A company looking for venture capitalist funding is deciding on the design of its operating system (OS) for its new phone. The first option is to simply buy the OS from another company

This would result in sales of either 10,000 units if the market is not crowded with similar phones, or sales of only 3,000 units if the market is crowded. If the company decides to design its own OS, the phone would have sales of 70,000 units if the OS was popular, but sales of only 2,000 if the OS was a failure. Suppose that to recoup the cost of designing their own OS the company would need to sell twice as many phones as when they simply buy the OS for the profit from the scenarios to be equal. Which option should the company choose if the probability that the market is crowded is 50% and the probability that the OS is popular is 75%?

EMV of buy OS is .5(3000 ) + .5(10000 ) = 6500 units
EMV of design OS is .75(70000 ) + .25(2000 ) = 53,000 units
However, the firm needs to sell twice as many designed OS phones as bought OS phones for equal profit, so that means 6500 bought OS phones are worth 13,000 designed OS phones. Since 13,000 is less than the 53,000 expected sales from the designed OS, the company should design their own OS.