I'd Gladly Pay You Tuesday for a Hamburger Today

Welcome to the fifth post in a series about bitcoin mining basics. Last time, we considered the cost of mined bitcoin using depreciation to spread out up-front costs over the life of the mine. Now, let's run the clock backwards to estimate the up-front value of bitcoin acquired over spread-out time.

Presenting Present Value

Our miner Chad ran into his old friend Jeremy, who badly needed one million satoshi to pay his electric bill. He promised to repay Chad 1,050,000 satoshi the following month. After brief consideration, Chad decided a 5% return in one month justified taking the chance that Jeremy might abscond, and transferred 0.01 BTC to Jeremy’s wallet.

To state this a little differently, Chad agreed to pay 0.01 BTC now to receive 0.0105 BTC later. The 0.0105 BTC future payment therefore had a ‘present value’ of 0.01 BTC. Later that day, Jeremy’s sketchy second cousin Brad made Chad the same offer. Chad responded that he could only lend Brad 0.009 BTC, but Brad would still have to pay Chad 0.0105 BTC next month. To Chad, Brad’s promise had lower present value than Jeremy’s. Brad declined less than politely, unhappy that Chad discounted his future payment so heavily.

We can apply the same time-collapsing mathematical trick to consider any possible future payout or series of payouts. We only need to know (or estimate) the incoming amounts and when to expect them, and apply the appropriate discount rate reflecting the risk that we won’t receive them.

Big, Prominent, Disclaimer:

The following is provided as an illustration only. It is not an endorsement of any product or a recommendation for the reader to take or not to take any action. The result of this sample calculation has no significance other than to demonstrate the discounted cash flow method in its simplest form.

To Go Big or To Stay Home, That is the Question

Undaunted but educated by his experience with the HashSettler 454, Chad ponders whether to expand his operation with high-end modern equipment. Everybody at his favorite internet forum says to get the one that runs 14 TH/s using only 1.4 kW. At $0.12/kW-hr, the new machine’s electricity will cost $4.03/day. At today’s exchange rate ($8,600/BTC), that’s 46,860 satoshi/day. At today’s difficulty (2.875 trillion), the new machine should produce about 122,450 satoshi/day, or 75,590 satoshi/day EBITDA.

Aware of rumors that more efficient equipment will come online soon, Chad expects to see only two profitable years with the new machine. He also holds a well-earned skepticism about the bitcoin market and network, and so starts his deliberations with a hefty 50% annual discount rate. Chad wants to know the present value of a steady stream of daily payments of 75,590 satoshi for two years, discounted at 50%. He could run the Jeremy/Brad calculation, above, for one day, two days … 730 days in the future, and add them all up. Chad knows, though, that his trusty Excel program has a formula to do it for him. He keys in

=PV(0.5/365, 2*365, 0.0007559).

The cell responds with ‘(0.3487),’ meaning the discounted present value of the bitcoin stream is 0.3487 BTC (about $3,000 at today's exchange rate). To the extent that buying the machine produces the expected steady stream of bitcoin for two years, and 50% adequately assesses the risk that it fails to do so, the calculation suggests $3,000 might be a reasonable price for the machine. Or not. We’ll explore this method (formally called ‘discounted cash flows’) in more depth in the next post.

Wait, What?

Only $3,000? But the mining calculators say 0.447 BTC/year, which would make $7,688 in two years! And that's just the beginning, because it will run much longer than that! And the price is bottoming out, so it should do even better! Buying the machine is a no-brainer!

Stop. If the paragraph above makes sense to you, please go back and read this series from the beginning. $7,688 ignores operating costs, assumes neither exchange rate nor difficulty changes over two years, and makes no attempt to correct for uncertainty about the future. It is nothing but an appeal to emotion. You are much too smart to fall for it. Also, please see Disclaimer, above.

Q & A

• Why calculate PV in bitcoin? A mine produces revenue in bitcoin, not dollars. Using bitcoin for PV calculations does much to remove the future price from the decision-making process. The net (after electricity) amount of bitcoin fluctuates day to day only through converting the power cost to bitcoin. The higher the exchange rate, the smaller such fluctuations become. Over the longer term, the bitcoin flow changes with the mining difficulty in steps rather than wild swings. Trying to calculate the present value in dollars means using inputs even less predictable than the bitcoin income stream.
• Why use EBITDA? Why not include depreciation? We want to estimate the value of the stream of bitcoin we expect from the mine. Only actual transfers of money or property count. Depreciation allows us to project the initial cost of the mine into the future as if paid a little at a time; it does not represent actual payments. Payment for the mine took place before starting to mine, so it has no place in the PV calculation. In fact, we want to develop a way to decide beforehand whether to spend money for the mine at all. For mines set up (or to be set up) with borrowed money, the method is easily modified to include cash outflows for principal and interest.
• Why does the PV function give a negative number? By convention, the financial functions use positive numbers for money coming in, and negative numbers for money going out. The negative result indicates that the payment stream is worth that much for you to pay. A positive result would indicate someone would have to pay you to take over the income stream.
• My spreadsheet has five arguments for the PV function. Why only use three? Other software may vary, but in Excel, the fourth argument is ‘future value.’ If the income stream ends with a single payment different from all the others (e.g., a balloon payment on a loan), that’s where you enter it. A bitcoin mine would not have that. The fifth argument is a switch for payments at the end or beginning of the period. Mining proceeds are usually paid at the end of the period (not paid in advance). Since Excel defaults to ‘end of period,’ we don’t have to use it.
• Where did you get that crazy 50% discount rate? Honestly, I made it up for demonstration purposes (see Disclaimer). We’ll delve deeper into discounts in the next post.
• What could possibly go wrong? We are trying to make a financial decision, based on guessing the amount and duration of future payments, and addressing uncertainties through a mysterious discount parameter. As bogus as that might sound, it has the potential to provide better guidance than just assuming nothing changes (or worse, assuming with no rational foundation that things change in some particular way). Any decision method involves attempting to predict future outcomes. A good method also includes accounting for the decision’s risks. A good decision maker uses a good method in a way that does not simply confirm his or her biases.

Of Course There’s More To It Than That

Like any analytical method using uncertain inputs, a user can manipulate the discounted cash flows to convince himself to do just about anything. Obviously, that would defeat the purpose. In particular, the method’s usefulness depends on wise choice of the discount rate. Next time, we’ll look at discount rates in more depth, along with more detailed ways to apply discounted cash flows to make better decisions. Thanks for reading!

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