Opportunity Cost Calculator

The comparison steps one month at a time, twice — once for each option, on one timeline. In each month a scheduled allocation is added at whichever end of the period you selected, and the balance changes at the monthly equivalent of that option’s annual value change. That is the whole of it. It is the same monthly step the Investment Fee Drag and Real Return calculators use, with no recurring fee to deduct, because the rates you enter here are already net.

The funding rule everything rests on

Both paths start from the same amount available today, receive the same recurring allocation at the same times, and run for the same horizon. Only the upfront cost and the annual value change differ.

That rule is what makes the difference attributable to the options rather than to the budget. A path given more money would end higher without the option producing more value, so this version supports no per-option allocation, no per-option horizon and no delayed start. The rule controls the money and the time, and it controls nothing else.

This comparison controls the money contributed and the time horizon. It does not control risk, liquidity, tax, volatility, effort or non-financial value.

Capital deployed at time zero

Each option’s upfront cost is non-recoverable and is paid out of the common amount at the moment the comparison starts. It never enters the option and never compounds, so what begins compounding is what is left after it:

Option A capital deployed = S - U_A
Option B capital deployed = S - U_B

S is the amount available today and U each option’s own upfront cost. An upfront cost may be zero, and it may be the whole of S — which deploys nothing and models a use of the money with no financial residual value at all. It may not exceedS, and a value that does is refused rather than quietly reduced to fit.

Converting annual rates to monthly ones

A rate quoted for a year is converted by the twelfth root, so twelve monthly steps reproduce the annual figure exactly. Dividing by twelve is a different quantity and is not used here:

monthly factor for Option A = (1 + r_A) ^ (1/12)
monthly factor for Option B = (1 + r_B) ^ (1/12)

Each annual value change is an effective annual figure after the recurring product costs you intend the scenario to include. UBWHY supplies no market assumption and prefills neither field.

The difference, and what it is called

D  = Option A ending value - Option B ending value
OC = the size of D, without its sign

Choosing the lower-ending path gives up OC of projected financial value relative to the other, under this model. Choosing the higher-ending path does not have zero opportunity cost in real life: whatever the other option offered that this model never measured is still given up, and that is exactly what the arithmetic cannot see.

Where the two ending values fall within a hundredth of a currency unit of each other the page reports them as equal rather than as one being ahead. A one-cent difference over twenty years is not a distinction anybody can act on, and printing it as one would be false precision.

Accounting view — not a causal attribution

Each option’s ending value is reached the same way, and each column adds up on its own:

  common amount available today
- this option's upfront cost
= initial capital deployed
+ recurring allocations
+ growth or decline
= ending value

Each column adds up on its own. The growth or decline line depends on how much capital was deployed and on when every allocation arrived, so it cannot be separated into an amount caused by the upfront cost and an amount caused by the value change. This version builds no counterfactual that would make such a split meaningful, and none is shown.

This is worth stating twice, because the split a reader most wants is the one that cannot honestly be made. It is tempting to read the table as “the upfront cost cost me this much and the lower rate cost me that much”, and those two numbers do not exist: the growth line already depends on how much capital the upfront cost left to deploy, so any split between them would depend entirely on which one you decided to charge first. A version that produced such a figure would have to build a third and fourth counterfactual path and say plainly which ordering it chose. This one builds neither, and shows neither.

Crossover

A crossover exists only where one path is strictly ahead before it and the other strictly ahead after it. The page reports the first whole month carrying the reversed direction, and claims no finer precision than that, because the model holds no state between months.

Two paths that begin at the same value and then separate have not crossed. Nobody was ahead, so nobody was overtaken, and calling it a crossover would tell you a path recovered from behind when it never was behind. The page says so explicitly whenever it happens. Where the paths meet and stay together, that is convergence and is reported as convergence.

The reversal rate

Where one path ends lower, the tool solves for the annual value change that path would need to reach the other path’s ending value, holding its upfront cost, the shared allocation schedule and the horizon exactly as they are:

find r such that  project(S, U_lower, r, C, frequency, timing, T) = higher ending value
additional rate = r - the rate entered for the lower-ending path

The answer is published in percentage points, which is the gap between two rates rather than a proportion of anything. There is no closed form once allocations are involved, so it is solved numerically, and where no reliable answer exists the page says so in words rather than printing a number that looks solved. This is a mathematical hurdle, not a forecast and not a claim that the rate is achievable. Nothing here establishes that the rate is available, that the option could produce it, or that an option which needs a larger one is therefore the weaker choice.

Assumptions

• Each annual value change is the figure you entered, constant across the whole horizon, and already net of recurring product costs.
• Both paths receive the same amount available today, the same recurring allocation, at the same frequency, with the same timing, over the same horizon.
• Each upfront cost is paid once, at the start, and is not recovered.
• Nothing is withdrawn from either path at any point.
• No intermediate value is rounded. Rounding happens only where a figure is displayed.

What the model does not do

• It does not adjust for inflation or measure purchasing power. Every figure on this page is nominal.
• It does not model tax, of any kind, at any point.
• It does not model risk, volatility, the sequence in which returns arrive, drawdowns or probability. One constant annual assumption per path cannot represent any of them.
• It does not model liquidity. Two paths ending at the same value can differ completely in how quickly, and at what cost, the money could be reached.
• It does not model dividends, coupons, rent or debt interest separately. Any reinvested financial effect has to be inside the annual value change you entered.
• It does not model a delayed start, unequal recurring allocations, changing rates or changing allocations, and it does not resolve a mortgage-overpayment, refinancing or rent-versus-buy question, where amortisation schedules and penalties decide the answer.
• It does not measure non-financial value: use, enjoyment, certainty, time saved, reduced worry or strategic flexibility. A financially lower path can be the right one because of any of them.
• It does not decide anything. It compares two modelled paths and reports the difference; the choice, and everything the model did not look at, stays with you.

Why a comparison needs a real alternative, why a higher annual rate can start behind, and what a break-even rate does and does not tell you: How to Compare Two Uses of Money Without Fake Certainty.