ࡱ> a{` Dbjbj *d3pppp\\\\2ØØØ+---Gt$hmØpp'''|p8+'+''+  ?lu\#|K<0`xxØ"'ØØØØØØ$|d pppppp Expected Return: E(R) The expected return from investing in a security over some future holding period is an estimate of the future outcome of this security. Although the Expected Return is an estimate of an investors expectations of the future, it can be estimated using either ex ante (forward looking) or ex post (historical) data. If the expected return is equal to or greater than the required return, purchase the security. Regardless of how the individual returns are calculated, the Expected Return of a Portfolio is the weighted sum of the individual returns from the securities making up the portfolio:  EMBED Equation.2  Ex ante expected return calculations are based on probabilities of the future states of nature and the expected return in each state of nature. Sum over all states of nature, the product of the probability of a state of nature and the return projected in that state. StatePsRsPs * RsGood30%20%0.3(0.2)Average50%15%+0.5(0.15)Poor20%-4%+0.2(-0.04) EMBED Equation.2  12.70% Ex post expected return calculations are based on historical data. Add the historical returns and then divide by the number of observations. YearRt200215%200320%20049%200510%20065% EMBED Equation.2  11.80% Variance (Standard Deviation): 2 () Variance is a measure of the dispersion in outcomes around the expected value. It is used as an indication of the risk inherent in the security. Standard deviation is the square root of variance. Ex ante variance calculation: The expected return is subtracted from the return within each state of nature; this difference is then squared. Each squared difference is multiplied by the probability of the state of nature. These weighted squared terms are then summed together. StatePsRsPs * Rs(Rs E(R))2 * PsGood30%20%0.3(0.2)0.3(0.2-0.127)2Average50%15%+0.5(0.15)+0.5(0.15-0.127)2Poor20%-4%+0.2(-0.04)+0.2(-0.04-0.127)212.70%0.00748.63%MeanVarianceStandard Deviation EMBED Equation.2  EMBED Equation.3  Ex post variance calculation: The average return is subtracted from each single period return; this difference is then squared. The squared differences are summed. This sum is divided by the number of periods (using population data) or the number of periods minus 1 (using sample data). YearRt(Rt E(R))2(Rt E(R))2200215%(0.15-0.118)2(0.15-0.118)2200320%(0.2-0.118)2(0.2-0.118)220049%(0.09-0.118)2(0.09-0.118)2200510%(0.1-0.118)2(0.1-0.118)220065%(0.05-0.118)2(0.05-0.118)2= Sum/5=Sum/5=Sum/411.80%0.00270.0034MeanPopulation VarianceSample Variance5.19%5.81%Population Std DevSample Std DevPopulation data EMBED Equation.2 Sample data EMBED Equation.2  Variance of a Portfolio: p Ex ante variance of a portfolio if portfolio returns for each state of nature and probabilities of the states of nature are known:  EMBED Equation.2  Ex post variance of a portfolio if portfolio returns for each historical time period are known:  EMBED Equation.2  The variance of a portfolio (ex ante or ex post) can be calculated using the weights and covariances of the assets making up the portfolio:  EMBED Equation.2   EMBED Equation.2  For a 2 asset portfolio the formula