000 $200,000 $100,000 $0 1 5 9 13 17 21 25 29 33 37 14-22 Discounting,Again $1,276.28 $1,000 At 5%, $1,000 compounds in 5 years to $1,276.28 ? 0 1 2 3 4 5 $1,276.28 What amount received now is equivalent to the future $1,276.28? ? 0 1 2 3 4 5 14-23 TheMathofPresentValue 1 2 3 4 5 1.00 (1.05) 0.95238 (1.05) 0.90703 (1.05) 0.86384 (1.05) 0.82270 (1.05) or 1/(1.05)5 = 0.95238 = 0.907029 = 0.863838 = 0.82270 = 0.783526 = 0.783526 PV of $1,276.28, five years from now, discounted at 5%: PV = $1,276.28 x 0.78526 = $1,000.00 14-24 TheKeystrokes $1,276.28 ? 0 1 2 5 ii 0 5 nn 3 PV PV 4 5 $1276.28 Pmt Pmt FV FV $1,000 Q: Would investors who want a 5 percent return favor: A. $1,000 now? B. $1,276.28 in five years? Q: What if they could buy the future $1,276.28: A. For $900? B. For $1,100? 14-25 PracticeProblem You have been offered an investment opportunity that is expected to generate at $4,000 the end of 3 years. Assume you can earn 10% on investments of this type. What is the most you should be willing to pay today? PV = FV x PVF (10%, 3 years) = $4,000 x 0.751315 = $3,005 Keystrokes: 3 nn 10 ii 0 PV PV Pmt Pmt $4,000 FV FV $3,005 14-26 PresentValueofanAnnuity $1,276.28 $1,276.28 1,215.50 1,000.00 ? Year Payment Year 1 2 3 4 5 0 1 Payment $1,276.28 $1,276.28 $1,276.28 $1,276.28 $1,276.28 2 3 4 Present Value Factor (1.05) = (1.05)2 = (1.05)3 = (1.05)4 = (1.05)5 = Sum = 5 Present Value $1,215.50 $1,157.62 $1,102.50 $1,050.00 $1,000.00 $5,525.62 14-27 TheKeystrokes $1,276.28 $1,276.28 1,215.50 1,000.00 ? 0 1 2 5 5 nn ii 3 4 5 1,276.28 0 Pmt Pmt FV FV PV PV $5,525.62 14-28 PracticeProblem What is the value of a 20 year (net) lease that pays $5,000 per year if you discount at 10 percent? PVA = Annuity x PVFA (10%, 20 years) = $5,000 x 8.513564 = $42,568 Keystrokes: 20 nn 10 ii $5,000 PV PV Pmt Pmt $0 FV FV $42,568 14-29 PracticeProblem What is the present value of $4,000 at the end of each year for 4 years if your opportunity cost is 10%? PVA = Annuity x PVFA (10%, 4 years) = $4,000 x 3.169865 = $12,679 Keystrokes: 4 nn 10 ii $4,000 PV PV $0 Pmt Pmt FV FV $12,679 14-30 PracticeProblem If I promise to pay $4,000 a year for 30 yrs, and you are a lender who expects a 10% return, what is maximum amount that you would loan me today? Loan = PMT x PVFATF (10%, 30 years) = 4,000 x 9.426914 = $37,707.65 or $37,708 Keystrokes: 30 nn 10 ii $4,000 PV PV Pmt Pmt $0 FV FV $37,708 14-31 ARealEstateApplicationofTimeValue Solutions: 1. Find the PVs of six different cash flows and sum the results. 2. PV of a five-year annuity + PV of a lump sum in year 5. $100,000 3. Solve as a combined PV problem. $10,000 0 1 2 3 4 5 14-32 TheKeystrokes 5 10 nn $10,000 $100,000 ii PV PV Pmt Pmt FV FV $100,000 $100,000 $10,000 0 1 2 3 4 5 14-33 ValuingaPropertywithUnevenCashFlows: LeeVista $560,000 Solutions: 1. Find the PVs of six different cash flows and sum the results 2. Use the variable cash flow capacity of your calculator 3. Spreadsheet (See Chapter Appendix) 50,923 52,451 54,025 48,000 49,440 0 1 2 3 4 5 14-34 CalculatorSolutionforUnevenCashFlows: