ࡱ> Oh+'0$ <H d p |LThe major formulas for present value (these will reappear again and again):he  RESEARCH foESE Normal.doto Qinghua Wangmul4ngMicrosoft Word 8.0f@xA@E[7j@dhj #q ՜.+,D՜.+,x4 hp|  MITF[(  LThe major formulas for present value (these will reappear again and again): Title 6> _PID_GUIDAN{E2FC7C04-D5BF-11D2-AF5C-0004ACA2The Major Formulas for Present Value (these will reappear again and again): Present Value formulas (these are used in calculating project values, IRRs, and equivalent annual costs): PVP (Present Value of a Perpetuity):  EMBED Equation.2  PVGP (Present Value of a Growing Perpetuity):  EMBED Equation.2  PVA (Present Value of an Annuity):  EMBED Equation.2  PVGA (Present Value of a Growing Annuity):  EMBED Equation.2  Compounding (only use when there is "compounding" mentioned in the problem, e.g. "pay {receive} interest rate X, compounded monthly"): Discrete period compounding:  EMBED Equation.2  Continuous compounding:  EMBED Equation.2  Inflation Rates: (1 + rreal)(1 + inflation) = (1 + rnominal) Fixed Income Bond Pricing: PV(Bond) = PV (coupon payments ) + PV (final principal payment) Two ways to price a bond: Spot Rates are known:  EMBED Equation.2  (1.1) on p.4 of Taggart Cash flows at different dates from the same bond are discounted at different spot rates. You can obtain these spot rates from market quotes. You should be able to derive spot rates from coupon bonds Example: Problem Set #2, Q3 and Q7 Yield to Maturity is known:  EMBED Equation.2  Yield to Maturity is the IRR of a bond. Pay attention to the compounding period n, which may not be a year. Use the yield to maturity, y, corresponding to the compounding period, which may not be the annual yield. U.S. Treasury securities are all semi-annually compounded European fixed income securities are normally annually compounded. Know the difference between annualized yield and effective yield Example: Problem Set #2, Q1, Q2, and Q7. Bond Arbitrage: If two cash flow streams are identical, assuming credit quality is the same for both, the present value of these two cash flows should be the same. Arbitrage opportunity implies that two or more cash flows at the same date are price at different spot rates. If cash flows at the same date are discounted at different spot rates, you can take advantage of the arbitrage opportunity by buying LOW and selling HIGH. By arbitrage, you can either earn a positive cash flow today and incurring zero cash flow in the future or vis versa. Example: Problem Set #2, Q8 Two Term Structure Hypotheses: Expectation Hypothesis: Forward rates are unbiased predictors of expected future spot rates very useful for your calculation The slope of the term structure shows the markets expectation of changes in future short-term interest rates. Liquidity Preference Theory: Investors are generally risk averse. Since long bonds are more risky than short ones, investors in long bonds expect and on average receive higher rate of return than investors in shorts. One average, Forward Rates overpredicts future short-term rates. The term structure will slope upward even when future short-term rates are expected to be constant. So, term structures reflect (i) expectations of interest rate changes and (ii) the risk premiums demanded by investors in long bonds. Spot and Forward Rates: Given a term structure, we can derive the forward rates using the following formula: (1 + rn)n = (1 + rn-t) n-t (1 + tfn) t rn: spot rate for n periods rn-t: spot rate for n-t periods tfn: forward rate for t periods ends at n. If t=1, the formula becomes: (1 + rn)n = (1 + rn-1) n-1 (1 + fn) fn: is the one period forward rate starts from n-1, and ends at n. Examples: Problem Set #2, Q4, Q7, and Q14. Covered Interest Rate Parity: The current spot FX rate, forward FX rate between two countries, and their interest rates should satisfy the following relationship to prevent any arbitrage opportunities:  EMBED Equation.2  rf: foreign countrys interest rate rd: domestic interest rate FX rate: is denominated in terms of the domestic currency Example:  EMBED Equation.2  See Problem Set #2, Q11. Duration: As a measure of a bonds interest rate sensitivity, it is a weight average of the maturities of individual cash flows. The weights are proportional to the cash flows present values.   