ࡱ> pro[ Kbjbj ,zjj@3lV"""8ZnV<  (6 6 6 ":I#\#0s<u<u<u<u<u<u<$= ?<#!@"##<(6 6 <(((#R6 6 s<(#s<(T(30r;T";6  =5/V"$k;;<0<y;V@;&V@;(.|Chapter 6 DISCOUNTED CASH FLOW VALUATION SLIDES  SLIDES CONTINUED CASES The following cases from Cases in Finance by DeMello can be used to illustrate the concepts in this chapter. Lottery Disbursement Retirement Planning Loan Amortization CHAPTER WEB SITES SectionWeb Address6.2www.collegeboard.orgwww.1stmortgagedirectory.compersonal.fidelity.comwww.datachimp.com6.3www.cmbmortgage.comEnd-of-chapter materialwww.stls.frb.orgwww.fincalc.com www.fcfcorp.com/onlinecalc.htm CHAPTER ORGANIZATION Future and Present Values of Multiple Cash Flows Future Value with Multiple Cash Flows Present Value with Multiple Cash Flows A Note on Cash Flow Timing Valuing Level Cash Flows: Annuities and Perpetuities Present Value for Annuity Cash Flows Future Value for Annuities A Note on Annuities Due Perpetuities Comparing Rates: The Effect of Compounding Periods Effective Annual Rates and Compounding Calculating and Comparing Effective Annual Rates EARs and APRs Taking It To The Limit: A Note on Continuous Compounding Loan Types and Loan Amortization Pure Discount Loans Interest-Only Loans Amortized Loans 6.5 Summary and Conclusions ANNOTATED CHAPTER OUTLINE Slide 6.1 Key Concepts and Skills Slide 6.2 Chapter Outline Future and Present Values of Multiple Cash Flows Future Value with Multiple Cash Flows There are two ways to calculate future value of multiple cash flows: compound the accumulated balance forward one period at a time, or calculate the future value of each cash flow and add them up. Slide 6.3 Multiple Cash Flows Future Value Example 6.1 Slide 6.4 Multiple Cash Flows FV Example 2 Slide 6.5 Multiple Cash Flows Example 2 Continued Slide 6.6 Multiple Cash Flows FV Example 3 Present Value with Multiple Cash Flows There are two ways to calculate the present value of multiple cash flows: discount the last amount back one period and add them up as you go, or discount each amount to time zero and then add them up. Slide 6.7 Multiple Cash Flows Present Value Example 6.3 Slide 6.8 Example 6.3 Timeline Slide 6.9 Multiple Cash Flows Using a Spreadsheet Lecture Tip, page 164: The present value of a series of cash flows depends heavily on the choice of discount rate. You can easily illustrate this dependence in the spreadsheet in Slide 6.9 by changing the cell that contains the discount rate. A separate worksheet on the slide provides a graph of the relationship between PV and the discount rate. A Note on Cash Flow Timing In general, we assume that cash flows occur at the end of each time period. This assumption is implicit in the ordinary annuity formulas presented. Slide 6.10 Multiple Cash Flows PV Another Example Slide 6.11 Multiple Uneven Cash Flows Using the Calculator Slide 6.12 Decisions, Decisions Slide 6.13 Saving for Retirement Slide 6.14 Saving for Retirement Timeline Slide 6.15 Quick Quiz Part I Valuing Level Cash Flows: Annuities and Perpetuities Slide 6.16 Annuities and Perpetuities Defined Slide 6.17 Annuities and Perpetuities Basic Formulas Slide 6.18 Annuities and the Calculator Present Value for Annuity Cash Flows Ordinary Annuity multiple, identical cash flows occurring at the end of each period for a fixed number of periods. Lecture Tip, page 166: The annuity factor approach is a short-cut approach in the process of calculating the present value of multiple cash flows and that it is only applicable to a finite series of level cash flows. Financial calculators have reduced the need for annuity factors, but it may still be useful from a conceptual standpoint to show that the PVIFA is just the sum of the PVIFs across the same time period. The present value of an annuity