Formulae for perpetuity due and annuity due 
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 A 2-step approach
    1) Treat it as a normal perpetuity or annual
    2) Multiply the above result by (1+R)

   pv(perpetuity due) = pv(perpetuity) *(1+R)

   pv(annuity due) = pv(annuity) *(1+R)

   fv(annuity due) = fv(annuity) *(1+R)

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Excel sign convention 
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There are two ways to explain the Excel sign conversion. 

1) Accounting approach: cash inflows vs cash outflows 
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 Example #1: we deposit $100 for 1 year. If the interest 
             rate is 10%, how much is the value 1 year later?

        When deposit $100, it is a cash output

     =fv(0.1,1,0,-100)   => 110   (a positive value)

2) Excel is designed this way
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  positive future value  -- > negative present value 

  negative future value  -- > positive present value 

  positive present value -- > negative future value 

  negative present value -- > positive future value 

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Definition of NPV (Net Present Value) and NPV rule 
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Method I: 
           NPV = PV(all benefits) - pv(all costs)

Method II: 
          if cash outflow is defined as a negative value
             cash inflow  is defined as a positive value

          NPV = PV(all cash flows)

  NPV Rule: for an independent project

        if NPV(Project) > 0 accept
        if NPV(Project) < 0 reject

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Excel's npv() is actually a pv function 
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Example 1: 
    If We invest $100 today and will get $120 at the end of year one. 
    if the discount rate is 10%, what is the NPV?

   1) Manually calculate the result =(120)/(1+0.1) -100 = 9.090909091
   2) Using the NPV function()
        we enter the following two values at A1 and A2
           -100
            120

           =NPV(0.1,A1:A2)   ==> 8.26 

     The correct formula should be 
           =NPV(0.1,A2)+A1   ==> 9.09 

Example 2: 
time cashflow
0   -100
1    40
2    30
3    40
4    20
5   -10
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