EMBED Equation.2   Duration assumes flat term structure Again, pay attention to the compounding periods. Example: Problem Set #2, Q12. Duration for a Perpetuity:   D = Duration for an annuity:  EMBED Equation.2  Modified Duration: It measures the sensitivity of bond price to change in interest rate, or yield to maturity. More specifically, it gives the percentage change in bond price due to 1% change in interest rate.   D* = D* is also called Volatility. Example: Problem Set #2, Q 13. Duration for Interest Rate Hedges: To hedge A with B:   Delta = = Delta gives the number of bond B needed to hedge A. The Major Formulas and Terms For Common Stock: Formulas : Denote rt-1 the companys capitalization rate (required rate of return, cost of equity capital) at Year t:  EMBED Equation.2  The price of a stock today is the discounted value of the dividends expected in the next year plus its forecast price o1 year before. DIV Discount Model:  EMBED Equation.2  The value of a companys stock is equal to the discounted steam of all future dividends paid on that existing stock. The Constant-growth Model: If dividends are expected to grow at a constant rate g, then,  EMBED Equation.2  (Provided g < r) Conversely, the market capitalization rate r is the dividend yield plus the rate of dividend growth:  EMBED Equation.2  Notice: Growth stage: rapidly expanding sales, high profit margins, high growth in EPS, many new investment opportunities, low pay out ratio Transition stage: growth rate and profit margin reduced by competition, fewer investment opportunities, high pay out ratio Maturity stage: earnings growth, pay out ratio and average return on equity stabilize Assume different stages with different growth rates Growth Opportunities: Investment projects that earn expected return higher than the appropriate discount rates represent growth opportunities.  EMBED Equation.2  Rearranging gives  EMBED Equation.2  Meaning of P/E ratio: A high P/E ratio doesnt indicate a low market capitalization rate r. A higher P/E ratio can be led by the following factors: A low market capitalization rate r A temporary decline in earnings More valuable growth opportunities Terms: Earnings Per Share (EPS) =  EMBED Equation.2  Dividend Per Share (DPS) = EMBED Equation.2  Retained Earnings = Earnings Dividends Book Value (BV) = Cumulative Retained earnings Return on Equity (ROE) =  EMBED Equation.2  =  EMBED Equation.2  Pay out Ratio (p) =  EMBED Equation.2 =  EMBED Equation.2  Plow back ratio (earnings retention ratio, b) = 1- p =  EMBED Equation.2 =  EMBED Equation.2  Dividend Yield =  EMBED Equation.2  Holding Period Return = Capital Gain Yield + Dividend Yield =  EMBED Equation.2  Capital Budgeting Basic Principles: Value depends on after-tax cash flows Incremental cash flows related to the project is what we care about A Dollar today is worth more than a Dollar tomorrow time value of money A safe Dollar is worth more than a risky Dollar Risk and return After tax incremental cash flows should be discounted at the opportunity cost of capital of the project Decision Rules: Accept when expected, incremental, after tax cash flows are worth than the project costs Accept when NPV > 0 Separate financing decision from investing decision, i.e. treat the project as if it is 100% equity financed Free Cash Flow to the Firm should be calculated as follows: Revenue- COGS= Gross Margin- S, G &A- Depreciation= EBIT- EBIT x t (t is the effective tax rate)= EBIAT+ Depreciation- Increase in Working Capital (WC = A/R + Inv. A/P)- Capex= FCF to the FirmExample: Problem Set #4, Q4. Note: Sometimes you are not given enough information to construct the whole thing above, so you only need to worry about all those incremental cash flows. Remember to tax effect any operating cash flows