Calculators

Illustrative purchase decision: assume a 70-billion-parameter model at one byte per parameter, 330 KB of KV cache per token, 32,000-token context, 64 concurrent requests and 15% framework overhead. Memory is (70 + 330 × 32,000 × 64 / 1,000,000) × 1.15 = about 858 GB per replica. Assume 288 GB per GPU and a separately qualified eight-GPU replica: the three-GPU memory floor does not replace that qualification.

Assume 50,000 output tokens/s peak demand, 11,200 tokens/s per qualified replica and 70% serving capacity. Round 50,000 / (11,200 × 0.70) up to seven replicas: 56 active GPUs. A stated 72-GPU purchase unit gives 72 installed GPUs, 16 stranded slots and one 72-GPU rack. At an assumed 135 kW nominal rack input and PUE 1.15, the nominal facility screen is about 155 kW. Fractional rental at an assumed $18/GPU-hour costs $1,008/hour for the active fleet.

Assume a $1,100/hour active-fleet rental allowance. The seven-replica case fits. Above 7 × 11,200 × 0.70 = 54,880 output tokens/s, demand needs an eighth replica: at 60,000 tokens/s, 64 active GPUs cost $1,152/hour and exceed the allowance, while the same 72-GPU purchase unit still fits. Acquire the exact serving qualification before committing the purchase.

Choose whether to release a 100 kW current / 150 kW future rack design. Assume 80% liquid capture in each profile: current liquid/air duties are 80/20 kW and future duties 120/30 kW. The 120 kW liquid capacity and 30 kW room capacity are assumed surviving-path ratings at the entered conditions. The Yes controls assume qualified liquid equipment, rack water and proven air delivery/inlet conditions at both duties; they are not test records. Rear-door assistance is absent.

Use the Chapter 5.1 teaching operating point at both duties: TCS 35 °C supply / 45 °C return; FWS 30 °C supply / 40 °C return. Cold-end approach = 35 − 30 = 5 K; hot-end approach = 45 − 40 = 5 K. Each meets the assumed 5 K requirement. Both heat paths pass this stated screen, with zero spare future liquid or room duty. Release equipment only after the suppliers and inlet map substantiate these assumptions.

Raise only future FWS supply to 31 °C: the cold-end approach becomes 4 K and fails; the crossover is 30 °C. Changing airflow qualification to No also leaves the design unestablished. A 200 kW future rack would require 160 kW liquid and 40 kW air, exceeding both ratings. Change the exchanger or the operating point and requalify before freezing density; no PUE is inferred.

Illustrative capital scope: assume 10 MW of usable IT capacity, facility/land/utility works at $10 million per MW, network infrastructure at $4 million per MW, a quoted 20% facility premium and a 1.10 regional factor. Facility cost is 10 × 10 × 1.20 × 1.10 = $132 million. Network cost is 10 × 4 × 1.10 = $44 million. The total is $176 million, or $17.60 per IT watt, excluding servers.

An illustrative $180 million allowance for those same two scopes passes with $4 million remaining. Raising only the facility premium to 25% raises the total to $181.5 million and fails. The topology drawing and supplier scope establish the premium; the reliability requirement buttons do not price it. Add the server purchase once in the shared program capital model.

The facility-premium crossover is 23.6%: (180 − 44) / (10 × 10 × 1.10) − 1. Above it, reduce scope or raise the same-scope capital allowance.

Decide whether candidate A merits the next diligence spend. Assume judgment scores of 7, 6, 6, 7, 6 and 5 for power, interconnect, price, land, water and incentives. The displayed rubric weights those axes 30%, 20%, 15%, 15%, 10% and 10%. These are an illustrative investment preference, not executed agreements or measurements. The weighted trace is (7×30 + 6×20 + 6×15 + 7×15 + 6×10 + 5×10) / 10 = 63.5/100: “Workable with mitigation.”

Advance A to evidence collection under this rubric; hold a site commitment until the service date, land rights, thermal/water design and workload latency are established under Chapter 3.13. Change the power score to 2: the score becomes 48.5 and the power kill gate disqualifies A. The crossover is power ≤2, regardless of incentives. Reallocate diligence to a candidate with a viable power path.

Decide which reliability requirements to carry into the design brief. Assume the owner requires both concurrent maintenance and ride-through of one component failure. The test is Boolean: Yes / Yes yields Required / Required. The topology result remains “Not determined from these two requirements.” Hold topology selection and pricing until named isolation/fault states identify the exact paths, surviving capacity, interruption, independent controls and workload recovery consequence.

Change the fault requirement to No while keeping maintenance at Yes. The fault requirement becomes “Not required by this screening input”; the crossover is the owner's acceptance of workload interruption on an unplanned component fault. That relaxes the design brief and accepts that service consequence. It does not select an N+1 or 2N topology or certify a Tier. Chapter 12.5 owns the state-by-state acceptance method.