of $C per period for t periods at r percent interest: PV = C[1 1/(1 + r)t] / r Example: If you are willing to make 36 monthly payments of $100 at 1.5% per month, what size loan can you obtain? PV = 100[1 1/(1.015)36] / .015 = 100(27.6607) = 2766.07 Or, use the calculator: PMT = -100; N = 36; I/Y = 1.5; CPT PV = 2766.07 (Remember that P/Y = 1 when using period rates.) Slide 6.19 Annuity Example 6.5 Slide 6.20 Annuity Sweepstakes Example Slide 6.21 Buying a House Slide 6.22 Buying a House Continued Slide 6.23 Annuities on the Spreadsheet - Example Slide 6.24 Quick Quiz Part II Lecture Tip, page 169: How could you answer the following questions without preparing an amortization table? You wish to purchase a $170,000 home. You are going to put 10% down, so the loan amount will be $153,000 at 7.75% APR (.6458333333% per month), with monthly payments for 30 years. How much will each payment be? How much interest will you pay over the life of the loan? How much is owed at the end of year 20? How much interest will be paid in year 20? Find the payment: PV = 153,000; N = 360; I/Y = 7.75/12; CPT PMT = 1096.11 Find the total interest cost: Interest paid = total payments principal = 360(1096.11) 153,000 = 241,599.60 Students are often amazed at how much interest is paid on a 30-year mortgage. The outstanding balance of the loan at any time equals the present value of the remaining payments. So, after 240 payments, the outstanding balance equals: PMT = -1096.11; N = 120; I/Y = 7.75/12; CPT PV = 91,334.41 Students are also surprised to find that after making 2/3 of the payments, 60% of the principal remains unpaid. The interest paid in any year is equal to the sum of the payments made during the year minus the change in principal. After 228 months (19 years), the outstanding loan balance is $97,161.79. The change in principal is 97,161.79 91,334.41 = 5,827.38. Total interest paid in year 20 = 12(1096.11) 5,827.38 = $7,325.94. Finding the payment, C, given PV, r and t PV = C[1 1/(1 + r)t] / r C = PV {r / [1 1/(1 + r)t]} Example: If you borrow $400, promising to repay in 4 monthly installments at 1% per month, how much are your payments? C = 400 {.01 / [1 1/(1.01)4]} = 400(.2563) = 102.51 Or, use the calculator: PV = 400; N = 4; I/Y = 1; CPT PMT = 102.51 Slide 6.25 Finding the Payment Slide 6.26 Finding the Payment on a Spreadsheet Finding the number of payments given PV, C and r PV = C [1 1/(1 + r)t] / r t = ln[1 / (1 rPV/C)] / ln(1 + r) Example: How many $100 payments will pay off a $5,000 loan at 1% per period? t = ln[(1 / 1 - .01(5,000)/100)] / ln(1.01) = 69.66 periods Or, use the calculator: PV = 5,000; PMT = -100; I/Y = 1; CPT N = 69.66 periods (remember the sign convention, you will receive an error if you dont enter either the PMT or the PV as negative) Slide 6.27 Finding the Number of Payments Example 6.6 Slide 6.28 Finding the Number of Payments Another Example Finding the rate given PV, C and t There is no analytical solution. Trial and error requires you to choose a discount rate, find the PV and compare to the actual PV. If the computed PV is too high, then choose a higher discount rate and repeat the process. If the computed PV is too low, then choose a lower discount rate and repeat the process. Or, you can use a financial calculator. Example: A finance company offers to loan you $1,000 today if you will make 48 monthly payments of $32.60. What rate is implicit in the loan? N = 48; PV = 1000; PMT = -32.60; CPT I/Y = 2% per month (Remember the sign convention.) Slide 6.29 Finding the Rate Slide 6.30 Annuity Finding the Rate Without a Financial Calculator Slide 6.31 Quick Quiz Part III Future Value for Annuities FV = C[(1 + r)t 1] / r Example: If you make 20 payments of $1000 at the end of