Estimate S₀ from expected procedure volumes, growth rates, and margins. Or check “Use S₀ override” above to skip this section and enter a value directly.

Drag to explore how your answer moves under different assumptions. Click Apply to push these values into the form above.

A 250-bed regional hospital is considering replacing its aging 1.5T MRI with a Siemens MAGNETOM Vida 3T system. Volume has been steady but neurology and orthopedic surgery want stronger imaging to retain referrals. Reimbursement is stable but Medicare site-of-service differentials are unsettled. The capital request is $2.5M including installation and magnet swap.

The MRI service line is built from four procedure families with hospital-outpatient global contribution margins:

The procedure-built PV ($10.42M) is well above the trigger ($4.50M), giving ρ = 2.31. This decisively clears the bar.

Before committing, test how robust this is to your most fragile assumptions:

The decision is robust to ordinary forecast error and survives a combined volume + margin shock with ρ barely above 1.0. A severe site-neutral payment shock, however, pushes the analysis into the Monitor band — renegotiate price or secure payer clarity before signing.

The same hospital is also considering a $1.8M PET/CT to launch a new service line. There’s no current PET volume, so the volume forecast carries far more uncertainty (σ = 0.45). Cost of waiting is lower (δ = 0.04) because no competitor is in the market.

This is the value of the framework. Two decisions that look superficially similar — both NPV-positive — have opposite recommendations because their uncertainty profiles differ.

The same model can produce very different recommendations depending on which input you got wrong. This tab shows how the readiness ratio ρ responds when each input is shocked ±20% from the values you’ve entered in the Calculator tab. Read it as a triage list: longer bars are the assumptions you most need to defend.

Update the inputs in the Calculator tab and the charts here will refresh.

A number on a dashboard is not a decision. This tab translates ρ bands into specific actions a radiology leader can take this week. The thresholds reflect standard real-options practice: leave a meaningful margin of safety below the trigger before treating it as a green light.

The 0.70 / 1.00 thresholds are a starting point, not a regulatory standard. Consider tightening or loosening them by organization context:

1. Pre-screen — use this tool early to decide whether to invest analyst time in a full pro forma. If ρ < 0.5 at first pass, document and table the request.
2. Capital request memo — include S₀, S*, ρ, and the Sensitivity Lab tornado as a standard exhibit alongside traditional NPV and IRR.
3. Board / finance committee — present zone designation (Wait, Monitor, Invest) and the specific actions taken to move ρ into the green band.
4. Post-implementation — revisit at 12 and 24 months against the Year-1 volume and margin assumptions used to compute S₀.

This tool implements the standard real options investment-trigger derivation from McDonald & Siegel (1986), as presented in Dixit & Pindyck’s Investment Under Uncertainty (1994). The decision is framed as a perpetual American call option on a project whose present value follows geometric Brownian motion.

The optimal stopping problem yields a smooth-pasting condition that produces a closed-form trigger. The trigger is always above the capital cost K, and the gap shrinks as uncertainty σ falls or the cost of waiting δ rises.

The fundamental quadratic rewrites as:

With a = ½σ², b = r − δ − ½σ², c = −r:

This is the positive root that satisfies β > 1. The discriminant b² − 4ac is always positive in the economically meaningful region, so the root is real.

The closed-form trigger is convenient but rests on assumptions that should be checked before treating the output as definitive.

1. Geometric Brownian motion for S. PV is assumed to evolve smoothly with constant volatility σ. Real radiology cash flows can jump (payer policy change, competitor entry, regulatory event). For known discrete-event risks, augment with scenario analysis.
2. Perpetual option. The closed form assumes you can wait forever. Set a finite decision window T using business logic (vendor pricing expiry, equipment end-of-life, certificate-of-need deadline). If T is short relative to the volatility, the trigger should be interpreted as a lower bound on the true threshold.
3. Constant parameters. r, σ, and δ are held constant. In practice all three drift. Refresh inputs at the date of the decision; don’t rely on a model run from 12 months ago.
4. Single decision. The model treats the purchase as a one-shot commitment. If the real decision is staged (buy a refurbished unit now, replace in 3 years), model it as a compound option or in stages.
5. Volatility is the hardest input to estimate. Common approaches: (a) coefficient of variation of historical service-line contribution margin over 3–5 years; (b) implied volatility from comparable public-company segment results; (c) expert elicitation with a triangular distribution and a parametric fit. State your method.
6. No taxes, no inflation, no operating leverage. The framework is pre-tax and treats margin per exam as constant in real terms. For heavily-leveraged organizations or material tax positions, run a parallel after-tax DCF before deciding.
7. Strategic value not captured. Reputation, recruiting, teaching mission, payer-mix steering, and downstream service-line effects don’t appear in the model. They can justify investing below ρ = 1.0 in specific contexts, but should be argued explicitly — not assumed implicitly.

• McDonald, R. & Siegel, D. (1986). The value of waiting to invest. Quarterly Journal of Economics, 101(4), 707–727.
• Dixit, A. & Pindyck, R. (1994). Investment Under Uncertainty. Princeton University Press. Chapters 5–6.
• Trigeorgis, L. (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. MIT Press.
• Copeland, T. & Antikarov, V. (2003). Real Options: A Practitioner’s Guide. Texere.
• Brennan, M. & Schwartz, E. (1985). Evaluating natural resource investments. Journal of Business, 58(2), 135–157.
• Emrick, K. (2024). Fiscal Fitness: Strengthening Hospital Financial Performance. Ch. on capital decisions under uncertainty.

This analyzer answers one specific question: given my best estimates, should I invest in this equipment now? A full capital decision benefits from companion tools that pressure-test the inputs, model the downstream operations, and frame the strategic context.