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01 The demo
Watch it run, right here. Tap a prompt, then hit Ask ↓
15% interest, build-up + DLOC/DLOM open ▾
TrueMath
Public Library ▾
···
FY24 net income was 662,500 with interest of 30,000…
▤ Business Valuation Analyst simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
FY24 net income was 662,500 with interest of 30,000, taxes of 220,000, and depreciation of 75,000. The owner takes 350,000 but a hired manager runs 200,000, rent to the family LLC is 180,000 against 120,000 market, and there's 40,000 of one-time legal fees to add back. Tax rate 25%. Build up the cost of equity from a 4.5% risk-free rate, 5.5% ERP, 5.8% size premium, 1.2% industry premium, and 3 points of company-specific risk, with 3% long-term growth. Apply a 10% DLOC and a 28% DLOM. What is the value of a 15% interest?
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
reported_net_income: 662500 USD
reported_interest_expense: 30000 USD
reported_tax_expense: 220000 USD
reported_depreciation_amortization: 75000 USD
reported_owner_compensation: 350000 USD
market_owner_compensation: 200000 USD
reported_rent_expense: 180000 USD
market_rent: 120000 USD
other_normalization_adjustments: 40000 USD
bv_tax_rate: 25%
risk_free_rate: 4.5%
equity_risk_premium: 5.5%
size_premium: 5.8%
industry_risk_premium: 1.2%
specific_company_risk_premium: 3%
long_term_growth_rate: 3%
dloc: 10%
dlom: 28%
subject_interest_pct: 15%
calculate: subject_interest_value
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Jul 9, 2026 12:15 PMResponse
Creating Scenario 1.

Build-Up Method Cost of Equity

Calculates cost of equity via the build-up method: risk-free rate plus equity risk premium plus size premium plus industry risk premium plus specific company risk premium.
• Specific Company Risk Premium: 3.00%
• Risk-Free Rate: 4.50%
• Equity Risk Premium: 5.50%
• Size Premium: 5.80%
• Industry Risk Premium: 1.20%
• Cost of Equity: 20.00%

Capitalization Rate

Calculates capitalization rate as cost of equity (or WACC, depending on basis) minus long-term sustainable growth rate.
• Long-Term Sustainable Growth Rate: 3.00%
• Cost of Equity: 20.00%
• Capitalization Rate: 17.00%

Related-Party Rent Normalization

Calculates the rent normalization adjustment as reported rent less market rent.
• Reported Rent Expense: $180,000
• Market Rent: $120,000
• Rent Normalization Adjustment: $60,000

Owner Compensation Normalization

Calculates the owner compensation normalization adjustment as reported owner compensation less market owner compensation.
• Reported Owner Compensation: $350,000
• Market Owner Compensation: $200,000
• Owner Compensation Normalization Adjustment: $150,000

Total Normalization Adjustments

Sums the owner compensation, related-party rent, and other normalization adjustments.
• Owner Compensation Normalization Adjustment: $150,000
• Rent Normalization Adjustment: $60,000
• Other Normalization Adjustments: $40,000
• Total Normalization Adjustments: $250,000

Normalized Earnings (After-Tax)

Calculates after-tax normalized earnings by adding the after-tax value of normalization adjustments to reported net income.
• Reported Net Income: $662,500
• Total Normalization Adjustments: $250,000
• Income Tax Rate: 25.0%
• Normalized Earnings (After-Tax): $850,000

Capitalization of Earnings

Calculates the income approach indication by dividing normalized earnings by the capitalization rate.
• Normalized Earnings (After-Tax): $850,000
• Capitalization Rate: 17.00%
• Income Approach Indication (Cap of Earnings): $5,000,000

Controlling Marketable Value from Capitalization of Earnings

Assigns the capitalization of earnings indication directly to controlling marketable value when used as the sole valuation approach.
• Income Approach Indication (Cap of Earnings): $5,000,000
• Controlling Marketable Value: $5,000,000

Minority Marketable Value

Calculates minority marketable value by applying DLOC to controlling marketable value.
• Discount for Lack of Control (DLOC): 10.0%
• Controlling Marketable Value: $5,000,000
• Minority Marketable Value: $4,500,000

Minority Non-Marketable Value

Calculates minority non-marketable value by applying DLOM to minority marketable value.
• Discount for Lack of Marketability (DLOM): 28.0%
• Minority Marketable Value: $4,500,000
• Minority Non-Marketable Value: $3,240,000

Subject Interest Value

Calculates the pro rata subject interest value as minority non-marketable value times subject interest percentage.
• Subject Interest Percentage: 15.00%
• Minority Non-Marketable Value: $3,240,000
• Subject Interest Value: $486,000
Requested result for Subject Interest Value is $486,000.
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Weighted conclusion → LOV waterfall open ▾
TrueMath
Public Library ▾
···
Weight the income approach at 60% on a 5,000,000 indication…
▤ Business Valuation Analyst simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
Weight the income approach at 60% on a 5,000,000 indication, market at 30% on 7,800,000, and asset at 10% on 2,800,000, then apply a 10% DLOC, a 28% DLOM, and a 15% subject interest. Show me the level of value waterfall.
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
selected_income_indication: 5000000 USD
income_weight: 60%
selected_market_indication: 7800000 USD
market_weight: 30%
asset_approach_indication: 2800000 USD
asset_weight: 10%
dloc: 10%
dlom: 28%
subject_interest_pct: 15%
calculate: level_of_value_waterfall
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Jul 9, 2026 12:18 PMResponse
Creating Scenario 1.

