Valuation method of intellectual property pledge financing based on income interval analysis and risk adjustment coefficient

The paper addresses how to more reliably value intellectual property (IP) for use as collateral in pledge financing, especially for small- and medium-sized technology firms that face financing constraints and high risk. Traditional valuation approaches (labor or cost-of-production theories; market and cost methods) are ill-suited for IP due to its originality, proprietary nature, and incommensurability. The authors ground IP valuation in marginal utility theory: IP-derived products create competitive advantage whose future income is the source of value; utility and scarcity underpin valuation. The income method is thus appropriate but suffers from sensitivity to appraiser judgments, changing conditions, and bargaining power, leading to indicator uncertainty. The study proposes an income interval analysis to capture indicator ranges (expected income, discount rate, useful life) and combines Analytic Hierarchy Process (AHP) with set-valued statistics to derive a risk adjustment coefficient. A final point value is computed from the interval and the risk coefficient, yielding a multi-indicator system (interval, risk coefficient, point value) to guide negotiations and reduce pledge financing risk. The approach is presented as generally applicable and motivated by the rapid growth of IP pledge financing in China.

The review outlines three standard IP valuation approaches: market, cost, and income methods. The market method requires active, transparent markets and comparable transactions, which are rare for unique, proprietary IP, especially in developing countries; transaction data are often confidential, limiting applicability to certain right-of-use or similar intangible assets. The cost method aggregates development expenditures adjusted for obsolescence, reflecting socially necessary labor time but ignoring future value; it best estimates minimum trading value given IP’s high-risk/high-reward nature. The income method discounts expected future income and is most used but hampered by difficulties forecasting income and choosing discount rates amid multiple risks. Scholars have proposed improvements (e.g., excess return–based expected returns; income sharing rates). Beyond these, mixed qualitative–quantitative methods (Delphi, AHP, TOPSIS, fuzzy evaluation) have been applied to structure multi-criteria decisions. Given IP’s uniqueness and risk, the authors propose combining income interval analysis with a risk adjustment coefficient derived via AHP and set-valued statistics to form a multi-indicator system (interval values, risk coefficient, point value) that better manages evaluation risk. They also position utility theory and interval theory as theoretical foundations for pledge financing valuation, arguing that labor and cost-of-production theories do not fit IP’s nature.

Overview: The method proceeds in three steps: (1) construct an indicator system and compute preliminary interval values of IP via income interval analysis; (2) build a change-structure model of risk indicators affecting IP value, compute indicator weights with AHP, refine via set-valued statistics, and derive a risk adjustment coefficient; (3) compute a point value from the interval values and the risk coefficient.

Income method and interval extension: The traditional income method values IP as V = Σ R_t / (1 + r)^t over its remaining useful life t, where R_t is expected IP-attributable income in year t and r is the discount rate. Recognizing uncertainty and variability across appraisers and economic/legal conditions, the method replaces point estimates with intervals for key indicators: income [R−, R+], discount rate [r−, r+], and useful life [t−, t+]. The IP value interval is computed by applying interval arithmetic over the discounted income stream to yield [V−, V+].

Interval arithmetic rules: Using interval theory, calculations employ rules for nonnegative intervals [a, a+] and [b, b+]: addition [a+b, a+ + b+]; subtraction [a − b+, a+ − b]; multiplication [a·b, a+·b+]; division [a/b+, a+/b] (b > 0); exponentiation [a^n, a+^n] for n ≥ 1; and averaging Ave([A_i]) = [Σ a_i/n, Σ a_i+/n]. These enable propagating uncertainty through discounting and summation.

Set-valued statistics: Expert judgments about indicator ranges are incorporated using set-valued statistics. For each plan-layer indicator i, n experts provide interval assessments; a drop-shadow function X(μ_i) aggregates the membership of point estimates within each expert’s interval. The estimated weight μ̄_i is obtained by integrating X(μ_i) over its domain. A confidence measure b_i = 1/(1 + g_i) is computed, where g_i is a dispersion metric based on deviations from μ̄_i. If b_i is below a preset threshold (typically 0.9), experts iteratively adjust intervals until consistency is achieved.

AHP weighting and risk change structure: A hierarchical model of risk factors affecting IP value changes is defined with three criterion-layer components—C1 (market value change), C2 (technical value change), C3 (legal value change)—each decomposed into plan-layer indicators: C1: P11 market value prospect, P12 readiness of commercialization, P13 fierceness of competition, P14 stability of IP rights; C2: P21 degree of standardization, P22 international presence, P23 irreplaceability, P24 economic life; C3: P31 scope of protection, P32 infringement judging, P33 useful life. Experts perform pairwise comparisons using a 1–9 Saaty scale to form judgment matrices for A–C and C–P levels. Weights are derived (e.g., C1=0.5390, C2=0.2972, C3=0.1638), and consistency is verified (CR < 0.1). Plan-layer weights are combined with criterion-layer weights to yield overall indicator weights.

