The new investor is willing to pay $100M for 25% of the company. That means they think the company will be worth $400M after they invest $100M. That means the current value of the company is ~$300M, not ~$400M.
No. What someone is willing to pay and what something intrinsically is worth is not the same thing. If the stated presumption is that the company was worth $400M before the $100M cash infusion, then it follows that it must be worth $500M after that.