To a significant extent, this book is about Cash Flow since cash is the basic resource required by a business. In the long run Net Income is the only source of cash and so its importance cannot be overemphasized.
Having made an unequivocal statement about the source of cash, the next step in understanding the power of the Envelope Equations is to incorporate IR and ROCE into the Net Income and Cash Flow equations, which is done by starting with the ultimate driver of Cash Flow – Net Income.
The assumptions are: The Net Income for Year n is NIn and during the year the company makes NetInvestn at a rate of IRn of Year n's Net Income. Since it takes time for investments to produce results this investment provides a return of ROCEn + 1 in the following year.42 Given these assumptions and Equation [2-8], the amount of Year n's Net Income invested in assets that will generate future cash flows is:
[2-8]NetInvestn = (NIn)(IRn)
Since NetInvestn provides a return of ROCE(n + 1) the following year, then the Incremental Net Income in Year n + 1 will be:
[2-10]ΔNI(n + 1) = (NetInvestn)(NiROCE(n + 1))
The NI in Year n + 1 is the sum of the NI from Year n and ΔNI in Year n + 1. Therefore, the NI in Year n + 1 is:
[2-11]NI(n + 1) = NIn + ΔNI(n + 1)
Substituting the results of Equation [2-10] into Equation [2-11] creates an expression for NI in terms of NetInvest and ROCE:
[2-12]NI(n + 1) = NIn + (NetInvestn)(NiROCE(n + 1))43
Equation [2-12] is the Second Envelope Equation. It enables the calculation of Any Year's Net Income by simply knowing the Current Year's Net Income, Net Investment, and Net Income Return on Capital Employed, thus enabling the calculation of the Cash Flow after Investing Activities for the year in question.
The Investment Rate IR can be incorporated into Equation [2-12] by substituting the results of Equation [2-8] for the term NetInvest in Equation [2-12].
[2-13]NI(n + 1) = NIn + (NIn)(IRn)(NiROCE(n + 1))
Factoring [2-13] gives an equation that defines NI in terms of IR and NiROCE.
[2-14]NI(n + 1) = (NIn)[1 + (IRn)(NiROCE(n + 1))]
Equation [2-14] is the Third Envelope Equation and differs from Equation [2-12] in the sense that it calculates a Future Year's Net Income by using the Current Year's Net Income in combination with the Investment Rate and Net income Return on Capital Employed.
In Year n + 1, investments are also being made and the magnitude of the NetInvest in Year n + 1 is:
[2-15]NetInvest(n + 1) = (NI(n + 1))(IR(n + 1))
which will prove to be a useful expression when estimating the Incremental Net Income and so forth in Year n + 2.
Equations [2-12] and [2-14] are powerful tools for doing quick estimates of a stream of Net Incomes that are the result of investments with expected returns. These equations together with Equation [2-8] constitute three of a set of five equations that are useful for predicting Net Income. The other two equations have to do with Cash Flow. They will be derived in the following section.
⧉ Incorporating IR into the expression for Cash Flow after Investing Activities
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
⧉ NI and CFaIA – A Sequential Year-by-Year Analysis
Once more, here is a summary of the requirements and process involved in order for these equations to give meaningful results.
• The Net Income for Year 1 is assumed or known.
• Historical values for the Investment Rate (IR) and Net Income Return on Capital Employed (NiROCE) are assumed to be reasonable estimates for future years or arbitrary numbers based on some rationale.
• The underlying assets that generated Year 1's Net Income will continue to do so for the estimating horizon.
• Net Investments (NetInvest) made during Year 1 don't provide an immediate return but take time and this incremental Net Income is generated in Year 2.
• Year 2's Net Income is the sum of the repeating Year 1's Net Income and the Incremental Net Income in Year 2.
• Like Year 1's Net Income, the incremental assets that generated Year 2's Incremental Net Income will also produce a stream of equal Net Incomes during subsequent years.
• The Cash Flow estimates for