Question

The EuropoTron europium (Eu) mine is currently mothballed (i.e., shut down). The EuropoTron mine cannot re-start production until one year from now. EuropoTron knows with certainty that the market price of europium per ton will be $930 next year. EuropoTron’s marginal cost of production is MC(q) = 10 + q, where cost is measured in dollars per ton of europium and q is measured in tons of europium. EuropoTron’s reserve is X = 900 tons. Assume that a competitor, MegaEuropo, is offering EuropoTron $400,000 for the nowdormant mine. If EuropoTron applies an annual discount rate of r = 0.05, should the company accept MegaEuropo’s offer and sell the mine now? Or should it start up the mine, which will allow it to extract europium next year and earn the associated rents? State which option you think EuropoTron should choose. Justify your conclusion using complete sentences, numerical evidence and, optionally, one or more economic graphs.

Answer 1

From reading the problem it seems two important pieces of information are missing:

1) Information on market demand for Europium; a constant exogeneous price is really indicative of price competition on the supply side i.e. there are enough producers for Europium constantly trying to undercut each other until P = MC and they can go no further. Information regarding the demand curve is missing - at a given price, how much quantity of it is demanded?

2) In exchange for the $400K does MegaEuropo also want the Europtron's europium reserves in addition to the machinery? It is reasonable to assume NO, because the value of the reserves next year will be $837000 and at a discount rate of 5% it'll be a full 15 years before the coumpounded effect of depreciation brings the inventory's worth down to less that $400K (to $387775 precisely)

But should the $400 be accepted today, it will also have appreciated - say, in the absence of better information, at 5% per annum. Some quick numbers:

In 7 years worth of existing reserves after depreciation is $584508 whereas $400K will have grown to $562,840.17. { Depreciated value of Europium > Appreciated value of financial asset }

In eight years depreciated value of Europium is $555283 which is less than appreciated value of $400K which is $590,982.18.

So if the the existing reserves are on the table for the deal, the question facing EuropoTron is really about expected demand, which is subject to unpredictable shocks to the economy.

If they expect the inventory to be sitting around for more than eight years (say, they're aware of some more cost/quality efficient substitute for europium ready to hit the market) then it makes sense to sell it for cash in hand which can grow steadily in the bank. If otherwise (e.g. expected that demand for Europium will stay constant or even grow AND/OR one or more of Eurotron's competitors are expected to go out of business) it makes sense to sit tight with the existing inventory instead of selling it.

As for the machinery, facing constant price a typical firm (with diminishing marginal cost) would equate p = MC (profit maximizing criteria for firms) giving optimal output at 920 units in the following year.

But an interesting feature of the given cost function is that MC is increasing instead of diminishing - this is atypical for cost functions in most standard microeconomics problems. This means profit per unit (Difference between selling price and cost price of the next unit) DECREASES with more units produced.

Thus it's an optimization problem and the maximally profitable output for the coming year is 310 units. The associated revenue is $195300, associated cost is $99200 and thus profit IF (and this is a big if because demand conditions are unknown) all output is sold will be $96100.

If price stays put at $630, this will be the profit every year. The profits from previous years accrue compound interest but even with no interest profits surpass the proposed sum of $400K in five years. So like in the case for the existing inventory (= 900 tons) of europium, whether or not they'd sell just the machine also comes down to deciding in the context of demand conditions.

Is demand for europium going up or down? Are there new competitors entering the market or are existing competitors leaving? With the previous question's in mind, should this be used as a an indicator for profitable market leverage in the future or as an omen of diminishing prospects of the industry (using social proof to inform expectations, herd behavior) ? All these are real considerations facing a real business.

If the context is the current status quo, then according to Berkshire-Hathway The Business Wire's 2018 report, "the Global Europium Market is accounted for $0.22 billion in 2017 and is expected to reach $0.39 billion by 2026 growing at a CAGR of 6.7% during the forecast period."

If Eurotron already has a strong market presence, then in the absence of better information it can be decisively concluded that they should NOT go with the deal.

Of course, information is everything today - and in an extremistan world of Black Swan events like COVID-19 - there are several other factors being brought into consideration by big firms.