Why can a small terminal-growth change move a valuation so much?

Locate the valuation date and first cash flow

NYU Stern’s terminal-value material describes a stable-growth approach for cash flows beyond an explicit forecasting period and emphasizes that the inputs must remain sustainable. Its separate discussion explains why sensitivity grows as the assumed growth rate approaches the discount rate.

Let H be a fictional valuation date. The first modeled cash flow is 100 exactly one year after H. Later cash flows grow by g each year and are discounted at r per year. All are in the same currency and use consistent nominal assumptions. No real business, security or forecast is being valued.

Calculate three cases with the next cash flow fixed

Under the positive-cash-flow model with r greater than g, value at H is 100/(r−g). Hold r at 8%. At g=0%, value is 1,250. At g=2%, it is 1,666.666667. At g=4%, it is 2,500. All three cases start with the same first payment of 100.

Moving growth from 2% to 4% raises this modeled value by 50%, although the input changed by only 2 percentage points. The comparison deliberately holds the next cash flow fixed to isolate denominator sensitivity. A full operating forecast might require more reinvestment to support higher growth; that cost cannot simply be omitted.

Compare the infinite model with ten payments

For the 2%-growth case, the first ten cash flows have present value at H equal to the sum of 100×1.02^(t−1)/1.08^t for t=1 through 10. That finite sum is approximately 725.616204. The infinite model’s remaining value after those ten payments, discounted back to H, is approximately 941.050462.

Using unrounded values, the finite-payment value plus the discounted tail reconciles to 100/(0.08−0.02), or 1,666.666667 rounded to six decimal places. More than half of this stipulated value belongs to payments after the first ten years. That observation describes dependence on a long tail, not confidence in those distant cash flows.

Avoid a date or growth double count

Because 100 is already the cash flow one year after H, do not multiply it by 1.02 again before using 100/(0.08−0.02). If 100 instead meant the cash flow at H, the next cash flow would be 102 and the numerator would differ. Label the date rather than silently changing it.

If H is five years after today, the 2%-growth terminal value must still be discounted five years to today:1,666.666667/1.08^5 is approximately 1,134.305328. This is only the present value of the modeled terminal component, not the value of any earlier cash flows.

Respect the model’s mathematical boundary

The series converges in this positive-rate example because the discounted growth factor 1.02/1.08 is below 1. Setting perpetual g equal to or above r makes that positive-cash-flow series fail to converge. A negative algebraic denominator is not a valid finite negative value for the same perpetuity.

A finite life, changing margins, capital needs, failures, inflation or discount-rate changes require a different cash-flow model. A growth input should not be raised merely to match a desired price. This sensitivity worksheet does not identify a defensible growth rate for any issuer.

Method, sources, and limits

The numerical cases, finite-series reconciliation and timing control are original hypothetical calculations checked on 27 October 2026. They are an explanation of assumptions, not a market valuation or return forecast. AI-assisted drafting and arithmetic checking are not qualified human valuation review.