before calculate NPV. For a detailed example, see Q5 of Problem Set #4. Equivalent Annual Costs: When we compare or choose between cash flow streams of different lengths, EAC should be used. Steps: 1. Calculate Projects NPVs 2. Calculate level real annuity based on the NPV and number of periods of each project Choose the project with the lower EAC Example: Problem Set #4, Q 6. Mistakes to Avoid: Do not use IRR Be consistent with the treatment of inflation Do not forget tax effect on operating items Do Include any Opportunity Costs Do Not Include Sunk Costs Use ACRS tax depreciation schedule, not the companys own financial reporting one Example: Problem Set #4, Q1. Choosing Projects Under Budget Constraints: Decision Rule: We must pick the projects that offer the highest NPV per dollar invested.  Profitability Index = Example: Problem Set #4, Q8. Book Profitability v.s. Economic Profitability: The major difference between the two is depreciation. Book Profitability: Book Value = Historical cost of assets Book Depreciation Change in Book Value during the year = Book Depreciation Book Income = Cash Flow + Change in Book Value Book ROI = Book Income / Book Value at the Beginning of the year Economic Profitability: Economic Value = NPV of all future cash flows discounted at opportunity cost of capital Change in Economic Value during the year = Economic Depreciation (could be negative) Economic Income = Cash Flow Economic Depreciation Rate of Return = Economic Income / Economic Value at the Beginning of the year Example, Problem Set #4, Q7. 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XɉcSfjނK&t.R(*x1Table')SummaryInformation(sDocumentSummaryInformation8{CompObjNativej Normal.doto Qinghua Wangmul2ngMicrosoft Word 8.0f@@E[7j@E[7jy՜.+,D՜.+,x4 hp|  MITC&  LThe major formulas for present value (these will reappear again and again): Title 6> _PID_GUIDAN{E2FC7C04-D5BF-11D2-AF5C-0004ACA21ECE}  FMicrosoft Word Document MSWordDocWord.Document.89q [$@$NormalmH 8`8 Heading 1 $$@&5CJ4`4 Heading 2 $@&50`0 Heading 3$@&54`4 Heading 4 $@&52`2 Heading 5$@&56<A@<Default Paragraph Font2B`2 Body Text$5CJ,8AJ&  ,8AJ&6*(+02589m ]zx6"F$T'f**),-/1367;<>?@ d"***.4:=A%9;auwey{*>@-ACm!57  CWYu,.DXZ]qsEY[&::::::::::::::::::::::::::::8@( h9N + NB  S D NB @ S D&H  #  N  3  NB   S D H   #  H   #  H  #  HB  C DH  #  " HB  C D NB  S D1NB  S D H  #  % NB  S D1 H  #  NB  S D1B S  ?()*+EFtuxy##& Xh 1tH  0t"Ztaat  t tRh "t t X/ t aatxa atU!tttt FbtE t u w ( * C E L N  i#l#,&T&V&&',* , L N +0"""",&s&t&& Xiaoyin Zhang(C:\DOS\AutoRecovery save of mid1form.asd Xiaoyin Zhang(C:\DOS\AutoRecovery save of mid1form.asd Xiaoyin Zhang(C:\DOS\AutoRecovery save of mid1form.asd Xiaoyin Zhang(C:\DOS\AutoRecovery save of mid1form.asd Xiaoyin Zhang(C:\DOS\AutoRecovery save of mid1form.asd Xiaoyin Zhang(C:\DOS\AutoRecovery save of mid1form.asd Xiaoyin Zhang(C:\DOS\AutoRecovery save of mid1form.asd Xiaoyin ZhangC:\My Documents\TA\mid1form.doc Xiaoyin ZhangC:\My Documents\TA\mid1form.doc Qinghua Wang"C:\Lijin\ta15.415\mid1form_all.docr2  ?4  ? <   t@L  FRH  I kq Zd K{ 5]$ D* ;O+ gb, ^? n s: s [\Kw`8Cx #| <~ hho()hhCJOJQJo(hhCJOJQJo(hhCJOJQJo(hhCJOJQJo(hhCJOJQJo(hhCJOJQJo(0o(. hhOJQJo(hhCJOJQJo( hhOJQJo(hhCJOJQJo(hhCJOJQJo(hh) hhOJQJo(hhCJOJQJo( hhOJQJo(hh.hhCJOJQJo(hhCJOJQJo( hhOJQJo(v OJQJo( 88OJQJo( OJQJo( OJQJo( ppOJQJo(   OJQJo( @ @ OJQJo(   OJQJo( hhOJQJo(v OJQJo( 88OJQJo( OJQJo( OJQJo( ppOJQJo(   OJQJo( @ @ OJQJo(   OJQJo( hhOJQJo( hhOJQJo( hhOJQJo(hhCJOJQJo(hho(.88o(. hhOJQJo(hhCJOJQJo(hhCJOJQJo(t@L s: sK{->nZd<~?4<?t+KI;O+*CJ5CJH*6 jUmH5655>*5CJj=CJEHUj: UVmH6CJCJ jCJUj;CJEHUj: UVmHAf*l*m*s*u*v**************j  & Fdx$/ =!"