Capacity decisions get made on a single-scenario spreadsheet far more often than they should. One demand number, one price, one NPV, one signature. The method below takes about an hour longer and routinely changes the answer.

The setup

A factory can either install a full second line now for 48 million, or install half the capacity now for 27 million with the option to add the second half in two years for 26 million. Demand over the next five years is uncertain: 45 per cent chance of high growth, 35 per cent moderate, 20 per cent flat.

Step 1: draw the tree, not the spreadsheet

Decision nodes are squares, chance nodes are circles, and the tree is drawn left to right in the order events actually happen. The discipline of drawing it is most of the value, because it forces you to be explicit about what you learn before you must commit.

[Invest now?] --- Full line (48M) ---o--- High  (0.45) --> NPV  +62M
                                      |--- Mod   (0.35) --> NPV  +18M
                                      |--- Flat  (0.20) --> NPV  -14M

              --- Staged (27M) ------o--- High  (0.45) --> [Expand?] -- yes --> +54M
                                      |                              -- no  --> +31M
                                      |--- Mod   (0.35) --> NPV  +21M
                                      |--- Flat  (0.20) --> NPV   -3M

Step 2: roll back from the right

At the expansion decision under high demand, expanding gives 54 and not expanding gives 31, so the branch value is 54. Now compute expected values at the chance nodes:

Full line:  0.45(62) + 0.35(18) + 0.20(-14) = 27.9 + 6.3 - 2.8 = 31.4M
Staged:     0.45(54) + 0.35(21) + 0.20(-3)  = 24.3 + 7.35 - 0.6 = 31.05M

The two are within one per cent of each other. On expected value alone this is a coin flip — which is exactly the situation where single-scenario analysis produces confident, arbitrary decisions.

Step 3: look at the downside, not just the mean

The expected values tie, but the distributions do not. The full line loses 14 million in the flat case; the staged option loses 3 million. If a 14 million loss would breach a covenant or force a layoff, the two options are not equivalent regardless of what the mean says. This is where expected value must give way to the organisation's actual risk tolerance.

Expected value of perfect information

If you knew demand in advance, you would pick the best branch every time: 0.45(62) + 0.35(21) + 0.20(-3) = 33.45M. Subtract the best decision without information (31.4M) and EVPI is about 2.05 million. That is the ceiling on what any market study, pilot, or delay is worth. Spending 3 million on research to resolve this uncertainty is provably a bad trade.

Step 4: sensitivity, done properly

Vary one input at a time across a plausible range and record where the preferred decision flips. Here, the switch point is the probability of flat demand: below about 17 per cent the full line wins, above it the staged option does. That single sentence is more useful to a board than the entire NPV table, because now the discussion is about one judgement everyone can have an opinion on.

What to watch for

  • Probabilities pulled from thin air. If nobody can defend 0.45, run the analysis over a range instead and report the switch point.
  • Ignoring the option value. The staged path is worth more than its expected value suggests precisely because it lets you decide later with better information. If your tree has no later decision node, you have probably modelled it wrong.
  • Sunk costs in the branches. Only future cash flows belong in the tree.