each period at 10% per period, how much will your account grow to be? FV = 1,000[(1.1)20 1] / .1 = 1,000(57.275) = $57,275 Or, use the calculator: PMT = -1,000; N = 20; I/Y = 10; CPT FV = 57,275 (Remember to clear the registers before working each problem.) Slide 6.32 Future Values For Annuities A Note on Annuities Due Annuity due the first payment occurs at the beginning of the period instead of the end. Lecture Tip, page 173: It should be emphasized that annuity factor tables (and the annuity factors in the formulas) assumes that the first payment occurs one period from the present, with the final payment at the end of the annuitys life. If the first payment occurs at the beginning of the period, then FVs have one additional period for compounding and PVs have one less period to be discounted. Consequently, you can multiply both the future value and then present value by (1 + r) to account for the change in timing. This is the essence of an annuity due in the next section. Slide 6.33 Annuity Due Slide 6.34 Annuity Due Timeline Perpetuities Perpetuity series of level cash flows forever PV = C / r Preferred stock is a good example of a perpetuity. Slide 6.35 Perpetuity Example 6.7 Slide 6.36 Quick Quiz Part IV Slide 6.37 Work the Web Example Slide 6.38 Table 6.2 Comparing Rates: The Effect of Compounding Periods Effective Annual Rates and Compounding Stated or quoted interest rate rate before considering any compounding effects, such as 10% compounded quarterly Effective annual interest rate rate on an annual basis, that reflects compounding effects, e.g. 10% compounded quarterly has an effective rate of 10.38% Lecture Tip, page 176: It is important to stress that the effective annual rate is the rate of interest that we effectively earn after accounting for compounding. That seems simple enough, but students still have a hard time remembering that the EAR already accounts for all of the interest on interest during the year. It may be helpful to point out that the EAR is not used directly in time value of money calculations, except when we have annual periods. TVM calculations compound (or discount) the values every period, but the EAR has already done that. The EAR is primarily used for comparison purposes, not for calculation purposes. Slide 6.39 Effective Annual Rate (EAR) Calculating and Comparing Effective Annual Rates (EAR) EAR = [1 + (quoted rate)/m]m 1 where m is the number of periods per year Example: 18% compounded monthly is [1 + (.18/12)]12 1 = 19.56% Slide 6.40 Annual Percentage Rate Slide 6.41 Computing APRs Slide 6.42 Things to Remember Slide 6.43 Computing EARs Example Slide 6.44 EAR Formula Slide 6.45 Decisions, Decisions II Slide 6.46 Decisions, Decisions II Continued Lecture Tip, page 178: Heres a way to drive the point of this section home. Ask how many students have taken out a car loan. Now ask one of them what annual interest rate s/he is paying on the loan. Students will typically quote the loan in terms of the APR. Point out that, since payments are made monthly, the effective rate is actually more than the rate s/he just quoted, and demonstrate the calculation of the EAR. Slide 6.47 Computing APRs from EARs Slide 6.48 APR Example Slide 6.49 Computing Payments with APRs EARs and APRs Annual percentage rate (APR) = period rate times the number of compounding periods per year The quoted rate is the same as an APR. Lecture Tip, page 179: Why would credit card issuers reduce minimum required payments? So the average outstanding balance will increase, of course! Suppose Joe Borrower has a $5,000 balance on his Mastercard, which carries a 10.5% stated rate. A minimum monthly payment will require 91 months to pay off the card (assuming no additional borrowing). Increasing