#$%The Major Formulas for Present Value (these will reappear again and again): Present Value formulas (these are used in calculating project values, IRRs, and equivalent annual costs): PVP (Present Value of a Perpetuity):  EMBED Equation.2  PVGP (Present Value of a Growing Perpetuity):  EMBED Equation.2  PVA (Present Value of an Annuity):  EMBED Equation.2  PVGA (Present Value of a Growing Annuity):  EMBED Equation.2  Compounding (only use when there is "compounding" mentioned in the problem, e.g. "pay {receive} interest rate X, compounded monthly"): Discrete period compounding:  EMBED Equation.2  Continuous compounding:  EMBED Equation.2  Inflation Rates: (1 + rreal)(1 + inflation) = (1 + rnominal) Fixed Income Bond Pricing: PV(Bond) = PV (coupon payments ) + PV (final principal payment) Two ways to price a bond: Spot Rates are known:  EMBED Equation.2  (1.1) on p.4 of Taggart Cash flows at different dates from the same bond are discounted at different spot rates. You can obtain these spot rates from market quotes. You should be able to derive spot rates from coupon bonds Example: Problem Set #2, Q3 and Q7 Yield to Maturity is known:  EMBED Equation.2  Yield to Maturity is the IRR of a bond. Pay attention to the compounding period n, which may not be a year. Use the yield to maturity, y, corresponding to the compounding period, which may not be the annual yield. U.S. Treasury securities are all semi-annually compounded European fixed income securities are normally annually compounded. Know the difference between annualized yield and effective yield Example: Problem Set #2, Q1, Q2, and Q7. Bond Arbitrage: If two cash flow streams are identical, assuming credit quality is the same for both, the present value of these two cash flows should be the same. Arbitrage opportunity implies that two or more cash flows at the same date are price at different spot rates. If cash flows at the same date are discounted at different spot rates, you can take advantage of the arbitrage opportunity by buying LOW and selling HIGH. By arbitrage, you can either earn a positive cash flow today and incurring zero cash flow in the future or vis versa. Example: Problem Set #2, Q8 Two Term Structure Hypotheses: Expectation Hypothesis: Forward rates are unbiased predictors of expected future spot rates  very useful for your calculation The slope of the term structure shows the market s expectation of changes in future short-term interest rates. Liquidity Preference Theory: Investors are generally risk averse. Since long bonds are more risky than short ones, investors in long bonds expect and on average receive higher rate of return than investors in shorts. One average, Forward Rates overpredicts future short-term rates. The term structure will slope upward even when future short-term rates are expected to be constant. So, term structures reflect (i) expectations of interest rate changes and (ii) the risk premiums demanded by investors in long bonds. Spot and Forward Rates: Given a term structure, we can derive the forward rates using the following formula: (1 + rn)n = (1 + rn-t) n-t (1 + tfn) t rn: spot rate for n periods rn-t: spot rate for n-t periods tfn: forward rate for t periods ends at n. If t=1, the formula becomes: (1 + rn)n = (1 + rn-1) n-1 (1 + fn) fn: is the one period forward rate starts from n-1, and ends at n. Examples: Problem Set #2, Q4, Q7, and Q14. Covered Interest Rate Parity: The current spot FX rate, forward FX rate between two countries, and their interest rates should satisfy the following relationship to prevent any arbitrage opportunities:  EMBED Equation.2  rf: foreign country s interest rate rd: domestic interest rate FX rate: is denominated in terms of the domestic currency Example:  EMBED Equation.2  See Problem Set #2, Q11. Duration: As a measure of a bond s interest rate sensitivity, it is a weight average of the maturities of individual cash flows. The weights are proportional to the cash flows present values.   EMBED Equation.2   Duration assumes flat term structure Again, pay attention to the compounding periods. Example: Problem Set #2, Q12. Duration for a Perpetuity:   D = Duration for an annuity:  EMBED Equation.2  Modified Duration: It measures the sensitivity of bond price to change in interest rate, or yield to maturity. More specifically, it gives the percentage change in bond price due to 1% change in interest rate.   