Final answer:
A shark's offer of $500,000 for 20% of a company values the company at $2,500,000. This valuation is based on proportional mathematics, where the offer for a fraction of the company is extrapolated to find the value of the entire company.
Step-by-step explanation:
When the shark offers $500,000 for a 20% stake in Joe's company, they are essentially valuing the entire company at $2,500,000. This is because if 20% is worth $500,000, then the full 100% (the whole company) would be valued at 5 times that amount (since 100 divided by 20 is 5).
The math behind this is simple; you divide the offer amount by the percentage the offer represents ($500,000 divided by 0.20 equals $2,500,000). In addition to the equity offer, the shark is asking for a 15% royalty on each unit sold, which means that for every sale, Joe would have to pay the shark 15% of the sale price as ongoing compensation.