05 October 2008

Financial Advice for Facebook Games

I got into Facebook recently, and started playing some of the games available there. I noticed that many games share a similar theme in how they operate, and many are simple variants on a basic game engine. One feature common to many is that you can invest your money into land or buildings which then return a regular income. What caught my interest here is that the best investment is not always obvious. I found several examples of where people had posted information about the ratio of income-to-cost (income-gained/cost), and suggested that the highest ratio will be the best investment. For example: if playing Dragon Wars a Meadow (the cheapest unit of land) initially costs $5000 and increases your income by $100 per hour. The income-to-cost ratio is then $100/$5000 = 0.002. The higher the ratio be better, but the cost goes up depending on the number of lots you already own (an additional 20% of the base cost for all the Meadows you already own). There is a “discount” if you purchase in lots of 5 or 10; This means you can save a lot of money in the long run - spending more efficiently - if you always buy in lots of 10.

Lesson One: Invest your money now, and it will eventually pay itself off. You cannot lose.

While the highest ratio might be the best available investment, it does not consider the time needed to save up money for a big purchase. Obviously investing in any sort of purchase will eventually pay for itself, but I think a more relevant metric is the time needed for the investment to pay for itself. If we flip this ratio over (Cost/income-gained) we get a measure of time. In the same Dragon Wars example above this ratio is $5000/$100 = 50, which I will refer to as Time To Payoff (T2PO). So after 50 hours the new income from the purchase repays the cost of the investment.

I would suggest that this T2PO ratio is a more intuitive way to judge how good a particular investment is - The shorter the payoff time the better. It also gives useful information about when you will accumulate enough money to make your next purchase of similar cost.

Now let’s consider when you should spend your money. It is more efficient to save your money until you can buy a lot of 10, but my intuition was that sometimes a small investment now would have a bigger payoff that a bigger investment later. This depends on your current income (CI) and your Cash-on-Hand (COH). If a purchase is going to cost (PCOST), and that is more than your COH, then you will have to save up for (PCOST-COH)/CI hours (round up) before you can make the purchase and then pay it off. I'll call this total Time Until Buy (TUB).

Example: Suppose your income (CI) is $500 per hour and you have $10000 to spend (COH). You can:
1) Purchase 1 meadow immediately, TUB+T2PO = 50 hours.
2) Purchase 2 lots immediately (one at a time), TUB+T2PO = 53 hours (rounding up).
3) Wait 3 hours and purchase 3 lots, TUB+T2PO = 58 hours.
4) Wait 16 hour and purchase 4 lots, TUB+T2PO = 74 hours.
5) Wait 20 hour and purchase 5 lots (at a discount), TUB+T2PO = 70 hours.

Here we see that 1 meadow has the fastest payoff, but 5 lots will pay off faster than 4. Buying 5 lots at once is more efficient, but we have to save up for so long to do it that we can do better by making a smaller investment sooner. All this of course depends on your current income, cash available, and cost of what you want to buy. The point is that sometimes a small investment made sooner will have a shorter payoff than one you have to wait for.

Lesson Two: You might do better if you wait, but don’t wait too long! Small investments made earlier might be better than saving your money for a long time.

I have mentioned that buying 10 lots at once is a better deal or more “efficient”, and this deserves more attention, because it implies that buying less than 10 lots at once is somehow inefficient. So far I have ignored this, but consider: If I purchase 2 lots instead of 5, I might get my investment back faster, but when we go to purchase more lots, it’s going to cost extra to do it. This is a little tricky because it considers the cost of a purchase I have not yet made. As an example, I will compare buying 2 lots now and 5 lots later, to the alternate of buying 5 now and 5 (prorated to 2) later, with the goal being to compare the cost to get to 7 more lots.

If I first by 2 lots and later buy 5, I pay $5000+$5500=$20500 for the first 2 and 5*$6,000=$30,000 the next 5, for a total of $55,500. On the other hand, if I buy 5 lots and then 5, I pay 5*$5000=$25,000 for the first 5 and (5*$6,000)*0.4=$12,000 for the next 2 (the 0.4 is the prorating), for a total of $37,000. The cost of making an inefficient purchase in this example is $55,500 - $37,000 = $18,500. You can make the less expensive purchase sooner, but you pay for it later.

I can take this inefficiency cost (ICOST) into account when calculating the time to payoff by adding the "cost of inefficiency" to the cost of the purchase. This represents that I will be paying that extra cost eventually. I can calculate an "Adjusted Time to Payoff" (AT2PO).


Starting with the last example, and assuming I have enough cash to make either purchase immediately (Time Until Buy is zero), then purchasing 2 lots has AT2PO= 0+($20,500+$18,500)/$200 = 195 hours, while purchasing 5 lots has AT2PO = 0+($30,000+0)/$500 = 60 hours. The more efficient purchase pays off in one-third of the time. This measure (AT2PO) meets my expectation that the most efficient purchase should have the shortest payoff time.
Again, the benefit of the earlier payoff depends on how long you might have to wait until you can afford the purchase, and how often you check in to play the game and reinvest your money.

Lesson 3: Make efficient purchases if you can afford the cost and the time.

Buying in lots of 10 saves a lot of money in the long run, but unless you can devote your time to be able to make the most efficient purchase at the right time, it won’t save as much as you might gain by simply spending what you have immediately – and unlike the real world of real estate investment, you cannot lose money at this game!

I will follow up with a spreadsheet that actually does some of these calculations - Stay tuned.
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