D* = D* is also called Volatility. Example: Problem Set #2, Q 13. Duration for Interest Rate Hedges: To hedge A with B:   Delta = = Delta gives the number of bond B needed to hedge A. The Major Formulas and Terms For Common Stock: Formulas : Denote rt-1 the company s capitalization rate (required rate of return, cost of equity capital) at Year t:  EMBED Equation.2  The price of a stock today is the discounted value of the dividends expected in the next year plus its forecast price 1 year before. DIV Discount Model:  EMBED Equation.2  In most applications rt is assumed to be equal across t, i.e., the term structure is flat. The value of a company s stock is equal to the discounted stream of all future dividends paid on that existing stock. The Constant-growth Model: If dividends are expected to grow at a constant rate g, then,  EMBED Equation.2  (Provided g < r) Conversely, the market capitalization rate r is the dividend yield plus the rate of dividend growth:  EMBED Equation.2  Notice: Growth stage: rapidly expanding sales, high profit margins, high growth in EPS, many new investment opportunities, low pay out ratio Transition stage: growth rate and profit margin reduced by competition, fewer investment opportunities, high pay out ratio Maturity stage: earnings growth, pay out ratio and average return on equity stabilize Assume different stages with different growth rates Growth Opportunities: Investment projects that earn expected return higher than the appropriate discount rates represent growth opportunities.  EMBED Equation.2  Rearranging gives  EMBED Equation.2  Meaning of P/E ratio: A high P/E ratio doesn t indicate a low market capitalization rate r. A higher P/E ratio can be led by the following factors: A low market capitalization rate r A temporary decline in earnings More valuable growth opportunities 5. Certainty equivalent  EMBED Equation.2  (1) and we often write CEQt = a t C t, (2) So solving from (1) and (2) we have,  EMBED Equation.2 , which is less than 1 since rf <= r, and we have a t = a1t That is, the appropriate adjustment factor (a t) is a geometric sequence, growing at rate  EMBED Equation.2 . Terms: Earnings Per Share (EPS) =  EMBED Equation.2  Dividend Per Share (DPS) = EMBED Equation.2  Retained Earnings = Earnings  Dividends Book Value (BV) = Cumulative Retained earnings Return on Equity (ROE) =  EMBED Equation.2  =  EMBED Equation.2  Pay out Ratio (p) =  EMBED Equation.2 =  EMBED Equation.2  Plow back ratio (earnings retention ratio, b) = 1- p =  EMBED Equation.2  =  EMBED Equation.2  Dividend Yield =  EMBED Equation.2  Holding Period Return = Capital Gain Yield + Dividend Yield =  EMBED Equation.2  Capital Budgeting Basic Principles: Value depends on after-tax cash flows Incremental cash flows related to the project is what we care about A Dollar today is worth more than a Dollar tomorrow  time value of money A safe Dollar is worth more than a risky Dollar  Risk and return After tax incremental cash flows should be discounted at the opportunity cost of capital of the project Decision Rules: Accept when expected, incremental, after tax cash flows are worth than the project costs Accept when NPV > 0 Separate financing decision from investing decision, i.e. treat the project as if it is 100% equity financed Free Cash Flow to the Firm should be calculated as follows: Revenue- COGS= Gross Margin- S, G &A- Depreciation= EBIT- EBIT x t (t is the effective tax rate)= EBIAT+ Depreciation- Increase in Working Capital (WC = A/R + Inv.  A/P)- Capex= FCF to the FirmExample: Problem Set #4, Q4. Note: Sometimes you are not given enough information to construct the whole thing above, so you only need to worry about all those incremental cash flows. Remember to tax effect any operating cash flows before calculate NPV. For a detailed example, see Q5 of Problem Set #4. Equivalent Annual Costs: When we compare or choose between cash flow streams of different lengths, EAC should be used. Steps: 1. Calculate Projects NPVs 2. Calculate level real annuity based on the NPV and number of periods of each project Choose the project with the lower EAC Example: Problem Set #4, Q 6. Mistakes to Avoid: Do not use IRR Be consistent with the treatment of inflation Do not forget tax effect on operating items Do Include any Opportunity Costs Do Not Include Sunk Costs Use ACRS tax depreciation schedule, not the company s own financial reporting one Example: Problem Set #4, Q1. Choosing Projects Under Budget Constraints: Decision Rule: We must pick the projects that offer the highest NPV per dollar invested.  