Question

Your startup has a new product that you can sell to a large company for $20m, or continue to develop yourself. If you develop yourself, you will need to invest $12m in your company.

If you develop yourself, your analysis suggests there is a 70% chance your product will succeed, and a 30% chance you fail. If you fail, your product will be worthless and you will earn gross profits of $0.

If you succeed, there is a 35% chance you will earn gross profits of $10m, a 40% chance you will earn gross profits of $50m, and a 25% chance your product will go viral. If it goes viral, there is a 60% chance it will earn gross profits of $80m and a 40% chance it will earn gross profits of $120m.

As an expected value maximizer, what is the expected value of your optimal decision?

Answer 1

Calculating the expected value of self-developing the product results in a net value of $21.25 million, which is greater than the fixed sale offer of $20 million. Thus, continuing to develop the product in-house is the optimal decision.

Step-by-step explanation:

To calculate the expected value of the startup's optimal decision, we must first determine the expected value (EV) of developing the product themselves, and then compare it with the fixed sale offer of $20m.

The expected value of the startup's success scenarios when developing the product itself can be calculated as follows:

• A 35% chance to earn $10m in gross profits (EV = 0.35 * $10m = $3.5m)
• A 40% chance to earn $50m in gross profits (EV = 0.40 * $50m = $20m)
• A 25% chance the product goes viral which leads to:

Add these values together for the total expected value from success:

EV(success) = $3.5m + $20m + $12m + $12m = $47.5m

Now, we apply the probability of overall success (70%) and failure (30%):

• Successful development EV = 0.70 * $47.5m = $33.25m
• Failure development EV = 0.30 * $0 = $0

Total EV of self-development = Successful development EV + Failure development EV = $33.25m + $0

After subtracting the initial investment of $12m:

Net EV of self-development = $33.25m - $12m = $21.25m

Comparing the net EV of self-development with the fixed sale offer:

• Sell to a large company for a fixed $20m
• Continue to develop in-house with a net EV of $21.25m

Therefore, the optimal decision based on expected value maximization is to continue to develop the product themselves, since $21.25m > $20m.