There is a certain subtlty that is hard to explain! ... I will try to be more clear here with an example (it is based on financial arbitrage):
If the market price of gold is $1000/oz today, and you think it is going to go to $900/oz tomorrow.. how much would you pay for it today?
The correct answer is $1000/oz.. which may seem counterintuitive - but if you could get it for any less, you'd just flip it and make an easy buck.
If you can buy it today but can't sell it until tomorrow how much would you pay? - You would pay $900/(1+riskfree) ... however, the market has already agreed that the price tomorrow is expected (on average) to be $1000*(1+riskgold) - which is a lot higher than your exectation -> otherwise why would people be willing to pay $1000 today? (on average the market pays tomorrows price/(1+riskgold)). When valuing using market pricing - you should use the market's assumption where possible - that means price at time n = 1000*(1+riskgold)^n. Note that the present value after discountng for time and risk is 1000.. (time n price) / ((1+riskgold)^n)
Now, here is some more practical proof! A market exists to lock in future prices today: the futures market.
1. Given that you can deliver gold at time 1, or time 2, etc. a company can lock in the price that will be paid for that future gold at time 0.
2. The price that will be paid in the futures market must be $1000*(1+riskfree)^n - (if prices were lower, people would just by gold at time0, sell a futures contract for time 1, deliver the gold at time 1 and get more than the risk-free rate of interest out of the whole transaction)
3. discounting that to the present time results in a present value of $1000/oz, -as there is no risk (apart from counterparty) in the transaction you should discount the guranteed cashflows at the risk-free rate
One more riddle: how else can you value a mine with a certain reserve than: the PV of the mineral (must be the reserve * the market price) less the PV of costs (use the risk-free rate for conservatism)
Anyway, comments welcome.