Profitability Index = Example: Problem Set #4, Q8. Book Profitability v.s. Economic Profitability: The major difference between the two is depreciation. Book Profitability: Book Value = Historical cost of assets  Book Depreciation Change in Book Value during the year = Book Depreciation Book Income = Cash Flow + Change in Book Value Book ROI = Book Income / Book Value at the Beginning of the year Economic Profitability: Economic Value = NPV of all future cash flows discounted at opportunity cost of capital Change in Economic Value during the year = Economic Depreciation (could be negative) Economic Income = Cash Flow  Economic Depreciation Rate of Return = Economic Income / Economic Value at the Beginning of the year Example, Problem Set #4, Q7. Weight Number of Periods for Cash Flow Ct Bond Price D 1 + y 1 + y y Price (A) x Volatility (A) Price (B) x Volatility (B) Price (A) x D* (A) Price (B) x D* (B) NPV Investment څ܅hj jlJLrt·}rfj]r: CJUVmHj#6 CJEHUj#6 CJUVmH5CJjgGCJEHUji: CJUVmHjDCJEHUj: CJUVmHjoB5CJEHUj#: CJUVmH 56CJj5CJUj1@CJEHUj: CJUVmH6CJ jCJUCJ$z|~"$Š$& & F hh & F$ & Ftvx~"$>Š&(NPRTZҍԍ֍؍ڍh2bJ P "(,2>@BDHLƽгݤCJH*CJH*566jsOCJEHUj: UVmHjLCJEHUj<: UVmH6CJ jCJU55>*CJCJH*5CJCJ jCJUjiJCJEHU="$jlڍ܍. bfhȔ & F & F h & Fh & F h02b0JęF PRLNʝ&(b & F h & F  & F & F hLRT̝ΝНҝ`bprtv>؟46\^`bjlrtڢnvxz֥إڥ此 5>*CJjWCJEHUjm: UVmHjCJUmHjTCJEHUj: UVmHj+RCJEHUj: UVmH6CJ jCJU5>*CJH*CJH*CJ>bd>@؟ڟ24df^`֢آڢܢޢhln`b֥ڥ PRTV & F 8 h8ڥܥޥ "HJLNRv:RV :F\| "2: "$&^`󱫡󱫌j: UVmHj\5CJEHUj܎: UVmH 56CJj5CJUCJH* 5>*CJ jUmH5jiZCJEHUj: UVmH6CJ jCJU5>*5CJCJjCJUmH3ި 68: "(46FH68p>  & F & F$H6 468:NX FHnprt駣駣}駣sjjkCJEHUj: UVmHj.iCJEHUji: UVmHjfCJEHUj: UVmH6CJ jCJU5 jwdEHUjߎ: UVmH jU5CJjb5CJEHUjpߎ: UVmH 56CJCJH*CJj5CJUjg_5CJEHU) <NXNbd>̵@ȶ & F & F & F & F & F h & F h & F h$ & F & FȶDFطڷ&(\^ҸԸιй8Ll & F & F$·Ʒȷ&(*PRTV¸Ƹ̸θԸ.02й 0246ln~ڻ퍄j{wCJEHUj": UVmHjiuCJEHUjA: UVmHjXsCJEHUj!: UVmH5CJjpCJEHUj: UVmHH*CJH*jmnCJEHUj̵: UVmH6CJ jCJUCJCJH*4ڻܻ޻ 2468<>dfhjܼ޼ 8:<>bd68:<FHNޮޛވuljCJEHUj: UVmHjɃCJEHUj: UVmHjCJEHUjA: UVmHjgCJEHUj: UVmHjq}CJEHUj: UVmHjm{CJEHUj{: UVmH6CJCJ jCJUjtyCJEHUjL: UVmH*lؼ@>@BDFHLNrtnVXxz,.Vh & F & F & F $ & FNrt6FTVzHnZTh0$,4~.0P\^np0NV5CJH*6 jUmH5655>*CJ5CJ4VX2(*8:24F$@0D ް$@( $$l$h & FFHnprtXZP & F & F8 h8$$ $$lLh N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2  FMicrosoft Equation 3.0 DS Equation Equation.39q4 PV=C 1 r<)lp9? 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L& &>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qRָcIgI PV(Bond)= t=1n " C t (1+y) t +P(1+y) n2"C#-x 8|ЮºO`!C#-x 8|Юº, `L"PxSA/A~tmu۪H9l"$!q#BSqSQAhB?w ~u&y 5}{{! R@m qdm`+/k'$09%I1$'VWx#-N8ʜhniK[-?f1`K}kx`-UJ2L t͆Z_e1F*qG^t7NQPj`B*@}SJ$Tg]Ezg³b:>#U7t:ż_Ƥ6T)iXFc)^~qͯc\)jS[ 9͟{1k.QGט_io| HxJ_=Q{VMIwM (6N4!(е 1\ۯKPkkǍ#Dd$B  S A? 2ƣ9>]F<ǨoR`!ƣ9>]F<Ǩ. 8z/dxRK@~RkZQAQ88 T阔FlMI#NN:89{?`w\}cP;EFD"fD<Fn3   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qR$I4{I ForwardFXrate=CurrentspotFXrate(1+r f )(1+r d )>/J\g:{ٶ{_R}PT kAÜt?G;p~8.iR؆cd#E-}81-I̝:ʣS6Nt ;G='_W,cUPyA+v࿷%rpY&$%<1gj`+vێـfWsDdB  S A?  2F!(Y)"T`!!(Y) 81dxcdd``$D@9@, fbd02,(1dbfaR`9 /d3H1ibY;AL& &>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qRcIgI Forwardrate(Book Antiqua}$)=Currentspotrate($)(1+r JPN )(1+r US )3PT obIFHeA*[~1AtF]F"L LM 0u & ;! 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D~6N`-7ߣp{ɔ֊{ϯ32YJ>(~BNvaSLh N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2  FMicrosoft Equation 3.0 DS Equation Equation.39qN8T P 0 =DIV 1 r"g1AFlWF+ǫuý1poH=u Tߏ!',nxUh?