Decision Analysis
Real Options Analysis for Strategic Decisions at a Small Café
Using six months of real sales data from a small café in Gapyeong, this study compares a traditional NPV valuation with a real options analysis of converting the café into a restaurant, and uses Monte Carlo simulation to estimate how long the business can keep operating.
- value of waiting a year over investing now (ROA vs. NPV)
- +87%
- off-season sales as a share of peak-season sales
- 42.3%
- KRW of monthly revenue needed to break even
- 3.33M
- Field
- Decision Analysis
- Period
- July 2025 (Grade 11)
- Researchers
- Siwoo Kim
- Updated
- October 2026
Overview
Carried out in Grade 11 as part of the 2025 Convergence Project (July 14–18, 2025), this study asks how a small café owner should decide whether, and when, to make a large irreversible investment when future demand is uncertain.
Research Questions
- How do NPV analysis and real options analysis (ROA) differ when applied to a café investment decision?
- How can Monte Carlo simulation quantify the risk of continuing to operate the café?
- How do seasonality and trend affect the café's long-term survival?
Data
- Monthly sales of a small café in Seorak-myeon, Gapyeong-gun, Gyeonggi Province, from July to December 2024 (six months)
- July 2,911,800 KRW, August 3,560,000 KRW, September 1,708,800 KRW, October 1,634,700 KRW, November 1,204,500 KRW, December 928,500 KRW
Monthly sales, July–December 2024 (KRW)
- Off-season
- Peak season
- Jul
- Aug
- Sep
- Oct
- Nov
- Dec
Break-even 3.33M
View data
| Item | Value | Group |
|---|---|---|
| Jul | 2,911,800 KRW | Peak season |
| Aug | 3,560,000 KRW | Peak season |
| Sep | 1,708,800 KRW | Off-season |
| Oct | 1,634,700 KRW | Off-season |
| Nov | 1,204,500 KRW | Off-season |
| Dec | 928,500 KRW | Off-season |
Seasonality and Trend
- Peak season (July–August in the data) averaged 3,235,900 KRW per month
- Off-season (September–December) averaged 1,369,125 KRW per month, 42.3% of the peak-season level
- Month-over-month change averaged −16.66%, with a standard deviation of 27.60%
- A linear fit shows sales falling by about 487,000 KRW per month
NPV and Real Options Valuation
The decision modeled is whether to convert the café into a restaurant.
- Investment cost 75,000,000 KRW, a one-year horizon, and a 5% risk-free rate
- Restaurant value of 112,000,000 KRW in a good market and 60,000,000 KRW in a bad market
- NPV: an expected value of 0.5 × 112,000,000 + 0.5 × 60,000,000 = 86,000,000 KRW gives an NPV of 11,000,000 KRW, which recommends investing immediately
- Real option to wait one year, valued with a one-step binomial model: payoffs of max(112,000,000 − 75,000,000, 0) = 37,000,000 KRW and max(60,000,000 − 75,000,000, 0) = 0 KRW
- With a probability of 0.583, the option is worth 21,571,000 KRW in one year, or 20,544,000 KRW in present value
- The option to wait is worth about 87% more than investing now, so ROA recommends waiting a year before deciding
- A simulation-based estimate of the option value came to 20,892,000 KRW (95% confidence interval 19,234,000–22,550,000 KRW), 1.7% from the binomial value
One-step binomial model for the option to wait
Survival Simulation
- Monte Carlo simulation with 10,000 runs over a horizon of up to 60 months
- Starting cash of 10,000,000 KRW, monthly fixed costs of 2,000,000 KRW, and variable costs of 40% of revenue
- Each month's revenue is the off-season average, scaled by the linear trend (floored at 30%), a seasonal multiplier drawn from a normal distribution (mean 1.8, SD 0.3 in peak months; mean 1.0, SD 0.2 otherwise), and a monthly variation drawn from a normal distribution with mean −16.66% and SD 27.60%, with a floor of 100,000 KRW
- A run ends in the first month cash falls to zero; survival probability is the share of runs still operating at each horizon
- Pessimistic (5,000,000 KRW cash, 2,500,000 KRW fixed costs, 50% variable costs) and optimistic (20,000,000 KRW, 1,500,000 KRW, 30%) scenarios were run alongside the current one
Results
- Current costs: every simulated run ran out of cash within 60 months; average survival 5.8 months, median 6.0 months; 75.8% of runs were still operating at 6 months and none at 12 months (seed 42)
- Optimistic scenario: average survival 16.7 months; pessimistic scenario: 2.0 months
- Break-even revenue is 2,000,000 / (1 − 0.4) = 3,333,333 KRW per month, a level reached only in August among the six months of data
Share of simulated runs still operating
- Current
- Optimistic
- Pessimistic
View data
| Month | Current | Optimistic | Pessimistic |
|---|---|---|---|
| 0 | 100.0% | 100.0% | 100.0% |
| 1 | 100.0% | 100.0% | 100.0% |
| 2 | 100.0% | 100.0% | 100.0% |
| 3 | 100.0% | 100.0% | 0.0% |
| 4 | 100.0% | 100.0% | 0.0% |
| 5 | 100.0% | 100.0% | 0.0% |
| 6 | 75.8% | 100.0% | 0.0% |
| 7 | 0.1% | 100.0% | 0.0% |
| 8 | 0.0% | 100.0% | 0.0% |
| 9 | 0.0% | 100.0% | 0.0% |
| 10 | 0.0% | 100.0% | 0.0% |
| 11 | 0.0% | 100.0% | 0.0% |
| 12 | 0.0% | 100.0% | 0.0% |
| 13 | 0.0% | 100.0% | 0.0% |
| 14 | 0.0% | 100.0% | 0.0% |
| 15 | 0.0% | 100.0% | 0.0% |
| 16 | 0.0% | 98.9% | 0.0% |
| 17 | 0.0% | 61.0% | 0.0% |
| 18 | 0.0% | 7.2% | 0.0% |
| 19 | 0.0% | 0.2% | 0.0% |
| 20 | 0.0% | 0.0% | 0.0% |
| 21 | 0.0% | 0.0% | 0.0% |
| 22 | 0.0% | 0.0% | 0.0% |
| 23 | 0.0% | 0.0% | 0.0% |
| 24 | 0.0% | 0.0% | 0.0% |
Conclusions
- NPV values only the average outcome, while ROA captures the asymmetric payoff of being able to wait, which here is worth more than investing now
- The steep drop in sales after the summer and the gap between peak and off-season revenue are the main threats to the café's cash flow
Limitations
- Six months of data cannot capture a full annual cycle or a long-term trend
- External factors are not modeled
- A single café limits how far the results generalize
Tools
Python (NumPy, pandas, SciPy, Matplotlib, seaborn)