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# 270 Note for B A 301 with Professor Gray at PSU

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Date Created: 02/06/15

BA 301 Discounted Cash Flow Valuation Woolridge amp Gray Text Chapter 10 Discounted Cash Flow Valuation Chapter Objectives Learn to calculate future and present value of level cash flow streams and uneven cash flow streams Learn to calculate loan payments effective interest rates and amortization schedules Learn to value stocks and bonds using the DCF approach Discounted Cash Flow Valuation Chapter Overview 101 Introduction to DCF Valuation 102Valuing Level Cash Flows 103Vauing Uneven Cash Flows 104 Summary Introduction to DCF Valuation I DCF determines the value of an investment I The markets determine the Qrice of an investment I You decide based on price or cost if the investment is undervalued overvalued or fairlyvalued I Your buysell decision should be based solely on price versus value Introduction to DCF Valuation Definitions The value of an investment stock bond mortgage etc equals the present value of its expected cash ows discounted reduced for their risk and timing I Expected cash ows are the most likely cash payments dividends interest capital gain or loss that you can expect not hope to receive Introduction to DCF Valuation Definitions uquot VV V I Discount multiply a number by less than one I Discount rate a function of time and risk discount rate f time risk I Discount factor a function of both time and the discount rate discount factor f time discount rate I Present value PV of an investment is the sum of the expected cash ows multiplied by their respective discount factors Introduction to DCF Valuation Loans I Level cash ows the interest rate and cash ows associated with the loans mortgages and annuities are xed and do not change I A loan is an obligation under which a person borrows money from a lender I Terms of the loan state an interest rate and a repayment or amortization schedule Introduction to DCF Valuation Mortgages I Home mortgage an obligation under which a person borrows money from a bank and uses the proceeds to purchase a house or condominium I Amortization schedule Level payments over a long time period usually 20 to 30 years Introduction to DCF Valuation Annuities I A life annuity is contract sold by pension funds and life insurance companies I Pays a speci ed amount of money per year to owner I Amortization schedule more complex than loans or mortgage I Investor makes a single payment or multiple payments then Withdraws funds upon her retirement Introduction to DCF Valuation Mortgage Example Table 97 Gary borrows 100000 from a bank at 8 and 25 year mortgage What is his annual payment 39 Calculator n 25 years PV 100000 r or i 8 FV 0 Solve for PMT 936788 39Using Tables PV PMT PVMP Factor 25 8 39100000 PMT 106748 39100000106748 PMT 39PMT 9368year ITotal Payments 25 9368 234197 39Interest 134197 Principal Repayment 100000 Introduction to DCF Valuation Mortgage EX Rates up 2 to 10 Interest rates on mortgages increase by 2 to 10 What is Gary s annual payment on a 10 loan 39 Calculator n 25 years PV 100000 r or i 10 FV 0 Solve for PMT 1101680 39Using Tables PV PMT PVMP Factor 25 10 39100000 PMT 90770 3910000090770 PMT 39PMT 10608year ITotal Payments 25 10608 265200 39Interest 165200 Principal Repayment 100000 Introduction to DCF Valuation Mortgage EXRates drop 2 to 6 If interest rates on mortgages decrease by 2 to 6 What is Gary s annual payment on a 6 loan 39 Calculator n 25 years PV 100000 r or i 6 FV 0 Solve for PMT 782267 39Using Tables PV PMT PVMP Factor 25 6 39100000 PMT 127834 39100000127834 PMT 39PMT 7823year ITotal Payments 25 7823 195567 39Interest 95567 Principal Repayment 100000 Introduction to DCF Valuation The ThreeStep Approach 1 Develop a set of expected cash ows 2 Estimate the discount rate and calculate the discount factors 3 Multiply the cash ows by the discount factors and add them to determine the value of the asset Decision Rule I If the value of an asset is greater than its price Buy it I If the value is less than its price Sell it Valuing Level Cash Flows Amortizing a Loan I Example Randy likes fast women Budweiser and expensive cars He wants to buy a BMW for 50000 He can nance it with a bank loan at 10 for 4 years His annual payment is 15774 What is his amortization schedule Interest Rate 1000 Discount Rate 1000 Beginning Interest Principal Annual Discount Ending Year Princial Pament Pament Pament Factor DCF Princial 50000 5000 10774 15774 09091 14340 39226 39226 3923 11851 15774 08264 13036 27375 27375 2737 13037 15774 07513 11851 14338 14338 1434 14340 15774 0683 10774 13094 50002 63096 50001 Valuing Level Cash Flows Spreadsheet An Excel Spreadsheet makes the DCF calculation easy Assume interest rates on similar car loans increase to 11 What s Randy s 10 loan now worth I Discount the cash ows now at 11 Plug 11 into the discount rate slot and the DCF value of Randy s 50000 car loan is 48938 Interest Rate 1000 Discount Rate 1100 Beginning Interest Principal Annual Discount Ending Year Princial Pament Pament Pament Factor DCF Princial 50000 5000 10774 15774 09009 14211 39226 39226 3923 11851 15774 08116 12803 27375 27375 2737 13037 15774 07312 11534 14338 14338 1434 14340 15774 06587 10391 1 3 094 50 002 63 096 48 938 Valuing Level Cash Flows Calculator I Using a nancial calculator for PV Five nancial function keys n number of periods r or i interest rate or yield