ӇNW:.9/ UsS2=Ԥ|!D 'I=-xGclXDd<B  S A? 2s&L^B$d`!s&L^B$r`` PdxQ=KA xE" A~`u"QqVAB E 'bjϙҸ޽w3o̮,&3ˢ X%119=  \]B 5IsrSkT Lh N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2  FMicrosoft Equation 3.0 DS Equation Equation.39qNs r=DIV 1 P 0 +g/L(ER{=EFyBOw$Aj"oz~49_g'WGkide]qe0!~#:h,qQp8xNau$os+[j =7उjjrew1a1/JG߉M@TEݴ@+G͖@8iKgS,3J /^_DdB  S A? 2OPIaBg`!OPIaBt _@2kxQKPwI0h(V:hBͽ '8tWLh N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2  FMicrosoft Equation 3.0 DS Equation Equation.39qZs P 0 =EPS 1 r+PVGOYx^/;EcM@9B!2$0MSd+c~;";Fh)H9 >4(2 ̦ ݱPa`6NLWa<.x-lM!MpƀRs: >"4̏=Y& ]+rkx(Y8pFjvS;5T>!a"^Ğ!/g(B_eQ Sw4+??dzr+!7>>}y0{   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q C t (1+r) t =PV t =CEQ t (1+r f ) t  S A? 2"oֻ;P)Lyk`!oֻ;P)Ly`(+xSM+DQ~0$BeGdE>&k Fbcc66JɊQ,eXXX؈5q{{;>qss.BFZPWHDBr]Q+V{v2٨{"^.QC856HH~)ѡNז=^M 'rZaP,sWC=*$*&V'L*WwXMHeҫP:.e&y)w9Eq u"dm,j^f(>) )Z! \[6;_/Sk?fXMD}#GbjsM+Y&o玃ie+{f|+ό~ ϧ7:Iމ|fji@:V~sp-Hw u_I|.P $˯f]yl9{hq':8Dd<B  S A? 2T+3۞An`!T+3۞A8` `\xRJ@&}q]H(R]~RVBPK](..t)v`LbNǹs"+/b|(@yM`7I-HS]_Jvq4D9LX:Q>iJ nW#L& &>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qy< a t =(1+r f ) t (1+r) t0~P&P7G,)*~#=d:_s좹`cm[_yquvTNZS2 YR^L\so+%vO ԟb"Î5M7]Gu)=k(o7g(1_Ó :?F,o~Tx-֟[]Ȇَ=brd{T HHv#sbv 8F&?+zjDd8B  S A? 2kTWU *2q`!kTWU *  v dvxcdd``$d@9`,&FF(L& &>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qN a 1 =1+r f 1+r`T̐ & ärMRcgb 6qfĒʂT/&`b]F"LL 0roneabM-VK-WMcjz[~ }6.Y.`0'tAe(LV ~">ڷa=i< W&Eظf"Csg [fd{`2`jp s$C6P>z?yc`~C H 2P? 0y{钑I)$5|&s8;C#|`Bd DdB   S A ? 2{ e..;1KLh N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2  FMicrosoft Equation 3.0 DS Equation Equation.39qjL  EarningsNumberOfSharesWs`!O e..;1K@ pdxcdd``$d@9`,&FF(`T̐ & ä-d3H1icY;@;C#lHlۘ?DdB   S A ? 2|Lh N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2  FMicrosoft Equation 3.0 DS Equation Equation.39qnh DividendsNumberOfSharesr" GS_ FA1Xu`!Pr" GS_ FA1@ pdxcdd``$d@9`,&FF(`T̐ & ä-d3H1icY;@$d@9`,&FF(`T̐ & 9MRcgb v fĒʂT/&`b]F"L L`0roneabM-VK-WMcjz[~ }v*.`zU@w 2Eyy\Pwr b;{F&&\` ] ؐ ;8DdlB  S A? 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FMicrosoft Equation 3.0 DS Equation Equation.39q== N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 Lh =  DIV 1 P 0N  . FMicrosoft Equation 3.0 DS Equation Equation.39q== N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 Lh "gz8 Earnings"DividendsEarnings .    & & FMicrosoft Equation 3.0 DS Equation Equation.39qTimes New RomanSy-N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 Lh  PVA=C1r(1+r) tr RetainedEarningsEarnings  FMicrosoft Equation 3.0 DS Equation Equation.39q &N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 Lh quation.39q*H DPSEPS 1r"g"(1+g t (r"g)(1+r) FMicrosoft Equation 3.0 DS Equation Equation.39qN  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 Roman-Lh "System--V8 DividendsEarnings FMicrosoft Equation 3.0 DS Equation Equation.39q1+r PeriN  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 & Lh FMicrosoft Equation 3.0 DS Eq.@ EPSBVPSEQ r Actua FMicrosoft Equation 3.0 DS Equation Equation.39qN  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 2 `~424Lh 15`` & ": EarningsBVFMicrosoft Equation 3.0 DS Eqon Equation.39q FMicrosoft Equation 3.0 DS Equation Equation.39qV(BondN  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 2 k9,` Lh "$8 2 `,` 2 `$,`  2 k, 282 2 1 nh DividendsNumberOfShares15`` & "em- FMicrosoft Equation 3.0 DS Equation Equation.39qoft Equation 3.0 DS EqN  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 - 2 `@PVALh ` =Times New Roman2 k$20 2 k9,` jL  EarningsNumberOfShares789 2 k, 282 2 1 065 2 `083 2 `~424 FMicrosoft Equation 3.0 DS Equation Equation.39q"N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 .Lh - mes New Roman- 2 `@PVAN a 1 =1+r f 1+rTimes New Roman- 2 k$20 2 k9,`  FMicrosoft Equation 3.0 DS Equation Equation.39q,` 2 `$,` &>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System-L& &>   .1   & & MathType- n=1P t=1T " C t (1+y) t tL&  .y< a t =(1+r f ) t (1+r) tes New Roman- 2 `@PVASymbol- 2 ` FMicrosoft Equation 3.0 DS Equation Equation.39q 2 k9,` &>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System-L&  . C t (1+r) t =PV t =CEQ t (1+r f ) t,` 2 .