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GSU FI 3300 - Fi3300_Chapter06

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2/19/20101FI3300Corporate Finance 010Spring Semester 2010Dr. Isabel TkatchAssistant Professor of Finance1NY Times Article - detailsIt was April 2006, a moment when the perpetual rise of real estate was considered practically a law of physics. Mr. Koellmann was 23, a management consultant new to Miami. Financially cautious by nature, he bought a small, plain one-bedroom apartment for $215,000, much less than his agent told him he could afford. He put down 20 percent and received a fixed-rate 2ffpp floan from Countrywide Financial.Not quite four years later, apartments in the building are selling in foreclosure for $90,000.“There is no financial sense in staying,” Mr. Koellmann said. With the $1,500 he is paying each month for his mortgage, taxes and insurance, he could rent a nicer place on the beach, one with a gym, security and valet parking.NY Times Article - questions1) Write down the transaction on April 2006 (buying the condo) as a balance sheet: point out the assets, liabilities and equity and their value.2) Assuming that by February 2010 Benjamin Koellmann paid 16% of the principal and the value of the condo does not change ($215,000); write down the same balance sheet for February 3($ , ); m f y2010. What is the value of equity?3) 3. Assuming that by February 2010 Benjamin Koellmann paid 16% of the principal and the value of the condo is marked-to-market ($90,000); write down the same balance sheet for February 2010. What is the value of equity?4) 4. How should we determine the financial value of the condo? How is the monthly CF of $1,500 related to this value?Where are we?FI 3300: Corporate FinanceAccounting Review (2) Firm’s Financial StatementsValuationTime Value of Money (6, 7)4Statement of Cash Flows (3)Financial statement Analysis (4)Strategic Financial Management (5)Financial Securities & Markets (8)Valuation of Bond & Stock (9)Capital Budgeting Basics (10)Capital Budgeting Advanced (11)Learning objectives☺ Present the Time Value of Money (TVM) concept☺ Define and demonstrate compounding and discounting☺ Define and describe each variable in the Present-Value Future-Value (PV-FV) equation and use it to l f5solve for:☺ The PV if the interest rate (r) and the FV are known☺ The FV if the interest rate (r) and the PV are known☺ The interest rate (r) if the PV and FV are known☺ Present the value additivity principal and use it to solve multi-period valuation problemsPreferences: assumption 1Magnitude: investors prefer to have more money rather than less:$100 are “better” than $806$100 are better than $80Value($100 today) > Value($80 today)2/19/20102Preferences: assumption 2Timing: investors prefer to get the money today rather than the same sum in the future:$100 now are “better” than $100 one year from now7$$yValue ($100 today) > Value ($100 one year from now)Why? 1. Positive rate of return on investment2. Option valueTime Value of Money - implicationsIfValue ($100 today) > Value ($100 one year from now)ThenValue ($100 today) + Value ($100 one year from now)8≠ Value ($200 today)Note: if we set Value ($100 today) = $100then Value ($100 one year from now) < $100We need a common basis to compare (or add)cash flows (CFs) received in different points in timeTime Value of Money: basicsDeposit: $100 in a savings account todayThe annual interest rate: r = 10%How much will you get one year from now?100 110+10 =9Principal Future Value+Interest=100 110+100(0.1)=100110x(1+0.10) =Time Value of Money: basicsHow much will you get in two years?Date t=0: deposit $100 for one year, r=10%Date t=1: get principal + interest$100+$10 = $100 x ( 1 + 0.1 ) = $11010deposit $110 for another yearDate t=2: get principal + compounded interest$110 x ( 1 + 0.1 ) = $121Summary:$100 x ( 1 + 0.1 ) x ( 1 + 0.1 ) = $100 x ( 1 + 0.1 )2= $121Compounding$100 FV|--------|-----> t r = 10% FV = $100 μ (1+0.1)1= $1100 1$100 FV2|--------|--------|---> t r = 10% FV = $100 μ (1+0.1)2= $1210 1 2PV FV|--------|--------|-----------|---> t FV = PV μ (1 + r)T0 1 2 … T11Present Value - Future Value FormulaFV PV ( 1 )TFV = Future ValueT = number of periods12FV = PV x ( 1 + r )TPV = Present Valuer = interest rate for one period2/19/20103Time Value of Money - CompoundingStarting point: CF in the present, say PV=$100Annual interest rate: r > 0, say r=10%Wanted: CF’s value on date T in the future, T=1213PV FV|--------|--------|-----------|---> t0 1 2 … T$100 FV=?|--------|--------|-----------|---> t0 1 2 … 1212(1100 (1 0.1))TFFVVPV r=×+=×+Time Value of Money - DiscountingStarting point: CF in the future: FV=$100, T=12Annual interest rate: r > 0, say r=10%Wanted: CF’s value in the present (today)14PV FV|--------|--------|------------|---> t0 1 2 … TPV =? $100|--------|--------|------------|---> t0 1 2 … 1212100(11.)01()TPPVFVVr=+=+DiscountingPV $100|--------|-----> t r = 10%0 1PV $100|||>t 10%()1100$90.911.1100PV =≅|--------|--------|-----> t r = 10%0 1 2PV FV|--------|--------|------------|---> t0 1 2 … T()2100$82.64(1 )1.1TFVPrVPV =+≅=15Note that:The interest rate r is always positive:r > 0(1 + r) is always greater than one:(1 ) 116(1+r) > 11/(1 + r) is always less than one:1/(1+r) < 1The PV of a CF is always less than its FV:PV(CF) < FV(CF)The Future Value and r$100 FV|-------------------------|-------------> time0 1FV = PV x (1+r)17r = 5% FV = $100x1.05 = $105r = 10% FV = $100x1.10 = $110r = 20% FV = $100x1.20 = $120r = 50% FV = $100x1.50 = $150If T and the PV are fixed (T=1, PV=$100) thenAs r (↑) increases the FV (↑) decreasesThe Present Value and rPV $100|-------------------------|-------------> time0 1PV = FV / (1+r)18r = 5% PV = $100/1.05 =r = 10% PV = $100/1.10 = r = 20% PV = $100/1.20 =r = 50% PV = $100/1.50 =2/19/20104The Present Value and rPV FV=$100|-------------------------|-------------> time0 1r = 5% FV = $100 = $95.24x1.05 10%FV $100 $90 9111019r = 10%FV = $100 = $90.91x1.10r = 20% FV = $100 = $83.33x1.20r = 50% FV = $100 = $66.67x1.50If T and the FV are fixed (T=1, FV=$100) thenAs r (↑) increases the PV (↓) decreasesThe Present Value and TimePV


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