Weighted Value Conclusion

Reconciles the income, market, and asset approach indications into a single controlling marketable value using the appraiser's assigned weights, deducting net debt when the indications are on an invested-capital basis.
• Selected Income Approach Indication: $5,000,000
• Income Approach Weight: 60.0%
• Selected Market Approach Indication: $7,800,000
• Market Approach Weight: 30.0%
• Asset Approach Indication: $2,800,000
• Asset Approach Weight: 10.0%
• Net Debt: 0
• Controlling Marketable Value: $5,620,000

Minority Marketable Value

Calculates minority marketable value by applying DLOC to controlling marketable value.
• Discount for Lack of Control (DLOC): 10.0%
• Controlling Marketable Value: $5,620,000
• Minority Marketable Value: $5,058,000

Minority Non-Marketable Value

Calculates minority non-marketable value by applying DLOM to minority marketable value.
• Discount for Lack of Marketability (DLOM): 28.0%
• Minority Marketable Value: $5,058,000
• Minority Non-Marketable Value: $3,641,760

Subject Interest Value

Calculates the pro rata subject interest value as minority non-marketable value times subject interest percentage.
• Subject Interest Percentage: 15.00%
• Minority Non-Marketable Value: $3,641,760
• Subject Interest Value: $546,264

Level of Value Waterfall

Builds a four-row waterfall table showing controlling marketable, minority marketable, minority non-marketable, and subject interest values.
• Controlling Marketable Value: $5,620,000
• Minority Marketable Value: $5,058,000
• Minority Non-Marketable Value: $3,641,760
• Subject Interest Value: $546,264
• Level of Value Waterfall:
Value
Controlling Marketable Value$5,620,000
Minority Marketable Value (after DLOC)$5,058,000
Minority Non-Marketable Value (after DLOM)$3,641,760
Subject Interest Value (Pro Rata)$546,264
Requested result for Level of Value Waterfall included above.
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DCF value, 5-yr FCF + Gordon terminal open ▾
TrueMath
Public Library ▾
···
Discount these free cash flows at 15% over a five-year forecast…
▤ Business Valuation Analyst simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
Discount these free cash flows at 15% over a five-year forecast: 800,000, 880,000, 960,000, 1,050,000, and 1,140,000, with a terminal-year cash flow of 1,175,000 growing at 3% in perpetuity. What is the DCF indicated value?
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
fcf_table: [800000, 880000, 960000, 1050000, 1140000] USD
wacc: 15%
dcf_periods: 5 yr
fcf_terminal: 1175000 USD
terminal_growth_rate: 3%
calculate: income_approach_indication_dcf USD
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Jul 9, 2026 12:21 PMResponse
Creating Scenario 1.

Terminal Value (Gordon Growth)

Calculates terminal value using the Gordon Growth Model: terminal FCF divided by WACC less terminal growth rate.
• Terminal Year FCF: $1,175,000
• WACC: 15.00%
• DCF Terminal Growth Rate: 3.00%
• Terminal Value: $9,791,667

Normalize DCF Forecast Periods

Converts the forecast horizon to a plain number of years for terminal value discounting.
• DCF Forecast Periods: 5 yr
• DCF Forecast Periods (Normalized): 5

PV of Projected FCFs

Discounts each year of the user-supplied FCF projection table at WACC and sums the results.
• Free Cash Flow Projection Table:
#Free Cash Flow
1$800,000
2$880,000
3$960,000
4$1,050,000
5$1,140,000
• WACC: 15.00%
• PV of Projected FCFs: $3,159,397

DCF Enterprise Value

Calculates DCF indicated value as PV of projected FCFs plus the present value of terminal value.
• PV of Projected FCFs: $3,159,397
• Terminal Value: $9,791,667
• WACC: 15.00%
• DCF Forecast Periods (Normalized): 5
• Income Approach Indication (DCF): $8,027,585
Requested result for Income Approach Indication (DCF) is $8,027,585.
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02 The comparison

Watch how LLMs really work.

One prompt. Ten runs each. Nothing staged.
The prompt, sent to each“A 7,000,000 deal: NOI 450,000 growing 3%, 5-year hold, 65% LTV at 7% on 30-year am, closing 1.5%, exit cap 6.5%, selling costs 2%. What's my levered IRR?”
The exact answer · 5-year levered IRR
10.8463781499708%
● RAW LLM
0/10 exact
methods10 distinct
avg time29.7 s
energy / call~1.5 Wh
● TRUEMATH
10/10 exact
method1, auditable
avg time3.1 s9.6× faster
energy / call~0.003 Wh~500× less
Claude Opus 4.8 vs TrueMath via natural language, 10 runs each. Energy is inference-only; datacenter cooling widens the gap.
TrueMath was 9.6x faster, 500x more energy efficient, and delivered 10 identically precise answers using one fixed auditable method.
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