PV present value PMT payment and FV future value I Randy s Car Loan Valuing a fouryear 10 loan with a payment of 1577354 discounted 11 I Inputs are n 4 i 11 FV 0 PMT 1577354 solve for PV which is equal to 4893655 Valuing Uneven Cash FlowsProjects Most real world investments such as projects stocks and bonds do not have a single cash ow or level expected cash ows A groiect or venture is an investment to produce a product or provide a service that Will generate money in the future Cash In ow additional revenues coming into the company as a result of the project Cash Out ow additional expenses being spent by the company as a result of the project Valuing Uneven Cash Flows Bonds A bond is a debt instrument Corporations the US Government and municipalities issue bonds Bonds are payable from taxes from US government or the general revenues of a corporation Cash in ows to an investor are bond interest payments usually every 6 months and repayment of principal Valuing Uneven Cash FlowsStocks A stock represents ownership interest in a corporation The cash in ows consist of dividends and increase or decrease in stock price There is no maturity associated With a stock n the life of a stock is in nite The risk of a stock is hard to quantify making it dif cult to determine the proper discounting rate Valuing Uneven Cash Flows Using a Calculator Most popular nancial calculators have their own speci c systems for entering uneven sequential cash ows and then discounting those cash ows at a uniform discount rate 39 HPl 01311 model 39First input the initial cash out ow or cost in CFj button 39Then input the subsequent cash ows one at a time in CFj button 39Then hit the gold button and NPV for the answer 39Refer to pages 8082 of Instruction Book TI BAII owners referto pages 4149 of Instruction Book Valuingjln ws of a Pro j ect 39 eet New Bill wants t E IIHChmEITm production ncrease paper r year initially r quot for the project is 2500000 of quot ense of the a rate of 6 per r rate of 4 per years and have no year and th year The n1 salvage val Projects of 1 rate of 14 How much 39 103 Valuing Uneven Cash Flows Using a Spreadsheet Lemont Paper Project M 1 39 Discount Rate 1 4 Cash Cash Net Cash Discount Year Inflow Outflow Flow Factor DCF 1 3000 2600 400 08772 351 3180 2704 476 07695 366 3 3 371 2812 559 0675 377 4 3 573 2925 648 05921 384 5 3787 3042 746 05194 387 6 4015 3163 851 04556 388 7 4256 3290 966 03996 386 8 4511 3421 1089 03506 5 735 Valuing Uneven Cash Flows of a Bond Using a Spreadsheet Assume that the US Government has issued a Bond with an 8 interest rate ve years to the maturity of the Bond and a principal payment of 1000 The Bond pays interest in the amount of 40 dollars equal to 1000 8 12 year two times per year April 1 and October 1 plus the 1000 repayment of the principal at maturity Also assume that the interest rate associated with this type of bond has increased to 10 in today s market What is the current value of this 8 Bond Valuing Uneven Cash Flows of a ngd Using a Spreadsheet KN 1 Semi Annual Rate Vquot Cash Discount Flow Factor 40 09524 40 0907 40 08638 40 08227 40 07835 40 07462 40 07107 40 06768 40 06446 06139 140000 Valuing Uneven Cash Flows of a Stock Using a Spreadsheet Valuing a stock involves the same analysis as valuing a xedrate mortgage loan or the US Government Bond However in estimating future cash ows there are two important exceptions The Bond and the mortgage have cash ows that are known with certainty while the range of future cash ows for a stock can be enormous Common stock represents ownership in a corporation which has an in nite life unlike bonds and mortgages luerZ nZ VPznn wa a m VaMePrn wmuw He s ValuanonDate 03242005 Valuel m 2002 General Invut Screen Intrinsic Stuck Value 5929 General Inputs Company Twcker ABC Cam Excess Return Permd vears m Deprematxon Rate u of Rev 7 2D Revenues m mam nvestment Rate u of Rev 2U ED Grawth Rate 2 3 u Workmg Capna u of Rev 7 2D Net Operatmg Pro t Margm Us 26 00 SwanTerm Assets 53m 0 Tax Rate 73 3 W ShomTerm Labhtesm 0 Stock Prwcew 47 75 Eqmtv Rwsk Premmm Va 3mm Shares Outstandmg m 594 E Companv Beta U 76 torvearTreasunme quot73 5 92 Vaue of Debt Out mH 4931 300d Spread 10 TFQSSLW 2 W Vaue of Pref Stock Out WM 368 Preferred Stock em 9 750 CompaanACC a 773 g ralueero zooz rezooznwe 7 3 File Edit Irtc39rluePro Window Help Valuation Date 5312412555 ValuePro 2002 General Pro Forma Screen IIIveer Excess Return Period ABC Corp Disc Excess Return Period FCFF 5527 Total Corporate Value 45455 Discounted Residual Value 35543 Less Debt 4531 ShortTerm Assets 555 Less Preferred Stock 355 Total Corporate Value 45455 Less ShortTerm Liabilities 55 Total Value to Common Equity 41155 Intrinsic Stock Value 5525 121 131 141 151 151 17 13 191 1101 1111 1121 1131 Chanqein 12 Months Adj Change in Working Discount Discounted Endino Revenues NOR Taxes NDPAT invest Deorec Invest Canital Factor FCFF 5312412555 1555 5312412555 12575 3145 515 2153 2455 555 1 515 139139 55253 521 531241255 13545 3545 1 153 2445 54 5312412555 15425 4555 124 2152 I I 514 5312412555 11425 4535 1 455 3121 552 5312412515 15555 5115 1552 3527 A 39 I I 531 5312412511 22255 5255 1 155 3555 552 5312412512 25142 5537 2533 4554 I I I I 1 39 39 555 5312412513 2541 1 135 225 5555 125 5312412514 32154 5342 2555 5151 154 5312412515 35 275 5432 2533 5455 1413 2512 4551 55 1 555 54755 552 35275 5432 2533 5455 2512 2512 5 5 54555 54755 35543

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