Sensitivity, scenarios, and Monte Carlo

A DCF point estimate is a fiction. Two assumptions can swing the answer by 30% in either direction. The sensitivity table is what turns the model from a number into a defensible analytical product.

The two-variable sensitivity table

Pick the two assumptions with the highest leverage on the answer — typically WACC and the terminal growth rate (or exit multiple). Build a 5×5 grid showing the implied valuation at every combination. The 'middle' of the grid is your base case; the corners give you a defensible range.

        WACC
         9%    10%   11%   12%   13%
  g 1.5%  $145  $128  $114  $103  $94
    2.0%  $158  $138  $122  $109  $99
    2.5%  $174  $151  $132  $117  $105
    3.0%  $194  $166  $144  $126  $112
    3.5%  $220  $185  $158  $137  $120

The grid shows three things at once: the base case (centre), the range, and which variable has more leverage (whichever gives the wider spread when held constant). For most mature businesses, WACC moves the answer slightly more than g, but only slightly.

Scenarios — three coherent stories

Sensitivity holds one or two variables constant; scenarios change everything coherently. A bear case might combine slower revenue growth, lower margins, higher capex, and a higher discount rate — because all four track the same underlying story (competitive pressure, weakening demand). A bull case has the inverse. Run three scenarios — bear, base, bull — and report the 25th, 50th, 75th percentile of the cross-product.

Monte Carlo — when it helps and when it does not

A Monte Carlo simulation samples thousands of random combinations of inputs, producing a distribution of valuations. It looks impressive and adds spurious precision when the inputs are correlated (which they almost always are — high revenue growth is correlated with high margins, with high WACC if rates rise on overheating). The two-variable sensitivity table plus three named scenarios usually conveys the same uncertainty more honestly.