Time Value of Money, NPV and IRR equation solving with the TI-86

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1 Time Value of Moey NPV ad IRR Equatio Solvig with the TI-86 (may work with TI-85) (similar process works with TI-83, TI-83 Plus ad may work with TI-82) Time Value of Moey, NPV ad IRR equatio solvig with the TI Other TI-Calculators... 2 Mauals... 2 Trasfer of Formulas Usig Cable... 2 NPV ad IRR... 2 The formula... 2 Expressio of the NPV Formula i TI-86 (ad possibly TI-85)... 3 Expressio of the Formula i TI-83, TI-83Plus (ad possibly TI-82)... 3 Usig the Equatio Solver i TI Solvig for NPV... 4 Solvig for IRR... 5 Time Value of Moey Calculatios... 6 The preset value of a auity formula... 6 The future value of a auity formula... 7 Future Value formula... 7 Future Value formula with cotiuous compoudig... 8 Effective Aual Rate... 8 Perpetuities ad Costat Growth Perpetuities... 9 EquatiosOTI86 1 of 9 Adrew Hall 2004

2 Time Value of Moey, NPV ad IRR equatio solvig with the TI-86 Other TI-Calculators This approach may work for the TI-85. You ca use a similar process with the TI-83 ad TI83Plus, so it may help you with the TI-82. O the TI-82 ad TI-83 variables i equatios appear to be limited to oe character; so you may eed to adjust the ames you use accordigly. Mauals Remember that pdf s of the relevat sectios of the mauals ca be dowloaded from the Course Web Page at Trasfer of Formulas Usig Cable Come to regular office hours with your calculator ad I will trasfer these equatios oto your TI-86 (ad if it works your TI-85!) NPV ad IRR The formula The formula which applies to both NPV ad IRR is { ( )} ( ) { } { ( ) }... { ( + ) } NPV C + 0 CF1 1 r + CF2 1 r + CF3 1 r + + CF = r Where C 0,CF 1,CF 2,CF 3...CF ca be positive or egative. For the IRR the formula assumes that NPV=0 ad looks as follows: { ( )} ( ) { } { ( ) } { ( ) } IRR IRR IRR IRR = C CF CF CF CF For coveiece, ad assumig problems o larger tha this o exams, let us work with the maximum umber of periods = 7 so =6: pv C1 C2 C3 C4 C5 C6 C = ( 1+r) ( 1+r) ( 1+r) ( 1+r) ( 1+r) ( 1+r) where r is either the Required Rate of Retur or the IRR (Iteral Rate of Retur); C0 is the iitial ivestmet; C1 is the cashflow at the ed of the first period; C2 is the cashflow at the ed of the secod period; NPV is either the value to be calculated for the et preset value or NPV is set to zero to calculate, r, the IRR. EquatiosOTI86 2 of 9 Adrew Hall 2004

3 Expressio of the NPV Formula i TI-86 (ad possibly TI-85) pv=c0+(c1/(1+r)^1)+(c2/(1+r)^2) +(C3/(1+r)^3) +(C4/(1+r)^4) +(C5/(1+r)^5) +(C6/(1+r)^6) O the mai scree: use 2 d ad ALPHA to eter the letter use 2 d ad ALPHA to eter the letters pv use ALPHA ad STO=> to eter a equals sig ALPHA C0 + Repeat (ALPHA C1 ( d ALPHA r)^1 ) six times. use the ENTER KEY to store expressio to expressio variable. Expressio of the Formula i TI-83, TI-83Plus (ad possibly TI-82) =i+(a/(1+r)^1)+(b/(1+r)^2) +(c/(1+r)^3) +(d/(1+r)^4) +(e/(1+r)^5) +(f/(1+r)^6) I have ot worked out how to use variable ames loger tha a sigle character i these calculators. It will oly really be relevat to the TI-82 users because TI-83 ad TI-83Plus already have the TVM_Solver fuctioality. Refer to the sectio above this oe o the Expressio of the NPV Formula i TI-86. For pv substitute ; for C0 substitute i ; for C1 a ; for C2 b,, for C6 f. Usig the Equatio Solver i TI-86 Oce the equatio has bee etered as a expressio i the TI-86, typig 2 d GRAPH will take you ito the equatio solver. Use CLEAR to clear ay text to the right of eq:. At the bottom of your scree are 5 fuctio ames each associated with oe of the fuctio keys. The MORE key brigs up the ext five fuctios ad aother MORE will brig up the ext five fuctios util it loops back to the first 5 fuctios. Use MORE to avigate util pv is oe of the fuctios offered. Use the fuctio key below pv to select the equatio you etered as pv= The lie should ow read eq:pv Hit the ENTER key. EquatiosOTI86 3 of 9 Adrew Hall 2004

4 The scree should cotai somethig like Exp=pv exp= C0= C1= r= C2= C3= C4= C5= C6= Boud=(-1E99,1E99) Up to C3 should be visible. Use the cursor up ad dow keys to look at the full set of values. If you cursor oto the top lie, the variables will disappear. Cursorig dow will make them reappear. Solvig for NPV If solvig for NPV eter the values of the variables C0, C1, r, C2, C3, C4, C5, C6. Use the (-) for egative values. Fill i somethig for each variable i.e. use zeros for values for which there is o data, for example Exp=pv exp= C0=-100 C1=0 r= 0.1 C2=0 C3=150 C4=0 C5=0 C6=0 Boud=(-1E99,1E99) Cursor to the secod lie exp= ad use the F5 key to ivoke SOLVE from the fuctios list. EquatiosOTI86 4 of 9 Adrew Hall 2004

