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operative equations are:

      [2-8]NetInvestn = (NIn)(IRn)

      [2-12]NI₍n _{+ 1)} = NIn + (NetInvestn)(NiROCE₍n _{+ 1)})

      [2-14]NI₍n _{+ 1)} = (NIn)[1 + (IRn)(NiROCE₍n _{+ 1)})]

      [2-16]CFaIAn = NIn − NetInvestn ± NetIntn ± ΔWCn

      [2-18]CFaIAn = (NIn)(1 − IRn) ± NetIntn ± ΔWCn

      These equations can be also classified according to the variables used and in the case study at the end of this chapter are referred to as such.

      Net Investment (NetInvest) Model or Form

      Equations [2-12] and [2-16] constitute the Net Investment Model.

      [2-12] NI₍n _{+ 1)} = NIn + (NetInvestn)(NiROCE₍n _{+ 1)})

      [2-16] CFaIAn = NIn − NetInvestn ± NetIntn ± ΔWCn

      Investment Rate (IR) Model or Form

      Equations [2-14] and [2-18] constitute the Investment Rate Model.

      [2-14]NI₍n _{+ 1)} = (NIn) [1 + (IRn)(NiROCE₍n _{+ 1)})]

      [2-18]CFaIAn = (NIn)(1 − IRn) ± NetIntn ± ΔWCn

       Year 1:

      Recalling Equation [2-8],

      [2-8]NetInvestn = (NIn)(IRn)

      if NI₁ is the Net Income for Year 1 in a company that has a Investment Rate IR₁, then by Equation [2-8] the Net Investment in Year 1 is:

      [2-19]NetInvest₁ = (NI₁)(IR₁)

      The Cash Flow in Year 1 is given by the use of Equation [2-16]:

      [2-16]CFaIAn = NIn − NetInvestn ± NetIntn ± ΔWCn

      Substituting subscripts in Equation [2-16] the Cash Flow after Investing Activities, CFaIA for Year 1 in terms of Net Income and Net Investments is:

      [2-20]CFaIA₁ = NI₁ − NetInvest₁ ± NetInt₁ ± ΔWC₁

      Or by using Equation [2-18] and making suitable substitutes for n the CFaIA in Year 1 is calculated knowing the Net Income and the Investment Rate IR₁45

      [2-21]CFaIA₁ = (NI₁)(1 − IR₁) ± NetInt₁ ± ΔWC₁

       Year 2:

      Year 2's Net Income can be calculated with either Equation [2-12] or [2-14] after making suitable adjustments to the subscripts.46

      [2-22]NI₂ = NI₁ ± (NetInvest₁)(NiROCE₂)

      Or:

      [2-23]NI₂ = (NI₁)[1 + (IR₁)(NiROCE₂)]

      In Year 2 investments are made at a rate IR₂, therefore the Net Investment in Year 2, NetInvest₂, is:

      [2-24]NetInvest₂ = NI₂(IR₂)

      And following the same logic that resulted in Equations [2-20] and [2-21] the CFaIA₂ for Year 2 is calculated by:

      [2-25]CFaIA₂ = NI₂ − NetInvest₂ ± NetInt₂ ± ΔWC₂

      or

      [2-26]CFaIA₂ = (NI₂)(1 − IR₂) ± NetInt₂ ± ΔWC₂

       Year 3:

      Repeating the above process for Year 3 produces the Net Income in Year 3 in terms of Net Investments and Net Income Return on Capital Employed:

      [2-27]NI₃ = NI₂ + (NetInvest₂)(NiROCE₃)

      or Year 3 Net Income in terms of the Investment Rate and Net Income Return on Capital Employed:

      [2-28]NI₃ = (NI₂)[1 + (IR₂)(NiROCE₃)]

      The Year 3 CFaIA equations are:

      [2-29]CFaIA₃ = NI₃ − NetInvest₃ ± NetInt₃ ± ΔWC₃

      [2-30]CFaIA₃ = (NI₃)(1 − IR₃) ± NetInt₃ ± ΔWC₃

      and so on.

      ⧉ NI and CFaIA – The General Model

      The preceding section provided a progressive year-by-year development of a year-specific set of the Envelope Equations that can be used to predict Net Incomes and Cash Flows for such things as a first cut at a multiyear business plan. The rigor involved is probably adequate for most readers. However, there are always those who also like to see the general treatment or at least would like to have it available for reference. The equations for Year n and Year n + 1 will hopefully be familiar since they have been derived in detail in the preceding sections. The equations for Years n + 2 and so on are the subject of Appendix D.

      If NIn is the Net Income for Year n in a company that has a Net Investment Rate of IRn and a Net Income Return on Capital Employed of NiROCEn, then in Appendix D it is demonstrated that:

      For Year n

      Net Income in Year n = NIn

      [2-8]

      Net Invest n NetInvestn = (NIn)(IRn)

      [2-16]

      Cash Flow n CFaIAn = NIn − NetInvestn ± NetIntn ± ΔWCn

      [2-18]

      Or CFaIAn = (NIn)(1 − IRn) ± NetIntn ± ΔWCn

      For Year n + 1

      [2-15]

      Net Invest n + 1 NetInvest₍n _{+ 1)} = (NI₍n _{+ 1)})(IR₍n _{+ 1)})

      [2-12]

      Net Income n + 1 NI₍n _{+ 1)} = NIn + (NetInvestn)(ROCE₍n _{+ 1)})

      [2-14]

      Or NI₍n _{+ 1)} = (NIn)[1 + (IRn)(NiROCE₍n _{+ 1)})

      Cash Flow n + 1 CFaIA₍n _{+ 1)} = NI₍n _{+ 1)} − NetInvest₍n _{+ 1)} ± NetInt₍n _{+ 1)}

      [2-31]

      ± ΔWC₍n _{+ 1)}

      [2-32]

      Or

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