Final answer:
The post-money valuation of the firm is $12.5 million, and the pre-money valuation is $7.5 million, derived from the $5 million venture capital investment for 1 million new shares and the total number of shares post-investment.
Step-by-step explanation:
To calculate the post-money valuation of a firm after venture capital investment, you sum the investment received with the pre-money valuation. In this case, a venture capitalist is investing $5 million for 1 million newly issued shares. To find the post-money valuation, you first need to acknowledge that the $5 million investment for 1 million shares means the price per share is $5. Since the company will have 2.5 million shares outstanding after the investment (1 million original + 500,000 from angel investors + 1 million from the VC), the post-money valuation would be $5 per share times 2.5 million shares, equaling $12.5 million.
The pre-money valuation is the valuation of the firm before the venture capital investment. This can be found by subtracting the venture capital investment ($5 million) from the post-money valuation, which gives us a pre-money valuation of $7.5 million. This represents the value attributed to the company before the new investment is taken into account.