style="font-size:15px;"> [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 each year don't suffer this complication and are relatively straightforward.
The 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
Readers who are comfortable with their grasp of the material covered so far can skip the next two sections.
Equations [2-20] and [2-21] both define CFaIA. The user is free to choose the one he or she prefers.
At this point it's worthwhile to recall the assumptions made about NI2. Specifically, the Net Income in Year 2 is the sum of the Net Income in Year 1 plus ΔNI2, which is the incremental income produced by the NiROCE2 acting on Year 1's investment.
