4.3. Survival Probability and Hurdle Rates

The previous sub-sections have discussed two popular implementations of the DCF approach for startup companies. The conceptual difference between the two approaches is the following:

• When working with hurdle rates, we implicitly assume a specific probability of default for each individual period. Consequently, the resulting present values of the annual cash flows are "expected values," in the sense that they already reflect the firm's failure probability.
• The alternative method with the survival probability applies a probability of default to the whole business plan. Consequently, the initial valuation (FCF @ "normal" WACC) reflects a potential valuation, which is then multiplied with the failure probability.

When consistently implemented, both methods should technically lead to the same result. We can show this using the previous example. Remember from before:

• Using the hurdle rates, we have estimated a firm value of 1.87 million.
• We also know from before that the valuation that ignores the specific risks of the startup was 4.82 million (going concern valuation).
• Finally, we have assumed that the firm will pay a liquidation dividend of 0.5 million in the case of failure.

With this information, we can now compute the implied survival probability. From the previous subsection we know:

Firm value = Going concern value × survival probability + Liquidation value × (1 - survival probability).

Solving this expression for survival probability yields:

Survival probability = $$\frac{\text{Firm value}-\text{Liquidation value}}{\text{Going concern value}-\text{Liquidation value}}$$

When we plug the previous valuations in this expression, we find a survival probability of roughly 32%:

Survival probability = $$\frac{1.87 - 0.5}{4.82 - 0.5}$$ = 31.7%.

Put differently, based on our assumptions, our analysis using hurdle rates is consistent with a valuation framework that assigns a success probability of 31.7% to the whole business plan.

As we have seen in the previous section, this overall success probability can be decomposed into 8 sources of success. If we assume that the firm does equally well on all 8 dimensions, a joint success probability of 31.7% implies that each individual dimension has an expected success probability of more than 86%!

This also helps us to put the hurdle rates we used into perspective. While an initial hurdle rate of 30% might seem large, we now see that the implied probability of default is still fairly small.