simplifies to:  EMBED Equation.2  The variance of a portfolio is not equal to the weighted sum of the individual asset variances unless all the assets are perfectly positively correlated with each other. ( ( ( ( (  EMBED Equation.3  ( ( ( ( ( Covariance: ij Covariance is an absolute measure of the extent to which two variables tend to covary or move together. Correlation Coefficient: ij The correlation coefficient is a standardized statistical measure of the extent to which two variables are associated ranging from perfect positive correlation ((i,j = +1.0) to perfect negative correlation ((i,j = -1.0). Ex anteStatePSRX,SRY,SPS * (RX,S E(RS)) * (RY,S E(RS))Good30%20%38%0.3(0.2-0.127)(0.38-0.174)Average50%15%16%+0.5(0.15-0.127)(0.16-0.174)Poor20%-4%-10%+0.2(-0.04-0.127)(-0.1-0.174)Mean12.70%17.40%Variance0.00740.0278 Std Dev8.63%16.69%Covariance0.0135Correlation0.9380 EMBED Equation.2  EMBED Equation.2  Ex postYearRX,tRY,t(RX,t E(RX)) (RY,t E(RY))200215%18%(0.15-0.118)(0.18-0.144)200320%15%(0.2-0.118)(0.15-0.144)20049%35%(0.09-0.118)(0.35-0.144)200510%9%(0.1-0.118)(0.09-0.144)20065%-5%(0.05-0.118)(-0.05-0.144)Mean11.80%14.40%PopulationVariance0.00270.0169 Sum / 5Std Dev5.19%12.99%Covariance0.0020Correlation0.2978SampleVariance0.00340.0211 Sum / (5-1)Std Dev5.81%14.52%Covariance0.0025Correlation0.2978Population data EMBED Equation.2 Sample data EMBED Equation.2  Beta: i Beta is a measure of volatility, or relative systematic risk, for single assets or portfolios.  EMBED Equation.2  Historical beta is usually estimated by regressing the excess asset returns for the company or portfolio (y-variable: Ri - Rf) against the excess market returns (x-variable: Rm - Rf) i.e., through the use of a characteristic line. The beta of a portfolio is EMBED Equation.3 . Sample risk and return ex ante calculations Returns per State of Nature for Each SecurityState of Nature Prob!RFMarketxyPortfolio10%40%30%20%!WeightsGood30%5%16%20%38%20.50%Average50%5%10%15%16%12.20%Poor20%5%6%-4%-10%-0.30%Mean5.00%11.00%12.70%17.40%12.19%Variance00.0013 0.0074 0.0278 0.0052 Std Dev0.00%3.61%8.63%16.69%7.21%beta0.00 1.00 2.04 4.54 1.92 RF,MktMkt,xx,RFMkt,yx,yy,RFCovariance00.0027 00.0059 0.0135 0Correlation00.8520 00.9807 0.9380 0 Sample risk and return ex post calculations Ex Post (Using historical population data) Returns per Year for Each Security YearRFMarketxyPortfolio10%40%30%20%!Weights20025%18%15%18%15.80%20036%12%20%15%14.40%20045%7%9%35%13.00%20054%10%10%9%9.20%20064%5%5%-5%2.90%Mean4.80%10.40%11.80%14.40%11.06%Variance0.0001 0.0020 0.0027 0.0169 0.0021 Std Dev0.75%4.50%5.19%12.99%4.64%beta0.0710.83 0.64 0.79 RF,MktMkt,xx,RFMkt,yx,yy,RFCovariance0.0001 0.0017 0.0003 0.0013 0.0020 0.0005 Correlation0.4396 0.7226 0.8647 0.2232 0.2978 0.5227  Ex Post (Using historical sample data) Returns per Year for Each Security YearRFMarketxyPortfolio10%40%30%20%!Weights20025%18%15%18%15.80%20036%12%20%15%14.40%20045%7%9%35%13.00%20054%10%10%9%9.20%20064%5%5%-5%2.90%Mean4.80%10.40%11.80%14.40%11.06%Variance0.0001 0.0025 0.0034 0.0211 0.0027 Std Dev0.84%5.03%5.81%14.52%5.18%beta0.0710.83 0.64 0.79 RF,MktMkt,xx,RFMkt,yx,yy,RFCovariance0.0002 0.0021 0.0004 0.0016 0.0025 0.0006 