PART ONE Business Valuation

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ness it seems silly to presume that you can accurately forecast cash flows as growing 8 percent in Year 11, 5 percent in Year 12, 7 percent in Year 13, 6 percent in Year 14, etc Nobody has a crystal ball that good It makes sense to say that the best we can do is assume that cash flows will grow at some reasonable average say 6 percent forever, value the remaining forecast cash flows accordingly, and discount them to net present value I should warn you that the next few pages have some mathematical detail Don t worry if you have some difficulty understanding the math My valuation spreadsheet in 7, which you can download from my Web site, will do the difficult calculations for you It s important, however, as I ve stated before when we ve encountered formulas and equations, that you develop an intuition of what these formulas are and why they work, which should empower you to use the valuation spreadsheet with more accuracy You ll find a rigorous mathematical derivation of the Gordon Model on my Web site, wwwabramsvaluationcom Once there, select Articles, then Articles in pdf, then download The Gordon Model: Derivation & Relation to PE Multiple More mathematically inclined readers would benefit by reading that first before proceeding The only skills required are algebra and the ability to work with exponents

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The Value of a Stagnant Perpetuity

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As the Gordon Model is the present value of a perpetuity with constant growth, it is a helpful preliminary step to discuss the value of a stagnant perpetuity A perpetuity is a cash flow that will pay a certain amount to you (and your heirs) forever A stagnant perpetuity is one with a constant cash flow forever, ie, growth is zero Let s say you are entitled to $100 per year forever The value of that perpetuity is the annual income divided by the appropriate market rate of return for that income If the rate of return is 10 percent, the value of the perpetuity would be $100/010 $1000

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CHAPTER 6 Valuation Using the Gordon Model

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We can check that by multiplying through the equation by 010, which would give us $1000 010 $100 In other words, at a value of $1000, a 10 percent annual return would mean we should receive $100 interest each year If the market rate of return for such a perpetuity is 8 percent instead, then its fair market value is $100/08 $1250 Again, we can check that by noting that an asset worth $1250 with an 8 percent annual rate of return would generate $100 per year income, $1250 08 $100

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Valuation Equations

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In Equation 61 we make the mathematical statement that the value of the perpetuity is equal to the economic cash flow that we forecast it will produce in the coming year, divided by the discount rate: FMV CFt r

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(61)

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This equation is fine for valuing a completely stagnant business for example, a firm with economic net income expected to stay at $100,000 forever and whose rate of return is, let s say, 25 percent The value would be $100,000/025 $100,000 4 $400,000 Note that dividing by 025 is mathematically equivalent to multiplying by 4 Thus, a 25 percent discount rate when there is no growth translates to a Price-to-Cash Flow multiple of 4 Now we must generalize the above formula in order to handle constant, perpetual growth (or decline), where g is the constant growth usually in the zero to 6 percent range If cash flow comes at the end of each year, then we use Equation 62, the End-of-Year Gordon Model formula, which is: FMV CFt 1 r g (62)

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Some observations on this formula: Notice the subscript t 1 in the numerator This means that we use next year s forecast cash flow, not the prior year s actual cash flow This causes much confusion,