Illustrative dense-model run: assume 70 billion parameters, 15 trillion training tokens, 10,000 GPUs at 2.5 dense PFLOPS each, 40% MFU and 90% goodput. Define MFU on productive compute time so goodput does not deduct the same lost time twice. Training work is 6 × 70 billion × 15 trillion = 6.3 × 10²⁴ FLOPs. Effective rate is 10,000 × 2.5 × 10¹⁵ × 0.40 × 0.90 = 9 × 10¹⁸ FLOP/s. The run takes 700,000 seconds, or 8.10 days and about 1.94 million GPU-hours.

At an assumed $18/GPU-hour, rental is $35 million. With assumed 1.2 kW GPU power, a 1.50 total-IT multiplier and PUE 1.20, constant-power energy is 4,200 MWh: $336,000 at $0.08/kWh and 1,680 tonnes at 400 gCO₂/kWh. Do not add electricity to rental when the rental already includes it.

The run passes an illustrative nine-day deadline. At 80% goodput it takes 9.11 days and fails. Change the training-work model for sparse or non-dense workloads; the screening formula does not qualify model placement or convergence.

The nine-day deadline requires at least 81.0% goodput: 6.3 × 10²⁴ / (10,000 × 2.5 × 10¹⁵ × 0.40 × 9 × 86,400). Below that, reserve more capacity or move the deadline.

Illustrative server-ownership decision: assume $30,000 per installed GPU, three-year straight-line cost allocation, $1,000 annual energy, annual opex equal to 5% of purchase cost, and 1.25 installed GPUs per active GPU. Annual cost per active GPU is (30,000 / 3 + 1,000 + 1,500) × 1.25 = $15,625. At 50% productive use, divide by 4,380 hours: $3.57 per productive GPU-hour.

An assumed like-for-like $4/hour rental crosses that cost at 15,625 / (8,760 × 4) = 44.6% utilization. Above that point ownership wins this stated numerator; below it rental wins. With all other inputs fixed, five- and seven-year ownership lives reduce the result to $2.43 and $1.94/hour. These are life sensitivities, not evidence that the fleet earns for those periods. The facility charge is set to zero here to isolate the server; a rental rate includes powered, cooled space, so enter the facility's capital recovery per kW-month and reconcile services outside either quote before making a full-service purchase decision.

At 40% productive use, ownership costs $4.46 per productive GPU-hour and the assumed $4 rental wins. Change productive use, not the independent electrical-load assumption.

Illustrative serving case: assume one qualified node produces 1,000 useful output tokens/s within the declared latency target and runs productively 50% of each paid hour. Useful output is 1,000 × 3,600 × 0.50 = 1.8 million tokens/hour. Assumed rental of $20/hour costs $11.1 per million output tokens; an assumed owned calendar cost of $10/hour costs $5.56 per million.

Against an illustrative $6 per million output-token cost allowance, ownership passes and rented capacity fails. At 40% productive use the owned cost rises to $6.94 and also fails. Keep the model, precision, prompt/output mix, batching, latency target and cost boundary identical; prompt tokens and cached tokens do not silently enter this output denominator.

The owned case crosses the $6 allowance at 46.3% productive utilization: 10 / (1,000 × 3,600 × 6 / 1,000,000).

Illustrative annual operating case: assume 10 MW nominal installed IT power, 60% annual-average load, energy-weighted PUE 1.20, electricity at $0.08/kWh and site-water WUE 0.40 L/kWh of IT energy. Average IT power is 6 MW; annual IT energy is 6 × 8,760 = 52,560 MWh. Facility energy is 63,072 MWh, costing $5,045,760. Site water is 52,560 × 1,000 × 0.40 = 21,024,000 litres.

Against an illustrative $5.2 million annual electricity allowance, this case passes with $154,240 remaining. The allowance crosses at 61.8% average load. Holding all other assumptions constant at 100% nominal operation raises electricity cost to $8,409,600 and fails that allowance. Productive utilization alone does not change either energy case; change the average-load assumption when the load study changes.

Illustrative retained-fleet case, all amounts in $M: assume capex 100, immediate operation, debt 50 at zero interest amortized over four years, revenue 40/year, opex 25% of revenue, cash tax 20%, tax depreciation over 3.5 years, no sustaining spend, no growth, four-year hold, zero exit proceeds and no reserve. Assume the original fleet supports all four earning years. These tax and earning periods are independent assumptions.

Closing equity is 50. Annual EBITDA is 30. Tax depreciation is 28.5714 in years 1–3 and 14.2857 in year 4, totaling 100. Cash tax is 0.2857 in years 1–3 and 3.1429 in year 4. Annual principal is 12.5; minimum DSCR is 26.8571 / 12.5 = about 2.15. Equity cash flow is 17.2143 in years 1–3 and 14.3571 in year 4. At a stated 10% hurdle, equity NPV is −50 + Σ[17.2143 / 1.1ᵗ, t=1…3] + 14.3571 / 1.1⁴ = about 2.62.

The case passes the assumed 1.50 covenant and positive-NPV hurdle. A stated covenant of 2.20 fails. An unestablished earning period leaves the return unresolved; a tax depreciation schedule does not supply that evidence. The bridge shows the complete annual lines, including zero terminal proceeds.