Correlation0.4396 0.7226 0.8647 0.2232 0.2978 0.5227  Matrix Calculations for Portfolio Variance Ex AnteWeights' (1x4)Variance/Covariance Matrix (4x4)Weights (4x1)10%40%30%20%000010%00.0013 0.0027 0.0059 40%00.0027 0.0074 0.0135 30%00.0059 0.0135 0.0278 20%Weights*Var/Covar matrix (1x4)Weights (4x1)0.00000.00250.00600.012010%40%30%20%Variance of Portfolio (1x1)0.0052Standard Deviation of Portfolio7.21% Ex Post (using population data assumption)Weights' (1x4)Variance/Covariance Matrix (4x4)Weights (4x1)10%40%30%20%0.0001 0.0001 0.0003 0.0005 10%0.0001 0.0020 0.0017 0.0013 40%0.0003 0.0017 0.0027 0.0020 30%0.0005 0.0013 0.0020 0.0169 20%Weights*Var/Covar matrix (1x4)Weights (4x1)0.00030.00160.00190.004510%40%30%20%Variance of Portfolio (1x1)0.0021Standard Deviation of Portfolio4.64% Ex Post (using sample data assumption)Weights' (1x4)Variance/Covariance Matrix (4x4)Weights (4x1)10%40%30%20%0.0001 0.0002 0.0004 0.0006 10%0.0002 0.0025 0.0021 0.0016 40%0.0004 0.0021 0.0034 0.0025 30%0.0006 0.0016 0.0025 0.0211 20%Weights*Var/Covar matrix (1x4)Weights (4x1)0.00030.00200.00240.005710%40%30%20%Variance of Portfolio (1x1)0.0027Standard Deviation of Portfolio5.18% Annualizing Values To annualize returns and standard deviations from periodic returns and standard deviations use the following set of equations which assumes compounding.  EMBED Equation.3   EMBED Equation.3  Note: m is the number of periods per year. MonthlyAnnual w/ compoundingAnnual w/o compoundingMean return1.1196%14.2928%13.4352%Standard deviation4.3532%17.1313%15.0799% Note: Without the compounding effects, the annualized equations would be m times the periodic average return for the mean  EMBED Equation.3  and the square root of m times the periodic standard deviation for the annualized standard deviation EMBED Equation.3 . Required Return: Req(R) The minimum expected rate of return that investors require before they would invest in a given security taking into consideration the investment's underlying risk. The Required Rate of Return for security j equals the Nominal Risk-Free Return plus the Risk Premium given the Risk(s) of security j. Req(R)j = RFree + RPj The Nominal Risk-Free Return equals (1 + Real Risk-Free Return)*(1 + Expected Inflation) - 1 RFree = [1 + RReal] [1 + E(I)] - 1 therefore RFree = RReal + E(I) + [RReal * E(I)] This is called the Fisher Equation. The approximate Fisher Equation equals RFree = RReal + E(I) where the cross-product term is dropped should only be used during periods of very low inflation. Note: The International Fisher Equation is defined as:  EMBED Equation.2  where D = Domestic; F = Foreign Two common methods used to calculate required returns are: Security Market Line (SML): Req(Ri)  EMBED Equation.2  Note: The SML is designed for both a single asset or portfolio. Capital Market Line (CML): Req(Ri)  EMBED Equation.2  Note: The CML is designed to be used for efficient portfolios. Realized Return The actual return that the investor earns on the investment. A key calculation for realized return is holding period return (or total return). 