Where: •
NPV: Net Present Value.
• t : Time period, where t 0 is the initial investment. • n : the number of periods. • C t : the costs / benefits or cash flow in period t (this can be positive or negative). • r : the discount rate • C 0 : the initial investment, or cost at t 0 .
When calculating NPV, a TV calculation is used to quantify the costs/benefits or cash flows beyond the forecasted period. The perpetuity formula is a common approach and is defined as follows:
Where: •
TV = Terminal value at the end of the forecast period • C n = Costs/benefits (e.g., free cash flow) in the last forecasted period • g = perpetual growth rate of free cash flows (assumed to be constant) • r = the discount rate • n = the last year of the projected period. o This is based on the Gordon Growth Model 18 .
The terminal value then needs to be brought back to present value and is therefore incorporated into the NPV formula as follows:
The first term represents the sum of the discounted costs/benefits (e.g., cash flows) over the forecasted period, the second term represents the present value of the terminal value, and the third term represents the initial investment. The efficacy of the NPV model depends on accurate assumptions, particularly for the terminal growth rate component ( g ) and the discount rate ( r ). Given that all cash flows are discounted using r , which captures the cost of capital, opportunity cost and risk, in its various forms, the correct choice of r is critical. The same can be said for the choice of g within the TV calculation, given its relative weight to the overall value. The growth rate within TV typically depends on long-term economic conditions and Gross Domestic Product (GDP) is often used. This paper discusses certain limitations of static discount rates ( r ), however, many of the arguments put forward are also interrelated to the choice of constant growth rates (g).
Although the Internal Rate of Return (IRR) remains a common metric, this paper focuses on NPV because it provides a clearer and more decisive basis for capital allocation. IRR suffers from two
18 In financial valuation techniques, such as the NPV, or DCF analysis, the Gordon Growth Model is commonly used to estimate the terminal value (TV) of a company, which represents the value of all future cash flows beyond a certain projection period.
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