01 · THE SCENARIO
THE SETUP
Kiana's donut shop is already profitable, and she's exploring how to grow it further. Buy into a well-known franchise for brand pull, or launch a food truck for lower overhead and mobility, both weighed against simply continuing to run the shop as-is.
THE STRUCTURE
A four-part workbook: Part 1 pivot table & chart, Part 2 seasonal index & regression forecast, Part 3 profit models for the shop and franchise, Part 4 adds the food truck model plus formal decision-analysis tools.
HISTORICAL DATA
36 mo.
Monthly donut demand, 2020–2022
TOTAL 3-YR DEMAND
116,319
Donuts sold across the sample
REGRESSION FIT
R² .654
Time-period trend explains 65% of variance
02 · DEMAND FORECAST
Raw monthly demand was deseasonalized, run through a linear regression against time period, then reseasonalized to build a 2023 forecast, one of three demand scenarios later feeding every profit model.
LOW DEMAND (20%)
36,163
Donuts forecast for 2023
AVERAGE DEMAND (55%)
48,868
Donuts forecast for 2023
HIGH DEMAND (25%)
59,619
Donuts forecast for 2023
03 · PROFIT UNDER UNCERTAINTY
Each alternative got its own monthly profit model, run three times, once per demand scenario, to build the payoff table every decision framework below draws from.
| ALTERNATIVE | LOW DEMAND | AVERAGE DEMAND | HIGH DEMAND |
|---|---|---|---|
| Current Operations | $83,591 | $107,615 | $101,709 |
| Franchise | $69,370 | $106,706 | $113,020 |
| Food Truck | $60,156 | $102,562 | $110,717 |
THE COUNTERINTUITIVE RESULT
Current Operations actually earns less under High demand ($101,709) than under Average demand ($107,615). The shop's 4,000-unit monthly production cap means excess demand just turns into lost sales and lost-sale costs, capping the upside that a franchise's higher capacity can still capture.
04 · FIVE DECISION FRAMEWORKS
With the payoff table built, five classic decision-analysis methods were applied, ranging from purely pessimistic to fully probability-weighted.
MAXIMIN
→ CURRENT OPSBest worst-case floor: $83,591, the highest guaranteed minimum of the three.
MAXIMAX
→ FRANCHISEBest best-case ceiling: $113,020, the highest possible upside if demand runs high.
LAPLACE
→ CURRENT OPSBest average across all three scenarios weighted equally: $97,638.
MINIMAX REGRET
→ CURRENT OPSSmallest worst-case regret for picking wrong: $11,312 vs. $14,220 and $23,435.
EXPECTED VALUE
→ CURRENT OPSHighest probability-weighted payoff at 20/55/25%: $101,334.
EXPECTED VALUE OF PERFECT INFORMATION
EVPI comes out to just $2,828. Even knowing exactly which demand scenario would occur ahead of time wouldn't move the payoff much, a sign that Current Operations is already close to the optimal choice under real-world uncertainty.
05 · RECOMMENDATION
★ RECOMMENDED PATH
KIANA SHOULD STAY WITH CURRENT OPERATIONS
Four of five decision frameworks, Maximin, Laplace, Minimax Regret, and Expected Value, all point the same direction. Only Maximax, the purely optimistic best-case view, favors the franchise. With a low EVPI and franchise/food truck upside only materializing under high demand that isn't the most likely outcome, staying independent is the financially sound choice unless Kiana is willing to bet on the 25% high-demand scenario.
4/5
Frameworks favor Current Ops
$101K
Expected annual profit
$2,828
EVPI
06 · REFLECTION
WHAT I LEARNED
Working through this individually meant every formula, from the regression forecast through all five decision-analysis tables, had to link back to a single source cell so the whole model would recalculate cleanly. The most useful realization was how much a simple constraint like a production cap can change a business decision: on paper, higher demand should mean more profit, but Current Operations' capacity limit flips that logic under the High scenario. It's a reminder that growth options need to be judged against the option you already have, not just against each other.