Max Coin Toss Willingness to Pay

This question presents a simple coin-flipping gamble with asymmetric payoffs, where a gain arrives in the future while a loss occurs immediately. The candidate is asked to determine the fair maximum entry price for the game, taking into account both the probability of each outcome and the timing of the associated cash flows. Because the payoffs are small and the setup is stylized, it sits in the core expected-value toolkit used in many quant, trading, and risk interviews rather than in a specific asset-pricing niche.

Solving it leans on computing expected values, understanding present value and discounting, and correctly handling different maturities with different interest rates. The interviewer is watching whether the candidate cleanly separates the probabilistic structure from the time-value-of-money calculation, applies the correct discount factors to each dated payoff, and is comfortable interpreting the result as a willingness-to-pay threshold. Attention to sign conventions, timing (immediate vs future), and consistent use of rates is also being tested, as well as the ability to articulate each step without algebraic shortcuts.

What it tests

Whenever a problem involves uncertain future payoffs and different timing for cash flows, the core structure is to compute the expected value of each possible outcome, then discount each to present value using the appropriate interest rate for its time horizon. This approach separates the randomness (probabilities and payoffs) from the time value of money (discounting). The principle holds because the value of a risky future cash flow is not just its expected amount, but its expected present value—each outcome must be weighted by its probability and then discounted according to when it occurs. This ensures that all cash flows are compared on a common, present-value basis, reflecting both risk and time. The pattern generalizes to any setting where payoffs are probabilistic and occur at different times, regardless of the specific numbers or context.