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and defined as:

      [2-1]

      At this point it may be worthwhile to comment on why ROCE uses NOPAT. The reason is: It excludes the impact of interest income or expense and since the cause of interest is the debt on the balance sheet (and it is already included in the denominator as part of Interest Bearing Debt), using NI would, in a sense, be double counting because it understates the NOPAT by an amount equal to the after-tax impact of interest. To the extent there is any interest expense, NiROCE would be less than ROCE, and vice versa. If there isn't any interest, the NiROCE and ROCE would be the same.

      Underlying Assumptions

      In their simplest form, the Envelope Equations are centered around the notion that Net Income and Cash Flow are driven by investments in property, plant, equipment, software, and the like and do not reflect the results of other operational improvements. The assumptions that are important to understand are:

      • The underlying assets that generated Year 1's Net Income will continue to do so for the estimating horizon and beyond.

      • Investments made during Year 1 don't provide an immediate return but take time, and the incremental Net Income from these investments 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 generated by the investments made in Year 1.

      • Like Year 1's Net Income, the investments that generated Year 2's Incremental Net Income will also produce a stream of equal Net Incomes during the subsequent years.

      Applying the Equations

      Since using the Envelope Equations involves a series of steps, it may be helpful to start the discussion with the end in mind and define the process involved in using the equations before defining the variables and developing the key relationships. Hopefully, by doing so the reader will have an appreciation of where all of this is headed.

      As stated earlier, the Envelope Equations provide a way of making rapid estimates of Net Income and Cash Flow. They are built around the concepts of Net Investments (NetInvest), Investment Rate (IR), and Net Income Return on Capital Employed (NiROCE).30 To use the equations, it's necessary to have (or make) estimates for the IR and NiROCE, assume some initial level of Net Income, and then sequentially apply the appropriate equation to calculate the Net Incomes and Cash Flows for the years in question. The way it works is as follows:

      • Establish the Investment Rate (IR) and Net Income Return on Capital Employed (NiROCE) that are to be used.

      • Start with or make an estimate of the Current Year's (Year 1) Net Income:

      Net Income in Year 1 = NI₁

      • Using the Investment Rate calculate the Net Investment (NetInvest) during Year 1:

      NetInvest ₁ = (NI₁)(IR₁)

      • With this information, estimate the Cash Flow for Year 1:

      CFaIA ₁ = NI₁ − NetInvest₁ ± NetInt₁ ± ΔWC₁

      • Using the NiROCE the company expects from the Net Investment made during Year 1 (the return on the investment is expected to take place the following year), calculate the incremental Net Income (ΔNI₂) for the following year (Year 2):

      ΔNI₂ = (NetInvest₁)(NiROCE₂)

      • The Net Income for Year 2 is the sum of NI₁ and ΔNI₂.

      NI ₂ = NI₁ + (NetInvest₁)(NiROCE₂)

      • With this information, estimate the Cash Flow for Year 2:

      CFaIA ₂ = NI₂ − NetInvest₂ ± NetInt₂ ± ΔWC₂

      • Repeating the procedure provides estimates of subsequent years' Net Incomes and Cash Flows.31

      At this point the reader shouldn't be troubled by the fact that the relationships given in the above procedure are not understood. In fact it would be surprising if this wasn't the case. All of the above relationships are a subset of the Envelope Equations. To give the reader some idea of what the complete set looks like and what will be developed in subsequent sections of this chapter and Appendix D, the complete set is shown here.

      [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 ± NetInt ± ΔWC

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

      [2-40]

      [2-43]NIgn = (IR₍n _{− 1)})(NiROCEn)

      With the assumptions defined and the application process illustrated, it is now time to develop the Envelope Equations. This process begins with a discussion of Net Investments.

      ⧉ Net Investments 32 , 33

      The equation for Cash Flow after Investing Activities that was introduced in Chapter 1, modified to include the impact of interest income and interest expense (NetInt), is:

      [2-2]CFaIA = NI + D & A ± NetInt ± ΔWC − Investments

      Usually investments are considered to be a “positive” or a good thing for a business. To accommodate this notion Equation [2-2] can be rewritten as:

      [2-3]CFaIA = NI − (Investments − D & A) ± NetInt ± ΔWC

      Now, when Investments > D & A, the term (Investments − D & A) is positive. The term (Investments − D & A) is also known as “Net Investments” where

      [2-4]NetInvest = Investments − D & A

      Substituting NetInvest for the term (Investments − D & A), Equation [2-3] becomes:

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

      The magnitude and sign of the Net Investments term is of interest because it may give an indication of what's going on with the cash flow–producing assets of the business. For example, three ways of looking at this term are:

      1. If Investments = D & A, then the net investment is zero. This may indicate the company is replacing its cash flow–producing assets at the same rate as they are wearing out or being depleted.

      2. If Investments < D & A, then the net investment is negative (adding to the Cash Flow) and the cash flow–generating assets may not be being replaced as quickly as they are being written off.

      3. If Investments > D & A, then the net investment is positive and the management team is making investments that in total are greater than the sum of depreciation and amortization and thereby increasing the company's future cash flow–generating assets.

      However, a lot of other things could also be going on. For example: If NetInvest equals zero, it doesn't necessarily follow that the cash flow–producing assets are simply being replaced. It could be that the existing assets aren't in need of replacement

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