Answer: A valuation multiple is a ratio of some measure of a firm's scale to the value of the firm.
Step-by-step explanation:
The Law of One Price does indeed allow for the determination of the value of the new firm using the value of the existing firm as they are identical. The value of a firm is also estimated based on the value of comparable ones.
It is also true that companies can be similar in many respects but still be different in size and scale.
Valuation multiples however, are not ratios of some measure of a firm's scale to the value of the firm but ratios of financial metrics in the company that can be used for analysis and comparison.