Expected Value of Continuing a Program

Why Evaluate the Decision at the Milestone?

At a development milestone, the relevant question is not how much a program has cost so far. Those expenditures have already occurred. The decision is whether the expected consequences of continuing from this point are more favorable than the expected consequences of stopping now. That comparison combines the chance of future outcomes with the costs and values attached to each outcome.

The analysis is conditional on what is known at the milestone. For example, a probability of technical success should describe the chance of the defined future success outcome given the evidence available now. The earlier material on conditional versus cumulative probability of success is important here: a probability from the beginning of development is not automatically the appropriate probability for a decision made partway through the program.

Definition: The incremental expected value of continuing is the expected net payoff from continuing, conditional on information available at the milestone, minus the net payoff from stopping at that milestone. A positive value favors continuing under an expected-payoff decision rule; a negative value favors stopping.

Set Up the Payoff Comparison

List the possible outcomes after continuing and assign each an appropriate conditional probability. For each outcome, specify the future program value and the additional costs that would be incurred after the decision. Separately specify the net payoff from stopping, including any salvage value or closeout cost if these matter.

For a simple case with outcomes indexed by $j$, let $q_j$ be the probability of outcome $j$ conditional on the milestone information, and let $Y_j$ be the net payoff from continuing if that outcome occurs. Let $S$ be the net payoff from stopping. Then:

\Delta EV = \sum_j q_jY_j-S, \qquad \sum_j q_j=1.

If $R_j$ is the future program value and $C_j$ is the additional cost in outcome $j$, then $Y_j=R_j-C_j$. Thus, when these quantities are already expressed on a comparable valuation basis:

\Delta EV = \sum_j q_j(R_j-C_j)-S.

All values must use the same currency and valuation basis. If the analysis has already adjusted future amounts for timing, use those adjusted amounts consistently; do not compare a future value at one date with a cost measured on a different basis. Costs incurred before the milestone are sunk for this choice and should not be counted as costs of continuing. Costs that would be incurred after the milestone belong in the continuation payoff, whether they occur in every outcome or only in particular outcomes.

Decision rule: If the decision criterion is to maximize expected monetary payoff, continue when $\Delta EV>0$, stop when $\Delta EV<0$, and treat $\Delta EV=0$ as a tie on expected monetary payoff. This rule does not by itself account for risk aversion, capital constraints, or strategic considerations unless those are represented in the payoffs or the decision criterion.

Why the Calculation Works

The calculation follows from the definition of expected value for a discrete set of outcomes. Conditional on the information available at the milestone, the expected payoff from continuing is the probability-weighted average of its outcome-specific payoffs. Subtracting the stopping payoff gives the expected advantage of one action over the other.

E(Y_{\text{continue}}\mid I) = \sum_j P(j\mid I)Y_j = \sum_j q_jY_j, \qquad E(Y_{\text{continue}}\mid I)-Y_{\text{stop}} = \sum_j q_jY_j-S.

Here $I$ denotes the information available at the milestone, and $Y_{\text{stop}}=S$ when stopping has a fixed payoff. If stopping also has uncertain consequences, its expected payoff must be calculated using its own possible outcomes rather than treated as a fixed number. The comparison remains between the two conditional expected payoffs.

The payoff structure should reflect the decision being made. In particular, success must be defined by the relevant endpoint and estimand, and the probability must refer to that same event. If the outcomes are not exhaustive, the omitted outcomes need to be added; if they overlap, the probabilities and payoffs need to be reformulated so each possible path is counted correctly.

Worked Example: A Single Success Probability and a Common Cost

Hypothetical data. At a milestone, a team estimates a 0.35 conditional probability that continuing will lead to the defined development success outcome. Reaching that outcome would produce a future program value of $240 million. Continuing requires an additional $45 million regardless of whether the program succeeds. If it does not succeed, assume no future program value. Stopping has a net payoff of $0.

The two outcomes are success, with probability 0.35, and no success, with probability $1-0.35=0.65$. The program value is $240 million only in the success outcome; the $45 million cost applies in both outcomes. Therefore:

\begin{aligned} EV_{\text{continue}} &=0.35(240-45)+0.65(0-45)\\ &=0.35(195)+0.65(-45)\\ &=68.25-29.25\\ &=39.0\text{ million dollars}. \end{aligned}

Equivalently, the expected program value is $0.35(240)=84$ million dollars, and the common additional cost is $45 million, giving $84-45=39$ million dollars. Since stopping is worth $0, the incremental expected value of continuing is $39-0=39$ million dollars. Under the stated expected-monetary-payoff criterion, continuing is favored.

Worked Example: Costs Differ Across Outcomes

Hypothetical data. Continuing has a 0.40 conditional probability of success. In the success path, the future program value is $190 million and additional costs are $70 million. In the no-success path, there is no future program value, but $25 million in additional costs are incurred before the program can be closed. Stopping now has a net payoff of $10 million, including any relevant salvage value net of closeout costs.

The net continuation payoffs are $190-70=120$ million dollars after success and $0-25=-25$ million dollars after no success. Thus:

\begin{aligned} EV_{\text{continue}} &=0.40(120)+0.60(-25)\\ &=48-15\\ &=33\text{ million dollars},\\ \Delta EV&=33-10=23\text{ million dollars}. \end{aligned}

Continuing has an expected payoff of $33 million, which is $23 million greater than stopping. The $25 million failure-path cost is weighted by the 0.60 probability of that path; it is not appropriate to subtract the full $25 million as though it were incurred in every outcome. Conversely, the success-path cost is included in the success payoff and is weighted by the success probability.

