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FIN 504 Financial Management

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					FIN 504: Financial
Management
   Lecture 1: Introduction and
   Mathematical Review
Course Material

        Instructor: Larry Schrenk
         (lschrenk@ubalt.edu)
        Course Web Page
         (http://home.ubalt.edu/ntsbschr/FIN%2050
         4/fin_504.htm)
        Textbook
        WebTycho




 2                                FIN 504: Financial Management
Calculations and Your
Calculator
Calculations and Your Calculator

        Required Functions:
         +, -, ×, ÷, (, ), e, ln, xy, 1/x, -/+ and a few
         memories
          A Possible Ambiguity: ln, log, logx, lng
          Use of Financial Functions




 4                                       FIN 504: Financial Management
Calculations and Your Calculator

        Working Financial Problems (Inside-
         Out)


                  100      1     
            PV       1           ?
                  .08  1.08   
                                10
                                 



 5                                 FIN 504: Financial Management
Calculations and Your Calculator

        Use of Calculator Parentheses
        Use of Calculator Memories




 6                                FIN 504: Financial Management
Mathematical Review

       Summation
       Exponents
       Logarithms and e
       Equations in One Unknown
       Equations in Two Unknowns
       Suggestions for Solving Word
        Problems

7                               FIN 504: Financial Management
Summation
Summation


       Single
             n

            x
            i 1
                   i



       Double
             n     m

            x y
            i 1 j 1
                        i   j




9                               FIN 504: Financial Management
Exponents
Exponents

     Description

      aaaa          a  a   n


      a a
       1



      a 1
       0



     a = base, n = exponent

 11                                  FIN 504: Financial Management
Exponents

     Inverses

          1

      a 
        x x
              a a
                 1




 12                   FIN 504: Financial Management
Exponents

     Rules for Exponent Operations

      a m  a n  a m n

      a 
               n
                        mn
          m
                   a

          n     1
      a         n
                a


 13                                   FIN 504: Financial Management
Exponents

    Some Notational Equivalents:

                  1
           a a a2   0.5

                  1
       4
           a a a4   0.25


           etc.

14                                  FIN 504: Financial Management
Exponents

     Solving an Equation for a Base (a)

         x  an
          1          1      n                   1
         x  a
          n
                   
                   n n
                          a  a1  a  a  x
                            n                   n




        15  a 4
              1                 1
        15  a  a  15  1.97
              4                 4




 15                                                 FIN 504: Financial Management
Exponents

    Caution!


      2  5   2  5   10
             3       3     3


      2  5  250
             3


      10  1, 000
         3




16                             FIN 504: Financial Management
Exponents

        Exponents in Financial Equations
         Discounting and Compounding
         Growth
         Forecasting
         Inflation




17                               FIN 504: Financial Management
Logarithms and e
Logarithms and e

         Description
           Natural Logarithms versus Logarithms to
            a Base
           e = 2.718281828…




 19                                   FIN 504: Financial Management
Logarithms and e

     Inverse Operations

      ln(ea )  a

          ln  a 
      e              a




 20                        FIN 504: Financial Management
Logarithms and e

     Rules for Logarithmic Operations

          
      ln a n  n ln  a 

      ln  a  b   ln  a   ln b 

         a
      ln    ln  a   ln  b 
         b



                                       a                         FIN 504: Financial Management
 21                                 ln    ln  a   ln  b 
                                       b
Logarithms and e

     Rules for e
       Since ex is an exponential expression, it
        follows the same rules as any other
        exponent function.