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Fa$gd!u$`^`a$ & F h^gdR$a$gd!u$a$$a$$`^`a$L:M:N:O:P:c:d:e:f:g:l:m:u:::::::::::::::::::;; ;!;";#;$;3;;⿷꫿ޏ~zz~ulhh5>*CJ h>B\h*`h!ujh >h >EHUjYsE h >CJUVh}hh5\ hB\ h*`\ h!u5\h!uh!u\ h!u\jhh >EHUj2sE h >CJUVhhjhhU hh\ h >\h >h >H*\aJ':::";#;4;;;jk $$Ifa$gd $a$gd:$a$gd>B$a$gd!u$ & Fa$$h^ha$ ;;;jk"#$%&':;<=?@STUVWXklmn<DƼ詟蒅xkggh!uj h:h:EHUj(fG h:CJUVjPh:h:EHUja(fG h:CJUVj(h:EHU$j 4> h:CJUVmHnHujh:EHU$j3> h:CJUVmHnHujh:U h:56h:hhU hh56 hi%56&: Percentage measure relating all cash flows on a security for a given time period to its purchase price. Holding Period ReturnAnnualized Holding Period ReturnThe return over a specified holding period.The annualized average return over a specified holding period EMBED Equation.2  EMBED Equation.2  EMBED Equation.2  EMBED Equation.2 Note: T is the number of years the investment is held. Total Return equals yield plus capital gain (loss). Yield is the income component (for example, dividend yield for stock and coupon yield for bonds), which is greater than or equal to zero (i.e., it can be positive or 0). Capital gain (loss) is the change in price on a security over some time period which can be negative, 0, or positive. Ending (or Terminal) Value is all income at the end of the holding period (i.e., cash flows received such as stock dividends or bond coupons; reinvestment income from these cash flows; and the value of the security at the end of the holding period). Beginning value is the price paid for the security at time 0. Return Relative: The total return for an investment for a given time period stated on the basis of a starting point of 1. Return Relative = EMBED Equation.2  Cumulative Wealth Index: Cumulative wealth over time, given an initial wealth (WI0) and a series of returns on some asset.  EMBED Equation.2   EMBED Equation.2  Miscellaneous Return Measures Arithmetic Average Return Simple average equal to the sum of all returns divided by the number of years (i.e., the arithmetic average return is equal to the ex post expected return).  EMBED Equation.2  Geometric Average Return Compounded average return equal to the product of (1 plus the total return for each period); take the Nth root; then subtract 1.  EMBED Equation.2   EMBED Equation.2  When return variability exists, the arithmetic average will always be larger than the geometric mean and this difference grows as return variability increases. The geometric average return is approximately equal to the arithmetic average return less one-half the variance (i.e., EMBED Equation.3 ). The arithmetic mean is a better measure of average performance over single periods and the geometric mean is a better measure of the change in wealth over multiple periods. An alternative for projecting future performance over multiple time periods consists of a weighted average of the Arithmetic and Geometric Means  EMBED Equation.3  Where T is the number of used in the historical mean calculations and H is the number of years in the forecasted period.   $$Ifa$gd lkd$$Ifl0$04 la &> $$Ifa$gd lkd5$$Ifl0$04 la>?Wo $$Ifa$gd lkd$$Ifl0$04 laopmmmY$ & F h^a$gdR$ & F h^a$gdR$^a$$a$gd:lkdN$$Ifl0$04 laDo46E(+,.UVijklmn\]{neahfhh5CJ]jhfhaEHUjA haCJUVjhhaEHUj|0C haCJUVjhaUh*`h*`H*aJh*` ha56hajh:h:EHUj-)fG h:CJUVjhhU hh6 hh56 h:56hhh`X&456Um\tu?