Derive and Use a Probability Threshold

A threshold makes explicit how the decision depends on the estimated probability of success, given the assumed payoffs. Suppose success has net payoff $A$, failure has net payoff $B$, and stopping has payoff $S$. If the conditional probability of success is $p$, the incremental expected value is:

\Delta EV=pA+(1-p)B-S.

When $A>B$, continuing is favored exactly when:

p>\frac{S-B}{A-B}.

This follows by rearranging $pA+(1-p)B-S>0$: expanding gives $pA+B-pB>S$, so $p(A-B)>S-B$. Since $A-B>0$, dividing by $A-B$ preserves the inequality. The threshold is meaningful only alongside its assumptions about payoffs and the probability definition. It is not a universal probability-of-success cutoff.

Worked Example: Finding the Success-Probability Threshold

Hypothetical data. If the program succeeds, its value is $300 million and the additional success-path cost is $80 million. If it fails, there is no program value and the additional cost is $20 million. Stopping now has a net payoff of $4 million. Let $p$ be the conditional probability of success at this milestone.

The net success payoff is $A=300-80=220$ million dollars. The net failure payoff is $B=0-20=-20$ million dollars. The threshold is:

p^*=\frac{S-B}{A-B} =\frac{4-(-20)}{220-(-20)} =\frac{24}{240} =0.10.

Thus, continuing is favored when the conditional success probability exceeds 0.10, under these payoff assumptions. For a hypothetical estimate of $p=0.28$:

\begin{aligned} EV_{\text{continue}} &=0.28(220)+0.72(-20)\\ &=61.6-14.4\\ &=47.2\text{ million dollars},\\ \Delta EV&=47.2-4=43.2\text{ million dollars}. \end{aligned}

The calculated incremental expected value is $43.2 million in favor of continuing. The threshold does not say that success is likely, nor does it establish that the probability estimate is reliable. It says only that, for the stated payoffs, probabilities above 0.10 produce a larger expected monetary payoff from continuing.

Diagnostics, Alternatives, and Limitations

A calculation can be arithmetically correct but decisionally misleading if its inputs do not describe the actual choice. Before relying on the result, check that the outcome probabilities are conditional on the milestone information, correspond to clearly defined outcomes, and sum to one. Check that each cost is counted once and only if it would be incurred under the relevant path. Confirm that stopping includes any applicable salvage value and closeout cost, and that all monetary amounts are on a consistent valuation basis.

The decision also depends on the quality of its estimates. Uncertain probabilities, future costs, and program values can make the estimated $\Delta EV$ unstable. Recalculate it under plausible alternative inputs or show which assumptions have the greatest influence. This is a sensitivity check on the current decision comparison, not a substitute for using calibrated probabilities and defensible outcome definitions.

Expected value is one approach to comparing actions. A probability-of-success estimate alone is not a decision: a low probability can still favor continuation if the success payoff is sufficiently large and the failure cost sufficiently small. Likewise, a high probability can favor stopping if future costs are large relative to future value. A threshold calculation summarizes the same payoff comparison in terms of the probability needed to favor one action. A decision tree is useful when several sequential outcomes and decisions must be represented explicitly; for a simple milestone comparison, the weighted-payoff formula may be clearer.

A common mistake is to reason, “The probability of success is 0.35 and the program value is $240 million, so the expected value is $84 million; therefore, continuing is favorable.” The $84 million is only the expected program value, not the expected net payoff. The additional $45 million cost must also be included, and the resulting $39 million must be compared with the payoff from stopping. Another mistake is to include costs already incurred before the milestone. Those costs matter for understanding the program’s history, but they do not change the incremental consequences of choosing to continue or stop now.

The comparison has limits. It represents the outcomes, values, and costs included in the model; omitted outcomes or unrepresented strategic considerations cannot be recovered by more precise arithmetic. Expected monetary payoff also treats equal expected dollars as equivalent, regardless of how risk is distributed. If the decision maker’s objectives, constraints, or risk preferences require another criterion, those considerations must be addressed explicitly rather than assumed to be captured by this calculation.

Check Your Understanding

For each question, identify the relevant payoff comparison before interpreting the result. Solutions are included after the questions.

A program has a 0.20 conditional probability of success. Success yields $100 million in value, and continuing costs $15 million in either outcome. Stopping is worth $0. What is the incremental expected value of continuing?
Why should a cost already incurred before the milestone generally be excluded from the incremental comparison?
A success path has a net payoff of $80 million, a failure path has a net payoff of $-$10$ million, and stopping is worth $5 million. What success-probability threshold makes continuing preferable?
A team uses a probability of success measured from the start of development to decide whether to continue after a milestone. What should it check before using that probability?

Solutions. (1) The expected value from continuing is $0.20(100-15)+0.80(0-15)=17-12=5$ million dollars. Stopping is worth $0, so the incremental expected value is $5 million and continuing is favored under the stated criterion. (2) The cost was paid under either current choice and cannot be avoided by stopping now; it is not an incremental consequence of continuing. (3) With $A=80$, $B=-10$, and $S=5$, the threshold is $p^*=(S-B)/(A-B)=(5+10)/(80+10)=15/90=0.1667$. Continuing is favored when the conditional success probability exceeds about 0.167. (4) It should verify that the probability is conditional on the evidence available at this milestone and refers to the defined future outcome. A cumulative probability from the start may not represent the remaining probability after the milestone has been reached.