` 2 , $132 W,` 2 000 2 1  FMicrosoft Equation 3.0 DS Equation Equation.39q- 2 x &>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System-  .L& -== mes New Roman:- 2 0$10w EPS1P 0 =r(1"PVGOP 0 )2 12 2 489Times New Roman- 2 x  FMicrosoft Equation 3.0 DS Equation Equation.39q" 2 Z"N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 .Lh -== mes New Roman:- 2 0$10Zs P 0 =EPS 1 r+PVGO1 06 2 12 2 489 FMicrosoft Equation 3.0 DS Equation Equation.39qol- 2 N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 .Lh -== mes New Roman:- 2 0$10Ns r=DIV 1 P 0 +g 2 1 06 2 12 2 489 FMicrosoft Equation 3.0 DS Equation Equation.39qol- 2 N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 .Lh -== mes New Roman:- 2 0$10N8T P 0 =DIV 1 r"g 2 1 06 2 12 2 489 FMicrosoft Equation 3.0 DS Equation Equation.39qol- 2 N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 .Lh -== mes New Roman:- 2 0$10 P 0 =DIV t (1+r t ) tt=1" "489Times New Roman- 2 x  FMicrosoft Equation 3.0 DS Equation Equation.39q" 2 Z"N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 .Lh -== mes New Roman:- 2 0$10s P t =DIV t+1 +P t+1 1+r t+12 489Times New Roman- 2 x  FMicrosoft Equation 3.0 DS Equation Equation.39q" 2 Z"N  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 .Lh -== mes New Roman:- 2 0$10RpcIgI D=1+yy"T(1+y) T "1 2 12 2 489Times New Roman- 2 x  FMicrosoft Equation 3.0 DS Equation Equation.39q" 2 Z"&>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System-pe-== L& l,` 2 .` 2 , $132 000 2 1 s Duration=1P t=1T " C t (1+y) t t 2 " 2 " 2 Z"2   2   2 Z  2  FMicrosoft Equation 3.0 DS Equation Equation.39q2      !&>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System-06 2 12 2 489L& PSymbol- 2 " 2 " 2 Z"RcIgI Forwardrate(Book Antiqua}$)=Currentspotrate($)(1+r JPN )(1+r US ) FMicrosoft Equation 3.0 DS Equation Equation.39q&>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System- & "SystemL& FMicrosoft Equation 3.0 DS Eq39qR$I4{I ForwardFXrate=CurrentspotFXrate(1+r f )(1+r d )h  FMicrosoft Equation 3.0 DS Equation Equation.39q.&>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System-L& Lh N  .edEarningsEarningsRָcIgI PV(Bond)= t=1n " C t (1+y) t +P(1+y) n @@& &thType-==  FMicrosoft Equation 3.0 DS Equation Equation.39q` 2 , $13&>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System-L&  .R8[I$mI PV(Bond)= t=1n " C t (1+r t ) t +F(1+r n ) n.` 2 , $132 W,` 2 000 2 1  FMicrosoft Equation 3.0 DS Equation Equation.39q- 2 x &>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System-  @@& &L& Times New Roman:- 2 0$10` 2 .` 2 , $13EQ r Actual =e rt "1489Times New Roman- 2 x  FMicrosoft Equation 3.0 DS Equation Equation.39q" 2 Z" nL 6 .1   & $ & MathTypepTimes New Roman- 2 ?r 2 e Times New Roman- 2 Contpp> 2 Comppp 2 rtJ> 2 y.8 2 L Ϡ5(3L,3 r EffectiveAnnual =1+r Periodic [] n -1n@ FMicrosoft Equation 2.0 DS Equation Equation.2vN=  .1  `&  & MathTypepSymbol-2 OB [Symbol-2 Oe]@Times New RomanSy- 2 @r 2 E rTimes New Roman-2  EffectiveATTppGGp2 ,nnualpG2  PeriodicpTGGp 2 n@Symbol- 2 = 2  + 2 -@Times New Roman- 2  1 2 \1 & "System-- 2 LvN L, PVGA=C 1 1r"g"(1+g) t (r"g)(1+r) t [] FMicrosoft Equation 3.0 DS Equation Equation.39q&>   .1   & & MathType- Times New Roman- 2 `@PVASymbol- 2 `= 2 ` =Times New Roman- 2 k$20 2 k9,` 2 k ,` 2 9( 2 A.` 2  ) 2 `"$8 2 `,` 2 `$,` 2 k789 2 k, 282 2 1 2 065 2 `083 2 `~424@Times New Roman- 2 S 15`` & "System-L& t PVA=C1r"1r(1+r) t [] FMicrosoft Equation 3.0 DS Equation Equation.39qV:  .1    & & MathType-\7 @Times New RomanSy- 2 @PVABB 2 C+ 2 Xr 2 XW r 2 XrTimes New Roman- 2 {tG@Symbol- 2 2= 2 - 2 X + 2  2  2  2 . 2 . 2 .@Times New RomanSy- 2 1 2  1 2 X 1 2 X ( 2 X) & "System- Ctrl+F4@Nex&t Ctrl+F6L 4<` PV=C 1 r"g FMicrosoft Equation 3.0 DS Equation Equation.39qN  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 Lh 4 PV=C 1 r FMicrosoft Equation 3.0 DS Equation Equation.39qN  .1  @@& & MathType-== Times New Roman:- 2 0$10 2 l,` 2 .` 2 , $13 2 W,` 2 000 2 1 2 06 2 12 2 489 Times New Roman- 2 x 60ppPSymbol- 2 + 2 " 2 " 2 Z" 2   2   2 Z  2  = & "System-365 2 Lh