Bitcoin as well as other cryptocurrencies are all plagued by the impact from bifurcation. Since the marginal cost of bifurcation is theoretically zero, it causes the coin holders to doubt on the existence of the coins intrinsic value. This paper suggests a normative dual-value theory to assess the fundamental value of Bitcoin. We draw on the experience from the art market, where similar replication problems are prevalent. The idea is to decompose the total value of a cryptocurrency into two parts: one is its art value and the other is its use value. The tradeoff between these two values is also analyzed, which enlightens our proposal of an image coin for Bitcoin so as to elevate its use value without sacrificing its art value. To show the general validity of the dual-value theory, we also apply it to evaluate the prospects of four major cryptocurrencies. We find this framework is helpful for both the investors and the exchanges to examine a new coins value when it first appears in the market.