Current-value decision model
Solve an attendance target from fixed and variable cost
Treat membership dues as a monthly hurdle: each completed visit absorbs part of that fixed commitment while commute and class add-ons remain marginal costs. The equation rejects any goal that those marginal costs already consume.
| Cost layer | Entered amount | Allocation basis | Monthly or marginal value |
|---|
Detailed calculation process
Formula, substitutions, intermediate results, and reconciliation
V* = F / (t - v), valid only when t > v
F is monthly dues plus allocated annual fees, t is the desired all-in cost per visit, and v is travel plus surcharge per visit.
Five-step target design
Set an achievable attendance threshold
- Add recurring dues and allocate the annual facility fee over the intended horizon.
- Estimate round-trip travel from real routes and typical parking or fares.
- Average only surcharges you expect on each visit.
- Choose a cost-per-visit target above the variable-cost floor.
- Use the rounded monthly result operationally and check it against available weekly slots.
Five target fundamentals
Understand the cost curve
Fixed monthly-equivalent
Dues and allocated annual fees exist even at zero attendance.
Variable-cost floor
Travel and session charges remain for every visit and cannot be diluted away.
Continuous solution
The algebraic threshold can be fractional and describes the exact cost boundary.
Whole-visit action
The operational target rounds upward because a partial workout does not satisfy a count.
Weekly translation
Calendar weeks per month translate the cost target into a schedule check.
Symbols and defaults
Inspect the feasibility condition
| Symbol | Meaning | Default | Unit |
|---|---|---|---|
| F | Fixed monthly-equivalent | 78 + 96/12 | USD/month |
| t | All-in target | 15 | USD/visit |
| v | Travel plus surcharge | 3.5 + 1.5 | USD/visit |
| V* | Continuous threshold | solved | visits/month |
| W | Weeks per month | 4.345 | weeks/month |
| ceil(V*) | Operational target | rounded up | whole visits |
Default substitution: V* = (78 + 96/12) / [15 - (3.50 + 1.50)]. The whole-visit reverse check must produce an all-in value at or below $15.
Three decision lenses
Connect arithmetic to a real routine
Feasibility boundary
The amount left after commute and class add-ons must be positive before it can absorb dues.
Travel sensitivity
A closer facility can improve the economics even when its sticker price is higher.
Schedule capacity
Compare the weekly result with actual opening hours, recovery needs, and free calendar slots.
Two planning cases
Reachable and impossible goals
Three weekly slots available
A member maps the rounded threshold to named weekdays before committing to the contract.
Commute consumes the budget
When the trip alone costs more than the desired session average, changing attendance cannot rescue the plan; location or budget must change.
Target glossary
Six cost-curve terms
- Fixed cost
- Cost that does not change with visits in the period.
- Variable cost
- Cost incurred for each additional visit.
- Cost floor
- The variable amount average cost approaches but cannot cross.
- Continuous threshold
- The exact fractional visit solution.
- Operational target
- The threshold rounded up to a whole visit.
- Reverse check
- Recomputing cost at the rounded target.
Target questions
Frequently asked questions
Why can the result be infeasible?
Average cost can never fall below travel plus other per-visit charges, so a target at or below that floor has no attendance solution.
Why round visits upward?
Rounding down would leave average cost above the chosen boundary; the next whole visit is the first operational count that meets it.
Should annual fees be divided by twelve?
Use the number of months that matches your comparison horizon and contractual benefit period.
Can I exclude travel cost?
Only if it is genuinely zero or you are intentionally evaluating facility charges alone and label the narrower basis.
Does a higher visit target mean better fitness?
No. Frequency should follow health, recovery, and schedule needs; this page calculates cost dilution only.
How should I use the weekly result?
Compare it with actual open hours and available calendar slots, then reject the membership if the routine is not credible.
Evidence and limits
A cost target is not a workout prescription
- The model omits time value, equipment, class quality, and health outcomes.
- Travel cost varies with route, occupancy, fuel, parking, and transit fares.
- Per-visit surcharges may not apply uniformly across sessions.
- Annual fees must be allocated over a period that matches the decision.
Evidence record: keep the contract, fee notice, route-cost estimate, class schedule, and calendar capacity. Do not increase exercise solely to meet a financial ratio.
Sources and related tools
Activity and contract boundaries
- HHS Physical Activity Guidelines — activity decisions require health context beyond cost.
- FTC gym membership consumer alert — examine costs and cancellation.