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Incorporating the Investment Rate, IR, into the expression for Cash Flow is done as follows.

Recall Equation [2-5]:

[2-5]CFaIA = NI − NetInvest ± NetInt ± ΔWC

This equation can be generalized by defining CFaIA for Year n as a function of the NI and NetInvest in Year n:

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

Equation [2-16] is the Fourth Envelope Equation and is very significant because it allows the user to calculate the Cash Flow after Investing Activities directly by knowing the Net Income, Net Investment, Net Interest, and Change in Working Capital.

Substituting the results of Equation [2-8] for NetInvestn in Equation [2-16] gives CFaIA for Year n as a function of NI, the Net Income in Year n, and IR, the Investment Rate.

[2-17]CFaIAn = NIn − (NIn)(IRn) ± NetIntn ± ΔWCn

Factoring,

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

Equation [2-18] is the Fifth Envelope Equation and it allows one to calculate the Cash Flow after Investing Activities by knowing the Net Income, Investment Rate, and Net Interest and Change in Working Capital. It differs from Equation [2-16] by using the Investment Rate in place of the Net Investment.

In summary, starting with a level of Net Income and values for the Investment Rate and Return on Capital Employed, by using equation [2-8] the Net Investment for any year can be calculated. Then with either Equation [2-12] or [2-14] Net Income for any year is obtained. The Cash Flow for any year is given by using Equation [2-16] or [2-18]. Together these five equations will enable the user to quickly create a stream of pro-forma net incomes and cash flows and constitute five of the seven equations known as the Envelope Equations. The remaining two equations are developed in Appendix C and discussed in a later section of this chapter.

Going through the process of deriving somewhat general equations like those previously listed is a useful exercise because it provides insights into the Envelope Equation framework and the range of their application. However, the methodology involved in calculating Net Income and Cash Flow after Investing Activities using the Investment Rate, IR, and Net Income Return on Capital Employed, NiROCE can take some time to fully appreciate. Therefore, before the remaining Envelope Equations are discussed (sixth and seventh), it's important to make sure that the assumptions underlying these equations are well understood. This will be accomplished by working through the process of applying them over a three-year period, doing away with the n's, and using numbered years in their place.44