the payment to $200 will reduce the time to pay off the loan to 29 months. Ethics Note, page 179: Rent-to-own agreements and tax refund loans have a lot in common. Because of the structure of the contracts, they do not have to provide information on interest rates. However, when you work out the rates implied in the contracts, they can be extraordinarily high. It is worthwhile to encourage students to use caution (and their newfound knowledge of time value!) when considering these situations. Example: Suppose you are in a hurry to get your income tax refund. If you mail your tax return, you will receive your refund in 3 weeks. If you file the return electronically through a tax service, you can get the estimated refund tomorrow. The service subtracts a $50 fee and pays you the remaining expected refund. The actual refund is then mailed to the preparation service. Assume you expect to get a refund of $978. What is the APR with weekly compounding? What is the EAR? How large does the refund have to be for the APR to be 15%? Using a financial calculator to find the APR: PV = 978 50 = 928; FV = -978; N = 3 weeks; CPT I/Y = 1.765% per week; APR = 1.765 (52 weeks per year) = 91.76%!!! Compute the EAR = (1.01765)52 1 = 148.34%!!!! You would be better off taking a cash advance on your credit card and paying it off when the refund check comes, even if you have the most expensive card available. Refund needed for a 15% APR: PV + 50 = PV(1 + (.15/52))3 PV = $5,761.14 Lecture Tip, page 179: Another point of confusion for many students is what to do when the payment period and the compounding period dont match. Its important to point out that we cannot adjust the payment to match the interest rate. We also cannot just divide the APR by any number we want to get a period rate; we can only divide it by the number of periods used for compounding. The EAR can be used as a common denominator to help us find equivalent APRs. Example: Suppose you are going to have $50 deducted from your paycheck every two weeks and have it placed in an account that pays 8% compounded daily. How much will you have in 35 years? You are depositing money every two weeks (26 times per year), but compounding occurs daily. You need a period rate that corresponds to every two weeks, but you can only divide the APR given by 365. What can we do? Find the EAR for the daily compounded rate. This is the rate we will earn each year after we account for compounding. EAR = (1 + .08/365)365 1 = .08327757179 (Point out that is extremely important that we DO NOT round on the intermediate steps.) What we need is an APR based on compounding every two weeks that will pay the same effective rate of interest. So we take the EAR computed above and convert to an APR based on 26 compounding periods per year. APR = 26[(1.08327757179)1/26 1] = .0801144104 At this point, many students feel like this is wasted effort, because there is not that much difference. As we will see, the small difference in rates can make a difference over long periods of time. Find the FV: PMT = 50; N = 35(26) = 910; I/Y = 8.01144104 / 26 = .308132348; CPT FV = $250,535.24 If you just use I/Y = 8/26, you would get a FV = $249,829.21; a difference of $706.03. Slide 6.50 Future Value With Monthly Compounding Slide 6.51 Present Value With Daily Compounding Slide 6.52 Continuous Compounding Slide 6.53 Quick Quiz Part V Loan Types and Loan Amortization Pure Discount Loans Borrower pays a single lump sum (principal and interest) at maturity. Treasury bills are a common example of pure discount loans. Slide 6.54 Pure Discount Loans Example 6.12 Interest-Only Loans Borrower pays interest only each period and the entire principal at maturity. Corporate bonds are a common example of