@ $`a$gd`X$^a$$`a$ $^a$gda$a$gda$^a$$a$$ & F h^a$gdR]pqrsu#$%&'(;<=>UVWjklmpht}pc}_[_[hfh./+jthJh./+EHUj+fG h./+CJUVjhJUh [hJjh*`h [EHUjv@ hhCJUVj`hhEHU$j> hhCJUVmHnHu hhH* hh5>* hJ5>*jhhUjhhEHU$jЂ}9 hhCJUVmHnHuhh#@p@ABCD$a$ $`^`a$gdf$a$gdf$ & F h^a$gdf$ & F h^a$gdR$ & F h^a$gdR ?@ACDhh hh\] hfhfh./+jhfhfEHUj.fG hfCJUVhfjhfU (/ =!"#$% dDd pJ  C A? 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 2 ?  2 3?  2 \ 2 \ 2 3\ Symbol- 2 `B=z 2 ` =z 2 `Y} 2 `x =zSymbol- 2 B 2 B  2 B  Times New Roman9- 2 ` ,9 & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q<bIfI  P2 =w j2  j2 ObjInfoMEquation Native X_913204577PFЫkuЫkuOle       !"#&)*-/0123456789:;<=>?@ABDGHIJMOPQRSTUVWXZ]^acdefghijklmnopqrstuvwxy{~+ j=1N " w j w k  k=1,k`"jN " j=1N "  jk []L!!  .PIC ORLMETA  CompObjQSfObjInfoT1  &4 & MathTypepPSymbol- 2 "s 2 s 2 vs 2 4s Times New Roman%- 2 jP 2 A 2 A 2 " A 2 B 2 A 2 A 2 SA 2 1BTimes New RomanU- 2 w 2  w 2 w 2 w Times New Roman!- 2 U2p 2 2p 2 12p 2 2p 2 2pTimes New Roman4- 2  1 2 2 2 l1PSymbol- 2 = 2 @+ 2  - 2 + 2 X-Times New Roman%- 2 z ( 2  ) 2 ( 2 b) Times New RomanU- 2 ,8 & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q*lJ,qJmJ s P2 =wEquation Native _957180798@WFЫkuЫkuOle $CompObjVX%f A2 s A2 +(1-w A ) 2 s B2 +2w A (1-w A )s A,B FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoY'Equation Native (_1101907311$o\FЫkuЫkuOle +xbI fI  P2 `"w ii=1N "  i2Lp   .1  &@0PIC [^,LMETA .CompObj]_CfObjInfo`E & MathType "-  Symbol- 2 "s Times New RomanX- 2 #i= 2 j= 2 i= 2  i= 2  sX 2  i= 2 j= 2 sX 2 j= 2 sX 2 SpTimes New Roman- 2 fP 2 ;R 2  R 2 oR 2 RSymbol- 2 = 2 } - 2 - 2  2 " 2 $ 2 & 2 "& 2 $& Symbol- 2  =zSymbol- 2 vTimes New RomanX- 2 ( 2  ) 2  ( 2 ) Times New Roman- 2 1p & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qII  ij =P s (R is "Equation Native F_957180982cFЫkuЫkuOle KPIC beLLE(R) i )(R js "E(R) j ) s=1S " []L!! L .1  `& XMETA NCompObjdfYfObjInfog[Equation Native \ & MathType "-<}< Times New Roman - 2 4r Times New Roman- 2 i= 2 Tj= 2 (i= 2 j= 2 (i= 2 ({j=Symbol- 2 7=Symbol- 2 h's 2 s 2 Is & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qtaIfI  ij = ij  i  j_1197875360ZjFp2kup2kuOle _PIC il`LMETA bL  .1  &@0 & MathType "-m U Symbol-2 [Symbol-2 ]Symbol- 2 "s Times New Roman- 2 #i= 2 j= 2 i= 2 Ft= 2 3 i= 2 j= 2 t= 2 j= 2 t= 2 T}Times New Roman)- 2 R 2 Q R 2  R 2 R 2 ~NSymbol- 2 = 2  - 2 W- 2  2 " 2 $ 2  2 " 2 $ 2  2 - Symbol- 2 =zSymbol- 2 vTimes New Roman- 2 B( 2  ) 2 h ( 2 $) Times New Roman)- 2 1pTimes New Roman- 2 2 & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q     ij =(R it "E(R) i )(R jt "E(RCompObjkmzfObjInfon|Equation Native }_11045701309qFp2kup2ku) j ) t=1T " []T[]L  .1  &@0 & MathType "-m Ole PIC psLMETA CompObjrtfU Symbol-2 [Symbol-2 ]Symbol- 2 "s Times New Roman- 2 #i= 2 j= 2 i= 2 Ft= 2 3 i= 2 j= 2 t= 2 j= 2 t= 2 T}Times New Roman)- 2 R 2 Q R 2  R 2 R 2 ~NSymbol- 2 = 2  - 2 W- 2  2 " 2 $ 2  2 " 2 $ 2  2 - Symbol- 2 =zSymbol- 2 vTimes New Roman- 2 B( 2  ) 2 h ( 2 $) Times New Roman)- 2 1pTimes New Roman- 2 2 & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfouEquation Native (_957181672a xFp2kup2kuOle V II  ij =(R it "E(R) i )(R jt "E(R) j ) t=1T " []T"1[]L _ PIC wzLMETA \CompObjy{fObjInfo| _  .1  @ &  & MathType "-! 