Valuing coins as the sum of the underlying asset and a perpetual American put option

Coins may be valued as the sum of the value of the component metals, plus a perpetual American put option with an exercise price equal to the face value. For widely circulated coins, the value of the component metals is sufficiently low compared to the face value that immediate exercise is optimal. For bullion coins the put option has only a trivial value. However, in some cases the value of the component metals is sufficiently close to the face value that the put option has a non-trivial time value. An example is provided of the 1966 Australian 50 cent coin.