interest-only loans. Slide 6.55 Interest Only Loan Example Amortized Loans Borrower repays part or all of principal over the life of the loan. Two methods are (1) fixed amount of principal to be repaid each period, which results in uneven payments, and (2) fixed payments, which results in uneven principal reduction. Traditional auto and mortgage loans are examples of the second type of amortized loans. Slide 6.56 Amortized Loan with Fixed Principal Payment Example Slide 6.57 Amortized Loan with Fixed Payment Example Slide 6.58 Work the Web Example Lecture Tip, page 185: Consider a $200,000, 30-year loan with monthly payments of $1330.60 (7% APR with monthly compounding). You would pay a total of $279,016 in interest over the life of the loan. Suppose instead, you cut the payment in half and pay $665.30 every two weeks (note that this entails paying an extra $1330.60 per year because there are 26 two week periods). You will cut your loan term to just under 24 years and save almost $70,000 in interest over the life of the loan. Calculations on TI-BAII plus First: PV = 200,000; N=360; I=7; P/Y=C/Y=12; CPT PMT = 1330.60 (interest = 1330.60*360 200,000) Second: PV = 200,000; PMT = -665.30; I = 7; P/Y = 26; C/Y = 12; CPT N = 614 payments / 26 = 23.65 years (interest = 665.30*614 200,000) Summary and Conclusions Slide 6.59 Quick Quiz Part VI A- PAGE 74 CHAPTER 6 CHAPTER 6 A- PAGE 73 Key Concepts and Skills Chapter Outline Multiple Cash Flows Future Value Example 6.1 Multiple Cash Flows FV Example 2 Multiple Cash Flows Example 2 Continued Multiple Cash Flows FV Example 3 Multiple Cash Flows Present Value Example 6.3 Example 6.3 Timeline Multiple Cash Flows Using a Spreadsheet Multiple Cash Flows PV Another Example Multiple Uneven Cash Flows Using the Calculator Decisions, Decisions Saving For Retirement Saving For Retirement Timeline Quick Quiz Part I Annuities and Perpetuities Defined Annuities and Perpetuities Basic Formulas Annuities and the Calculator Annuity Example 6.5 Annuity Sweepstakes Example Buying a House Buying a House Continued Annuities on the Spreadsheet - Example Quick Quiz Part II Finding the Payment Finding the Payment on a Spreadsheet Finding the Number of Payments Example 6.6 Finding the Number of Payments Another Example Finding the Rate Annuity Finding the Rate Without a Financial Calculator Quick Quiz Part III Future Values for Annuities Annuity Due Annuity Due Timeline Perpetuity Example 6.7 Quick Quiz Part IV Work the Web Example Table 6.2 Effective Annual Rate (EAR) Annual Percentage Rate Computing APRs Things to Remember Computing EARs Example EAR Formula Decisions, Decisions II Decisions, Decisions II Continued Computing APRs from EARs APR Example Computing Payments with APRs Future Value with Monthly Compounding Present Value with Daily Compounding Continuous Compounding Quick Quiz Part V Pure Discount Loans Example 6.12 Interest Only Loan Example Amortized Loan with Fixed Principal Payment - Example Amortized Loan with Fixed Payment Example Work the Web Example Quick Quiz Part VI 2345iy!"Z q jhjQKLBC0K!L!!!1#H#|%(0(*++{+}+t,,.~../+/000Z5\5o5p5u566W6X6g6i66f:i:;;j= 6H*] 5CJ\H* 56\]6]j5CJU\mHnHu5\jCJUmHnHuN )*124IJP  !$If $d N DEK!"&;h$If $$Ifa$n$$Ifl  0,"LL t0  64 la;<=Z|$If $$Ifa$n$$Ifl  0,"LL t0  64 laZ[\rst`P$If $$Ifa$n$$Ifl  0,"LL t0  64 lad$If $$Ifa$n$$Ifl  0,"LL t0  64 la$If $$Ifa$n$$Ifl  0,"LL t0  64 laL$If $$Ifa$n$$Ifl  0,"LL t0  64 laHn~yssss^ & F$If $$Ifa$n$$Ifl  0,"LL t0  64 la  &>KL@Thxy!  & F $d N ^ & F! H  G u   ' Y Z ghEdf & F & Ff)*Pkl'Pj- & F & F & F-n1U !!!=!W!"""""1#}%%%%% & F & F%%&3&4&X&x&&&&& '~'()*****J++++++ ,#, & F & F & F#,F,s,t,..