Economy planning & discussion

[BOS]

Ice cream shops
T-shirt stands
House
Fish store


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Go to the "add mafia" subsection of the forum. This is not the place. Thanks

[BomberAl123]

The correct way to compare upgrades is to realise that, as you're paying a lump sum now in order to receive a stream of known cashflows in the future, you're essentially buying an investment with bond characteristics. Specifically, you're paying now to receive a series of negative cashflows, which represent the loss of earnings during the upgrade, followed by a series of positive cashflows in perpetuity when the upgrade is complete, which represent the increase in income.

Fortunately, the procedure for comparing the profitability of bonds is well-developed. This involves, for each investment (upgrade or purchase), calculating the single interest rate such that the discounted value of its cashflows is equal to its upgrade price. The upgrade that has the highest interest rate will be the best investment. The formula for doing this is as follows:

Where:

Co = Old cashflows
Cn = New cashflows
r = interest rate
Pn = Payout time (e.g. for Pawn Shop: P1 = 24, P2 = 48 etc. Note that we assume that the upgrade begins just after a payout)
T = Upgrade time

Then:

Upgrade price = - Co/((1+r)^P1) - Co/((1+r)^P2)... - Co/((1+r)^Pn)... + ((Cn-Co)/r)/((1+r)^T)

To explain:
-Co: are the old cash flows that you're missing out on
(Cn-Co)/r: is the value of the increase in cashflows in perpetuity (the standard formula for valuing a perpetuity bond)
(1+r)^Pn and (1+r)^T: are the discount rates used to reflect that the cash flows you receive now (or if negative, that you're missing out on) are more important than the ones you will receive in the future

This formula cannot be rearranged as an expression of 'r'. It can only be calculated by a computer by iteration. Using Excel to achieve this, we would: (i) Project the (negative) discounted cashflows that we miss out on by using a series of IF( ) statements that reference a description of the upgrade's characteristics [the -Co/((1+r)^Pn) series]. (ii) Calculate the (positive) discounted value of the increase in cashflows in perpetuity [((Cn-Co)/r)/((1+r)^T)]. (iii) Sum the values of the first two steps. (iv) Use Goal Seek to discover the single interest rate such that the sum of those values is equal to the upgrade price. The upgrade or build with the highest interest rate is the best investment.

Of course, this is all rather complicated, but we can simplify the process by pretending that instead of forgoing a series of the old cashflows during the upgrade, we just forgo one big cashflow during the middle of it. This big cashflow is determined by:

- Co*((T/P)/2)
or: - Co*T/2P

Where: P = Payout period (e.g. 24 for Pawn Shop)

Its discounted value is then:

- (Co*T/2P)/((1+r)^(1+T/2))

Therefore the simplified formula is:

Upgrade price = - (Co*T/2P)/((1+r)^(1+T/2)) + ((Cn-Co)/r)/((1+r)^T)

To simplify the formula further we can value the perpetuity, (Cn-Co)/r, as if it starts now (i.e. there is zero build-time), but then to increase the deduction in the middle of the upgrade time so as to reflect that not only are you not getting the old cashflow, but you're actually not getting the new cashflow for that period either. The deduction is now: ((Cn-Co)+Co)*T/2P, which simplifies to Cn*T/2P. Therefore the formula is now reduced to:

Upgrade price = (Cn-Co)/r - (Cn*T/2P)/((1+r)^(1+T/2))

Note that, unless somebody can rearrange this formula to express it as a function of 'r', the Goal Seek function on Excel would still have to be used for each calculation. Running this manually for every build or upgrade would be quite onerous, so a macro or VBA code to automate this could be downloaded from the Internet.

In addition, a few things to consider with any strategy where you choose your upgrades based on a simple formula are:

i) It assumes all money can be invested. Remember that upgrading your building is just like making an investment in a bond: cost now for future gains. If you have lots of money in the bank earning nothing, then your priority will be looking to put it to work, and so you will accept lower rates in order to invest a greater proportion of the money. If you're trying to calculate the fastest way to gain a set level of wealth, perhaps for a big purchase, then there's no alternative but to model combinations of builds and upgrades.

ii) It assumes land is always free and available. If land is fixed or exhorbitantly expensive and we are considering new builds or the prospect of demolition, then we must focus on cashflow per square, and Co and Cn should be replaced with (Co/A) and (Cn/A), where A is the building area in tiles (e.g. 2x2 = 4 for Pawn shop).

iii) It assumes that this upgrade is the final one, and ignores the fact that one upgrade is just a bridge to another that may be much more profitable.

I hope you found this interesting or useful. If you did, then please add me!

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