5 The Net Preset Value will be calculated ad etered ito the secod lie as Exp=pv exp= C0=-100 C1=0 r= 0.1 C2=0 C3=150 Solvig for IRR If solvig for IRR eter the values of the variables exp (equals zero for the IRR), C0, C1, C2, C3, C4, C5, C6. Use the (-) for egative values. Fill i somethig for each variable i.e. use zeros for values for which there is o data, for example Exp=pv exp=0 C0=-100 C1=0 r= C2=0 C3=150 C4=0 C5=0 C6=0 Boud=(-1E99,1E99) Cursor to the fifth lie r= ad use the F5 key to ivoke SOLVE from the fuctios list. EquatiosOTI86 5 of 9 Adrew Hall 2004

6 The Iteral Rate of Retur will be calculated ad etered ito the fifth lie as Exp=pv exp=0 C0=-100 C1=0 r= C2=0 C3=150 Time Value of Moey Calculatios The preset value of a auity formula PVA PVA DUE A { 1 r} 1 r ( 1+ r) { 1 r } r( 1+ r) = A = ca be expressed to the calculator as: 1 *(1 + r) pva=(pmt*((1/(r/m)-(1/((r/m)*(1+(r/m))^(yrs*m))))*(1+(r/m)*beg) m is the umber of periods i a year yrs is the umber of years r is the aual iterest rate where (r/m) is the periodic iterest rate (yrs*m) is the umber of periods beg = 1 if the questio asks for a auity due beg = 0 if the questio asks for a auity I the solver, as with the NPV ad IRR, exp refers to the left had side of the equatio or the PVA i this case. As before you ca eter a value for exp ad calculate oe of the other variables: so if you wat to calculate the paymet give the PVA, yrs, m, r ad kowig the mode (beg/ed) you fill i exp=pva, yrs =umber, m= umber, r = decimal expressio of rate, ad beg =1 or beg=0. The go to the pmt lie ad hit F5 to solve. EquatiosOTI86 6 of 9 Adrew Hall 2004

7 The future value of a auity formula FVA FVA DUE A {( 1+ r) 1} ( 1+ r) = A { } = r ca be expressed to the calculator as: 1 r *(1 + r) fva=(pmt*((1+(r/m))^(yrs*m))-1)/(r/m)))*(1+(r/m)*beg) Where m is the umber of periods i a year yrs is the umber of years r is the aual iterest rate where (r/m) is the periodic iterest rate (yrs*m) is the umber of periods beg = 1 if the questio asks for a auity due beg = 0 if the questio asks for a auity I the solver exp refers to the left had side of the equatio or the FVA i this case. As before you ca eter a value for exp ad calculate oe of the other variables: so if you wat to calculate the paymet give the FVA, yrs, m, r ad kowig the mode (beg/ed) you fill i exp=fva, yrs =umber, m= umber, r = decimal expressio of rate, ad beg =1 or beg=0. The go to the pmt lie ad hit F5 to solve. Future Value formula FV = PV 1 + { rm} m ca be expressed to the calculator as: fv=pv*((1/(r/m)) ^(yrs*m) where fv is the future value pv is the preset value m is the umber of periods i a year yrs is the umber of years r is the aual iterest rate where (r/m) is the periodic iterest rate (yrs*m) is the umber of periods EquatiosOTI86 7 of 9 Adrew Hall 2004

8 I the solver exp refers to the left had side of the equatio or the FV i this case. As before you ca eter a value for the FV beside exp= ad calculate oe of the other variables. Eter values for the kow variables (if aual the let m=1). The go to the lie with the variable for which you wat to solve ad hit F5 to solve. Future Value formula with cotiuous compoudig * FV = PV r e ca be expressed to the calculator as: fvc=pvc*e^(r*yrs) where fvc is the future value uder cotiuous compoudig pv is the preset value uder cotiuous compoudig yrs is the umber of years r is the aual iterest rate e^ is obtaied usig 2 d ad LN keys. I the solver exp refers to the left had side of the equatio or the FVC (uder cotious compoudig) i this case. As before you ca eter a value for the FVC beside exp= ad calculate oe of the other variables. Eter values for the kow variables. The go to the lie with the variable for which you wat to solve ad hit F5 to solve. Effective Aual Rate Effective Aual Rate 1 + ca be expressed to the calculator as: ear=((1+(r/m))^m) 1 where ear is the effective aual rate yrs is the umber of years m { rm} 1 = m is the umber of periods i a year r is the aual iterest rate I the solver exp refers to the left had side of the equatio or the EAR i this case. Eter values for the kow variables. The go to the exp= lie ad hit F5 to solve. EquatiosOTI86 8 of 9 Adrew Hall 2004

9 Perpetuities ad Costat Growth Perpetuities PVP PVCGP CF 1 = A r is equivalet to if A= ad g=0 { CF ( r g) 1 } = IF we express the Preset Value Costat Growth Perpetuity to the calculator as cgp=pmt/((r/m)-(grw/m)) where pmt is either A or CF1 m is the umber of periods i a year r is the aual iterest rate grw is the aual growth rate I the solver exp refers to the left had side of the equatio or the PVCGP i this case. Eter values for the kow variables. The go to the exp= lie ad hit F5 to solve. To solve for the growth rate or the iterest rate or the paymet eter the kow variables go to the lie for the variable you wat to calculate ad hit F5 to solve. m should be equal to oe uless the paymet is occurrig more frequetly tha aually. grw should equal zero if the calculatio is for the simple perpetuity. EquatiosOTI86 9 of 9 Adrew Hall 2004

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