LeeVista 1. Set calculator for one payment per year 2. Clear calculator 3. Enter zero for initial cash outlay: 0 CF CF 4. Enter first-year cash flow: 48000 CF CF 5. Repeat for years 2 through 4 6. Enter sum of year 6 C.F. plus reversion: j j 54025 + 560000 = 614025 7. Enter discount rate: 14 8. Find PV: NPV NPV Solution: $464,479.86 $560,000 j j CFj CFj ii 0 49,440 50,923 48,000 1 2 52,451 3 4 54,025 5 14-35 LongerMaturityMakesPVMoreSensitive totheDiscountRate Present Value of $1,000 Exhibit 14-9: 1200 1000 800 600 400 200 0 PV of $1,000 Lump Sum Payment $784 $621 $481 PV @ 5% PV @ 10% $239 1 3 5 7 9 11 13 15 17 19 21 Year in w hich $1,000 is received 14-36 Yield/InternalRateofReturn Purchased for $95,000: 5 $95,000 $10,000 $100,000 nn ii PV PV Pmt Pmt $100,000 FV FV 11.37 Purchased for $105,000: 5 nn $105,000 $10,000 $100,000 ii PV PV Pmt Pmt 8.72 FV FV $10,000 0 1 2 3 4 5 14-37 Yield/IRRDependsontheSellingPrice Purchase for $100,000 and sell for $90,000: 5 -$100,000 $10,000 $90,000 nn ii PV PV Pmt Pmt $100,000 FV FV 8.31 Purchase for $100,000 and sell for $110,000: 5 nn -$100,000 $10,000 $110,000 ii PV PV Pmt Pmt FV FV $10,000 11.59 0 1 2 3 4 5 14-38 RequiredYieldAffectsValue:TheCaseof LeeVista 560,000 At a required yield (discount rate) of 14%, the value of Lee Vista was $464,480. Question: What is its value at these required yields? 10 percent? $539,841 12 percent? $500,264 16 percent? $432,059 48,000 49,440 18 percent? $402,628 0 1 2 50,923 52,451 54,025 3 4 5 14-39 TheSpectrumofRiskinInvestments 14-40 InformationonRequiredYields/IRRs Many real estate investors think of required yields as composed of two parts: E(Rj) = Rf + RPj Rf is a relevant rate free of default risk (commonly the Ten-year U.S. Treasury rate) RPj is risk premium for a particular property. 14-41 InformationonRequiredYields/IRRs Since risk premiums vary, so do required yields. High quality, safe real estate investments: 10% or less Development: 30% or more 14-42 RepresentativeRequiredYieldsfor InstitutionalGradeRealEstate Exhibit 14-12 Required Returns on Investment-Grade Properties vs. Comparable Treasury Securities: 19952008 1Q97 RequiredReal EstateReturn Return on 10year Treasuries Spread over Treasuries 1Q99 1Q01 1Q03 1Q05 1Q07 4Q08 11.5% 11.4% 11.5% 11.2% 9.6% 8.4% 8.9% 6.6% 5.0% 5.1% 3.9% 4.3% 4.7% 3.5% 4.9% 6.4% 6.4% 7.3% 5.3% 3.7% 5.4% Source: Real Estate Research Corporation, Chicago, Ill. www.rerc.com Note that Gatorlink users have access to this website: Username: uflorida Password: gators 14-43 LeeVistavs.ColonyPark Colony Park Lee Vista $597,000 $560,000 52,451 57,400 58,835 60,306 54,025 56,000 49,440 50,923 48,000 0 1 2 3 4 5 0 1 2 3 4 61,814 5 14-44 ComparingInvestmentswithNPV If an investor requires a yield of 14%, can one determine which is the better investment? Is further information needed? Price: $425,000 NPV = Value Price = $464,480 425,000 = $39,480 Price: $540,000 NPV = Value Price = $510,875 540,000 = $29,125 14-45 End of Chapter 14

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