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f4$$If!vh5 58595585#v #v8#v9#v#v8#v:V 40 +5 5859558544 f4$$If!vh5 58595585#v #v8#v9#v#v8#v:V 40 5 5859558544 f4$$If!vh5 58595585#v #v8#v9#v#v8#v:V 40 5 5859558544 f4$$If!vh5 58595585#v #v8#v9#v#v8#v:V 40 5 5859558544 f4$$If!vh5 58595585#v #v8#v9#v#v8#v:V 40 5 5859558544 f4$$If!vh5 58595585#v #v8#v9#v#v8#v:V 40 5 5CompObjfObjInfoEquation Native _1208933451Fp2kup2ku® 2R annual =1+2R Periodic () m "1 FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjfObjInfoEquation Native p̬  annual =  Periodic2 +1+2R Periodic () 2 [] m "1+2R Periodic () 2m_1208933490Fp2kup2kuOle CompObjfObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39qŸXoT 2R annual =m*2R Periodic ()() FMicrosoft Equation 3.0 DS EqEquation Native _1198576429Fp2kuluOle CompObjfuation Equation.39qŠP   annual = m   Periodic ()L ObjInfoEquation Native _1165218936FluluOle PIC LMETA  CompObjfObjInfo  .1  @@& & MathType "-@( &Times New Roman%- 2 `T( 2 `) 2 X( 2 ) 2 `( 2 `J ) 2 ( 2 G ) 2 ** 2 `"[ 2 `( 2 `)] 2 %[ 2 ( 2 )] 2 `1 2 1 2 `h1 2 l1 2 `1 2 1Symbol- 2 `+ 2 + 2 = 2 `U + 2 Y + 2 `+ 2 +Times New Roman%- 2 `RF 2 RF 2 ` RR 2  RR 2 `E 2 `kI 2 E 2 nI Times New Roman5- 2 D 2 F 2 n D 2 r F 2 D 2 F & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native |_1165218098}FluluOle PIC L     !"#$%&'()*+,-.03458:;<=>?@ABCDEFGILMNQSTUVWXYZ[\]^_`befghkmnopqrstuvwxyz|`0> (1+R Free,D )(1+R Free,F )=(1+R Real,D )(1+R Real,F )*[1+E(I D )][1+E(I F )]L4l @4  .1  & & MathTypePTimes New Roman- 2 `LE 2 `R 2 `RF 2 `0 E 2 ` R 2 `/RF Times New Roman- 2 i= 2  i= 2  MMETA  @CompObjfObjInfoEquation Native Times New Roman- 2 `Z( 2 `_) 2 ` [ 2 `> ( 2 `) 2 `%]Symbol- 2 `K= 2 `+ 2 `-Symbol- 2 ` b & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q8. =R Free + i [E(R M )"R Free ]L 4  ._1165218137FluluOle PIC LMETA 1   & & MathType "- Times New Roman- 2 LE 2 R 2 RF 2 ' E 2  R 2 lRF Times New Roman- 2 P 2  pp 2 `M 2 MTimes New Roman- 2 Z( 2 ) 2 5 ( 2 b)Symbol- 2 = 2 @+ 2 3- 2 [  2 [  2 ,[  2 [  2  2  2 , 2 Symbol- 2 P s 2 (s & "Systemn- FMicrosoft Equation 3.0 DS EqCompObj/fObjInfo1Equation Native 2_1052128255Fluluuation Equation.39q<T =R Free + p E(R M )"R Free  M []L Ole 6PIC 7LMETA 9CompObjHf  .1  @& & MathType "-Times New Roman- 2 LHPR2 Endingh2 4 Valueh2 ( Beginninghh2 ( Valueh Times New Roman- 2 NSymbol- 2 = 2  2  2 d 2  2  2 d 2 #- Times New Roman- 2 r(J 2 -/= 2 Q)J 2 1pTimes New Roman- 2 d1 & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qָ$vIpI HPR=EndingValueBeginningValue[]"1ObjInfoJEquation Native K_1052128267FluluOle OPIC PLMETA RCompObjafObjInfocL   .1  @& & MathType "-Times New Roman- 2 LHPR2 Endingh2 4 Valueh2 ( Beginninghh2 ( Valueh Times New Roman- 2 NSymbol- 2 = 2  2  2 d 2  2  2 d 2 #- Times New Roman- 2 r(J 2 -/= 2 Q)J 2 1pTimes New Roman- 2 d1 & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qНI8mI AnnualHPR=EndingValueBeginningValue[] (1/T) "Equation Native d _1197877345FluluOle iPIC jL1 L77  .1  2&2 & MathTypeP "-Bt2Times New RomanMETA lCompObj{fObjInfo}Equation Native ~c- 2 `.TR?