                           a                         FIN 504: Financial Management
 22                     ln    ln  a   ln  b 
                           b
Logarithms and e

     Solving an Equation for an Exponent

           b  ax
           ln  b   ln a x 
           ln  b   x ln  a 
                 ln  b 
            x
                 ln  a 


 23                                FIN 504: Financial Management
Logarithms and e

     Solving an Equation for an Exponent

          5  3x
          ln  5   ln 3   
                             x


          ln  5   x ln  3
                ln  5 
           x               1.46
                ln  3


 24                                 FIN 504: Financial Management
Logarithms and e

     Caution!
             ln  5       5
                       ln  
             ln  3       3
             ln  5 
                         1.465
             ln  3 
                5
             ln    0.511
                3
 25                               FIN 504: Financial Management
Logarithms and e

         Logarithms in Financial Equations
           Discounting and Compounding
           Growth
           Forecasting
           Inflation




 26                                FIN 504: Financial Management
Equations in One Unknown
Equations in One Unknown

    To solve for one unknown variable, use
     mathematical operations to isolate that
     variable alone on one side of the
     equation.




28                              FIN 504: Financial Management
Equations in One Unknown

    EXAMPLE: Solve for b.

     a  b2  c
     a  c  b2
      ac  b b  ac




29                           FIN 504: Financial Management
Equations in One Unknown

    EXAMPLE: Solve for b.

     20  b 2  5
     20  5  b 2
     b  20  5  15  3.9




30                           FIN 504: Financial Management
Equations in One Unknown

    Note that you cannot always do this, i.e., find a
     ‘closed form solution’, in all cases, e.g., you
     cannot solve the following expression for r:

              100       200       50
        20                    
             1  r  1  r  1  r 
                              2        3




    Excel has the ‘Goal Seek’ and ‘Solver’
     functions for this type of problem.

31                                    FIN 504: Financial Management
Equations in One Unknown

        Equations in One Unknown in Finance
         Many of the problems we have looked at
          already are equations in one unknown,
          and we shall use this frequently when we
          come to the sections on the time value of
          money.




32                                   FIN 504: Financial Management
Equations in Two Unknowns
Equations in Two Unknowns

    A system of two equations in two unknowns
     often has the form:

         2 x  2 y  12
         4 x  y  16



34                                FIN 504: Financial Management
Equations in Two Unknowns

    You can think of these graphically:




35                               FIN 504: Financial Management
Equations in Two Unknowns

    To solve:
      1) Solve either equation for one variable.
      2) Substitute that into the other equation, so
       that it becomes one equation with one
       known.
      3) Solve for that unknown.

      4) Use that unknown to get an equation that
       solves for the other unknown.


36                                   FIN 504: Financial Management
Equations in Two Unknowns

    To solve:
                 2 x  2 y  14 (1)
                 4 x  y  16 (2)
     1) Solve either equation for one variable.

                  2 x  2 y  14
                  2 x  14  2 y
                  x  7  y (3 from 1)

37                                        FIN 504: Financial Management
Equations in Two Unknowns

    To solve: 2 x  2 y  14 (1)
                4 x  y  16 (2)
     2) Substitute that solution into the other equation,
       so that it becomes one equation with one known.

                4  7  y   y  16 (3 into 2)




38                                       FIN 504: Financial Management
Equations in Two Unknowns

    To solve: 2 x  2 y  14 (1)
                4 x  y  16 (2)
     3) Solve for that unknown.
                4  7  y   y  16 (3 into 2)
                28  4 y  y  16
                28  3 y  16
                3 y  16  28
                3 y  28  16 (multiply by -1)
                3 y  12
                y  4 (4)
39                                                FIN 504: Financial Management
Equations in Two Unknowns

    To solve: 2 x  2 y  14 (1)
                4 x  y  16 (2)
     4) Use that unknown to get an equation that
       solves for the other unknown.
                4 x  4  16 (4 into 2)
                4 x  12
                x3
                 x  3, y  4

40                                        FIN 504: Financial Management
Equations in Two Unknowns

    Equations in Two Unknowns in Finance
      Portfolio Problems
      Immunization




41                            FIN 504: Financial Management
Suggestions for Word
Problems
Suggestions for Word Problems

     Two Stages
       Story
       Formula

   Use the Type of Data as Information
   Break the Larger Problem into Smaller
    Steps.
   Ask if Everything Makes Sense. Do You
    Have a Reasonable Answer?

 43                          FIN 504: Financial Management

				
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