>.W..../00p56h6i67k=l====>>1>F> & F & F & FF>>>>>?????? A!AbAAAADDDDDDEEE1E & F$a$ & F & F & Fj=AADDDDDDDD E EEEEEK0JmHnHu0J j0JU6] 56\]1EAEpEEEEF%FMFvFFFFFG)GUGrGGGGGG H HEHrHHHH & FHI I,IAIZIoIIIIIIIII J#JEJ^JlJJJJJJ"K?KuKK & F & FKKKKKK & F* 001hP?/ =!"#$% i8@8 NormalCJ_HaJmH sH tH 2@2 Heading 1$@&5\D@D Heading 2$$d @&N 5\NN Heading 3$<@&5CJOJQJ\^JaJ8@8 Heading 4$$@&a$6]<A@< Default Paragraph FontBOB RWJ Chapter Heading6CJ .O. RWJ Title5CJ 6O6 RWJ Slides 56CJ]21"2 Heading 10 $a$,B2, Body Text6].U@A. Hyperlink >*B*ph>V@Q> FollowedHyperlink >*B* ph,@b, Header  !, r, Footer  !&)@& Page NumbervGvGz ?z @z Az Bz Cz Dz Ez Fz Gz Hz Iz Jz4 2%+3:G(8K   )*124IJP  !"&;<=Z[\rstHn &>KL@Thxy!H Gu'YZ g h  E d f  ) * P kl'Pj-n1U !=W1}!!!!!!"3"4"X"x""""" #~#$%&&&&&J'''''' (#(F(s(t(**>*W****+,,p12h2i23k9l9999::1:F:::::;;;;;; =!=b====@@@@@@AAA1AAApAAAAB%BMBvBBBBBC)CUCrCCCCCC D DEDrDDDDE E,EAEZEoEEEEEEEEE F#FEF^FlFFFFFF"G?GuGGGGGG00000010000J0J0J0J0J0J000000000000000000000000000000000 00000 000000 000000 000000000000 0 0 0!000000 0 000000 00 0 0 00000000 000000 0f  0*  0*  0*  0* 00000000 0*  0*  0*  0* 000 0*  0 *  0 *  0 * 000 0 *  0 *  0* 00000 0f  0! 0!000 0f  0 0000 0f  0! 0! 0!000000 0 0" 0" 0" 0" 0"000 0" 0& 0&000000000 0&0000 0" 0* 0* 0* 0* 0* 0* 0*0 0* 0*000000 0 0: 01:000 0: 0:000 0: 0;00000 0; 0000@00@0 0 0 0 0 0 0 0 0 0 0 0  0  0  0  0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0! 0" 0# 0$ 0%0 0& 0' 0( 0) 0 0 0 0 0 0 0 0 0 0  0  0  0  0  0 0 00222225j=K(9!;Z! f-%#,F>1EHKK)+,-./012345678:;<K* %,/5!!8@P(  Z  S  T  C  B S  ?24G)TLX PT _Hlt531182045 _Hlt531182046 _Hlt531182077 _Hlt531182078 _Hlt531182206 _Hlt531182232 _Hlt531182233 _Hlt531182258 _Hlt531182259 _Hlt531182276 _Hlt531182277((II{G@@@@@@@@@ @ @))JJ|G}HMMOY\cec g ++:;@@@ AAAAGG\qr3?lbjRFL-@Cn=BDW"%"1"3"&''z'}''?1R1\1p12G2J2h2S6b6i66777I8@@@ AAAAGG::::::::::::::::::bcADLUw Oefghr| -.12FGX"X"a"b""""".$/$%%++|2~233::====8@G@N@N@b@@@@@@@@@@@ AAAEEEEGG Cheri Etling`C:\WINDOWS\Profiles\etling\Application Data\Microsoft\Word\AutoRecovery save of IM Chapter 6.asd Cheri Etling`C:\WINDOWS\Profiles\etling\Application Data\Microsoft\Word\AutoRecovery save of IM Chapter 6.asd Cheri Etling`C:\WINDOWS\Profiles\etling\Application Data\Microsoft\Word\AutoRecovery save of IM Chapter 6.asd Cheri Etling`C:\WINDOWS\Profiles\etling\Application Data\Microsoft\Word\AutoRecovery save of IM Chapter 6.asd Cheri Etling[\\Cetling-laptop\c_drive\My Documents\Word Files\Brads Book - Fundamentals\IM Chapter 6.doc Cheri EtlingEC:\My Documents\Word Files\Brads Book - Fundamentals\IM Chapter 6.doc Cheri EtlingPC:\WINDOWS\Application Data\Microsoft\Word\AutoRecovery save of IM Chapter 6.asd Cheri EtlingEC:\My Documents\Word Files\Brads Book - Fundamentals\IM Chapter 6.doc Cheri EtlingEC:\My Documents\Word Files\Brads Book - Fundamentals\IM Chapter 6.docMcGraw-Hill Higher EducationF:\IM\chap006.doc5f\"8}&Sz?B30^`0o(0^`0o(6.0^`0o(..0^`0o(... 88^8`o( .... 88^8`o( ..... `^``o( ...... `^``o(....... ^`o(........0^`0o(0^`0o(6.0^`0o(..0^`0o(... 88^8`o( .... 88^8`o( ..... `^``o( ...... `^``o(....... ^`o(........0^`0o(+0^`0o(6.0^`0o(..0^`0o(... 88^8`o( .... 88^8`o( ..... `^``o( ...... `^``o(....... ^`o(........hh^h`o(P8^`Po(6..p0p^p`0o(.pp^p`o(  ^ `o(  X@ ^ `Xo( ......  ^ `o(....... 8x^`8o(........ `H^``o(.........5&"8z?B !"&;<=Z[\rstG@ߗG`@UnknownG:Times New Roman5Symbol3& :Arial#1h[gNc 5 r !0A@2Q Chapter 5 Cheri EtlingMcGraw-Hill Higher Education Oh+'0 $0 L X dpx Chapter 5 hap Cheri Etlingoherher Normal.dotgMcGraw-Hill Higher EducationMi7GrMicrosoft Word 9.0E@T @l>jt@d;5/ c 5 ՜.+,0 hp  University of TamparA2  Chapter 5 Title  !"#$%&'()*+,-./0123456789:;<=?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^`abcdefhijklmnqRoot Entry F@,=5/s1Table>V@WordDocument,zSummaryInformation(_DocumentSummaryInformation8gCompObjjObjectPool@,=5/@,=5/  FMicrosoft Word Document MSWordDocWord.Document.89q