A construction company is considering taking on a new project. The total project cost is $5 million, and there is a 70% chance that the project will be completed on time and within budget, resulting in a profit of $3 million. However, if the project is delayed, the company will incur additional costs of $1 million for every month of delay. There is a 30% chance of delay, and the expected delay is 2 months. The company has the option to purchase penalty insurance for $500,000, which will cover any additional costs incurred due to project delays. Should the company purchase penalty insurance, and what is the expected value of the investment with and without the insurance?

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