_ 2 rCash~  2  Inflows  ~2 Purchase_    2 ice2 "Selling    2 Mice2 y$Purchase_    2 /ice2 `Purchase_    2 (icePSymbol- 2 `e=< 2 `$+< 2 y"-<Times New Roman- 2 Pr? 2  Pr? 2 -Pr? 2 p&Pr? & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q Go  HPR=CashInflowsPurchaseprice+SellingpricePurchaseprice"1L77  ._1197877425FluluOle PIC LMETA 1  2&2 & MathTypeP "-Bt2Times New Roman- 2 `.TR?_ 2 rCash~  2  Inflows  ~2 Purchase_    2 ice2 "Selling    2 Mice2 y$Purchase_    2 /ice2 `Purchase_    2 (icePSymbol- 2 `e=< 2 `$+< 2 y"-<Times New Roman- 2 Pr? 2  Pr? 2 -Pr? 2 p&Pr? & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjfObjInfoEquation Native _1197877549Flulu œ\ AnnualHPR=CashInflowsPurchaseprice+SellingpricePurchaseprice[] )1T() "1Ole PIC LMETA CompObjfLA;!A;  .1   5&5 & MathTypeP "-$>'}5Times New Roman%- 2 @Re~ 2 MRe~ 2 APr? 2 j/Pr? 2 A0Pr?Times New RomanA- 2 turn  2  lative  2 kRR__ 2 Cash~  2 Inflows  ~2 APurchase_    2 A"ice2 (Selling    2 1ice2 A'Purchase_    2 A2icePSymbol- 2 =< 2 =< 2 c%+< & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q cd RR=CashInflowsPurchasepriceObjInfoEquation Native _1127220348FluluOle +SellingpricePurchaseprice=1+HPRL'qGP'q o .1   $&#PIC LMETA CompObjfObjInfo & MathTypeEPSymbol-2 Bu (FPSymbol-2 C)EPSymbol-2 B(FPSymbol-2 C)EPSymbol-2 BM(FPSymbol-2 C#)Times New RomanL- 2 .CWI~ 2 uWI 2 TR?_ 2 BTR?_ 2 TR?_Times New Roman)- 2 fn 2 -"nPSymbol- 2 =< 2 L +< 2 +< 2 $+<Times New RomanL- 2 / 0 2 A1 2 2Times New Roman)- 2  1  2 1  2 1  2 . 2 . 2 . & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qh$ CWI n =WI 0 1+HPR 1 ()1+HEquation Native ,_1103012612FluluOle PIC LPR 2 ()"1+HPR n ()L'qGP'q o .1   $&# & MathTypeEPSymbol-META CompObjfObjInfoEquation Native 2 Bu (FPSymbol-2 C)EPSymbol-2 B(FPSymbol-2 C)EPSymbol-2 BM(FPSymbol-2 C#)Times New RomanL- 2 .CWI~ 2 uWI 2 TR?_ 2 BTR?_ 2 TR?_Times New Roman)- 2 fn 2 -"nPSymbol- 2 =< 2 L +< 2 +< 2 $+<Times New RomanL- 2 / 0 2 A1 2 2Times New Roman)- 2  1  2 1  2 1  2 . 2 . 2 . & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q" IpI =WI 0 RR 1 ()RR 2 ()...RR n ()_964526800FluluOle PIC LMETA hLp |p   .1  @` &  & MathType "-dhdPTimes New Roman- 2 LR 2 pR 2 N    !"#%(),./0123456789:<?@CFILMOPQRSTUWXYZ\Times New Roman- 2 Yt= 2 t= 2 NSymbol- 2 = 2  Symbol- 2 =zSymbol- 2 Times New Roman- 2 ( 2 ) Times New Roman- 2 1p & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qF\I_I 2R=(R tt=1T " )TL<` CompObj fObjInfo Equation Native  x_1051526677FluluOle PIC LMETA CompObj$f< M .1  &n & MathType "-]sTimes New Roman- 2 4G 2 bR Times New Roman)- 2 `K t= 2 Qt= 2 O`N 2 NSymbol- 2 = 2 (+ 2 - 2 S- 2 [- 2 b  2 Sb  2 [b  2  - Symbol- 2 Qp=zSymbol- 2 7Times New Roman- 2 ( 2  ) Times New Roman)- 2 s /=Times New Roman- 2 ;1 2 1 Times New Roman)- 2 Q1p 2  1p & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qՔ`~II 2G=(1ObjInfo&Equation Native '_1082357492FluluOle *+TR t ) t=1T " [] 1/T "1L 0\a  .1  &6 & 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"2m@8hH]%(A5 `!m@8hH]%(H` uxڕJAgf.ABEr`rFH@SP"ŽڤIq\# Vv̯u @9)Cpb2_3 id3WAۖs:X$Q::-(ipK? 3'ԜX *~zVo>[\~XX\_4zWW:06g4]]! ղkNf1u ĽD~FV{Dd hb  c $A? ?3"`?2fD55 `!fD5 @%|txڝKQǿo_ uX,$Uk@ĀtafZӹvUH"|迨0i?CA-XuBTy=2L7[QsU zih?ƻDd 8 hb  c $A? ?3"`?2e12cq0903 @h7T obIFHeA*CPD.