We can define the time varying growth rate as follows:
Where: ●
g 0 = the initial growth rate at time t = 0. ● λ = is the decay rate, controlling how quickly g(t) declines over time. ● e -λt = is the exponential decay term, ensuring that the growth rate decreases as time progresses. o For this to hold Or must be greater than g. For terminal value calculations, the relevant growth rate is the one that applies at the end of the explicit forecast horizon n , and possibly over an additional buffer period t . Rather than assuming a constant growth rate in perpetuity, a natural decline over time is acknowledged. This long-run stabilized growth rate is denoted:
Where:
● n = the number of explicitly forecasted years (e.g., 25 out to 2050). ● t = an additional buffer period where growth rate continues to decay before stabilizing.
We define g∞ as the long-term growth rate that the model approaches under exponential decay. This reflects the idea that growth slows and converges to a stable rate rather than remaining constant or falling to zero. Substituting g∞ into the standard Gordon Growth expression gives the modified terminal value formula:
Together these elements constitute the complete ONPV formula as:
Where:
• ONPV: Outcomes-based Net Present Value. • t : Time period, where t 0 is the initial investment. • N : the total number of periods. • Or : the outcomes-based discount rate.
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