Risk adjustment coefficient: For each plan-layer indicator, μ_i is estimated via set-valued statistics with consistency b_i ≥ 0.9. The risk adjustment coefficient AC is computed as the weighted sum of μ_i across all plan-layer indicators using their combined weights. AC represents the probability (or confidence) that the realized value lies within the upper portion of the preliminary interval.

Point value computation: Given the preliminary IP value interval [V−, V+], the point value is V_point = V− + (V+ − V−) × AC. This reflects how far the negotiated loan amount may deviate upward from the lower bound in line with quantified risk control.

Application procedure and case study steps: (1) Indicator selection and weighting: draw from recent cases, policies, literature, and the CTEX manual; experts rate indicators on a 1–9 scale; compute normalized weights (using yaahp); filter to 11 key indicators after removing overlaps/unclear items. (2) Preliminary interval estimation: appraisers compile a report with baseline estimates; five experts set intervals for r, t, and annual R based on indicator weights and information; compute [r−, r+], [t−, t+], and yearly [R−, R+]; propagate via interval arithmetic to obtain [V−, V+]. (3) Risk modeling: build the change-structure hierarchy (C1–C3; P11–P33); derive AHP weights with consistency checks; elicit expert interval judgments for plan-layer indicators; apply set-valued statistics to obtain μ_i and b_i; compute AC. (4) Point value: combine [V−, V+] and AC to produce V_point for financing decisions.

• In the case of XTX Technology’s pledged patent (No: ZLNJ027), experts estimated intervals for discount rate, useful life, and annual IP-attributable income. Aggregated intervals included [r−, r+] ≈ [8.22%, 10.43%] and [t−, t+] ≈ [6.1, 7.1] years.
• The preliminary IP value interval was [V−, V+] = [419.2327, 454.6850] (ten thousand yuan), equivalent to [4.192327, 4.54685] million yuan.
• The AHP-derived combined weights for the risk change structure emphasized market and economic-life-related risks (e.g., C1=0.5390; P14 stability of IP rights combined weight 0.2511; P24 economic life 0.1434; P12 readiness of commercialization 0.1494). All consistency ratios were below 0.1.
• Set-valued statistics produced high-confidence μ_i estimates with b_i ≥ 0.994 across indicators. The overall risk adjustment coefficient was AC = 0.8864.
• The point value computed as V_point = 419.2327 + (454.6850 − 419.2327) × 0.8864 = 450.6576 (ten thousand yuan) = 4.506576 million yuan.
• The multi-indicator system (interval values, AC, point value) provides a negotiation range and a quantified risk-based point estimate, supporting bank risk control and facilitating pledge financing.

The findings demonstrate that extending the income method to an interval framework captures inherent uncertainty in IP valuation while preserving economic meaning (utility and scarcity–based income). The interval [V−, V+] offers a transparent negotiation band for lenders and borrowers. By modeling risk via a structured AHP hierarchy and refining weights with set-valued statistics, the method quantifies how changes in market, technical, and legal factors may shift value, yielding a risk adjustment coefficient that directly informs how far above the lower bound a bank might reasonably lend. Consistency checks ensure robustness of expert judgments. In practice, this approach addresses the primary limitations of point-estimate income methods—sensitivity to assumptions and appraiser subjectivity—by incorporating uncertainty and expert consensus formally. The case study indicates feasibility and practical relevance, particularly aligning with financial institutions’ risk control requirements in pledge financing. The authors argue the approach is broadly applicable beyond the Chinese context, as it relies on generalizable theories and procedures rather than market-specific transaction data.

The study proposes and validates a multi-indicator valuation framework for IP pledge financing that integrates income interval analysis, AHP-based risk modeling, and set-valued statistics to compute a risk adjustment coefficient and point value. In the XTX Technology case, the IP’s value interval was [4.192327, 4.54685] million yuan, and the point value was 4.506576 million yuan, providing practical guidance for loan negotiations. The method reduces valuation ambiguity, supports banks’ risk management, and facilitates financing operations. The approach is theoretically grounded (utility and interval theories) and practically efficient, and is presented as widely applicable to SMEs’ IP pledge financing.

The study involved a limited number of experts due to strict qualification criteria (familiarity with IP valuation theory, certification by the China Appraisal Society, and prior valuation experience). This constraint may affect generalizability of expert-derived judgments. Future work should expand expert input via broader survey instruments and apply reliability, validity, and factor analyses (e.g., with SPSS) to build indicator systems. The study also did not fully utilize objective AHP variants; future research will incorporate more objective weighting methods to reduce bias in expert evaluations.