#l8D0KfU1A~1vc G3@penR~,. v,\~ Ws߈k65* uyL`@2Wdf% NG0q OQLprK/ DYd++& B*a|WnΗ|>6T^,@ wbgxՆ b`aaX=\6b;'+KRs΁ePdk)YO`b/SummaryInformation(NDocumentSummaryInformation8V<CompObj[q< \ h t RETURN CALCULATIONS Valued Gateway 2000 CustomerNormalRichard J. Kish68Microsoft Office Word@j@~Njg@Ȳdƽ@Vu+՜.+,0  px   ]J3 RETURN CALCULATIONS Title  FMicrosoft Office Word Document MSWordDocWord.Document.89q<@< NormalCJ_HmH sH tH J@J Heading 1$$@&a$5B*hphL@L Heading 2$$@&a$6B*\hph@@@ Heading 3$$@&a$5>*D@D Heading 4$$@&a$ 56]:@: Heading 5$@&56P@P Heading 6$$@&a$56B*\hph@@@ Heading 7$$@&a$5hF@F Heading 8$@&5B*\hphDAD Default Paragraph FontVi@V  Table Normal :V 44 la (k(No List 4>@4 Title $1$a$5j@j o Table Grid7:V0g3g3Pf~  s"#(,09IJRVZewx}./ 0 5 8 E R S X \ j x y ~   " # $ + 2 9 : ; @ T d e f g m s t u v        ( ) xst|}"'EFKLSZ[\efmuvw$(,EFKOSklqtx !)/678CJKLX_`ahiry(=>GNOUX_acmnoptx| "*2:BCKQW]djkpv| 67bc !$'*.56;>BFIOPUX[^bhijkpv}   !'+01<DLT\dlmy #*,.89:>BFJSTY\`dhopux| $,45=CIOV\]bgiou{|}~ GHPQ`  -;<=DKRY]^_`defgklmnrst+,048<DLT\`abjrz #$%&*+,-123489:V]^_    " # $ , 4 < D H I J R Z b j n o p x !! !!!A!G!H!I!]!^!!!"""+","-"X"Y"Z"b"x""""""""""""""#$$$9%:%P%Q%%%%&&'&&&&&''8'9't'u''''-(l(m(~( ))))))))0*1*I*a*b*z******+,-W-X-Y----x......////20b0c011@222c3d3e3h300 0 0 0000000 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 00 000000 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 00000 0 0 0000 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 000 0 0 0000 0 0 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 00 00 00 0 00 0 0000000000000000 0000 00000000 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 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 0 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000000 0 00000 0 00 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 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 0 000 0 0 0 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 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 00 0 0 0 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 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 0000 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 0 0 0 0 0 0 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 0 0 0 0 0 0 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 0 0 0 0 0 0 00000000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00000000000000 0 0000000000 000 000000000 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0000000000(0(00000000 0 0 0 00000X ~ s t $KOklqt!$56;>OPXhiYux0*1*a*b***h3{00{00{00A@0 {00{00@c0Gd {00{00@z  {00{00@0 {00@0 {00@0 {00 @0 {00@0 {0 0 @0 @0 {0 0P@0 {00:{00{008{00 {00{00@"0&', {00 @"0&',/0 {00@0 {00=@0 {00@0 {0 0 @0 @0 {0 0@0O {002{0+0%,l{00 {002{002@R0 {00{00H0 {005H0 {00@0 {00H@0' {00@0 {0 0 Hb@0 E= F {0 0bE= F {00{00@0 {00PX@0 {00 @ {00[ @0 {00@ p0 {0 0 ^@ p0 {00 {0 0|]{00 {0T0U虳0{0T0U虳0 {0X0YX0 0  %#")/46L:;D]D#+06<FHIKU_ln A_@T[,B]u,Rx2GOu p"$<$B$t$$$$$%:%>%%%&&?&A&d&z&&&&&['y''(J(d((((() )p)))**3*V*j*****A+^+l+,J,d,,,,,- -p---..3.V.j.....E/c/////00!0(0M0u0001<1^1t1111112;2d2222 363L33333334E5l557: >o@D!"$%&'()*,-./12345789:;=>?@ABCDEGJLMNOPQRSTVWXYZ[\]^`abcdefghijkmopqrstuvwxyz{|}~C fz|       $ & ! 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