A study on the value assessment of corporate intangible assets using machine learning techniques

Identifiable non-monetary assets that are not physical and are held for the production or supply of goods or services, leasing to other units or management purposes are considered intangible assets. Intangible assets generally bring economic benefits by relying on physical assets, so we usually think that intangible assets can obtain economic benefits as the embodiment of their value. Since intangible assets have the characteristics of non-physical materiality and the perspective of the interrelationship between intangible assets and tangible assets when they play a role in making judgments. This characteristic is particularly important for intangible assets, which can help appraisers identify, grasp, and evaluate them better.

Knowledge-based intangible assets refer to intangible assets created by relying on intellectual labor and containing the fruits of intellectual labor. Rights-based intangible assets refer to the rights that can bring excessive benefits to a specific party, which are authorized by the enterprise or others and usually obtained in the form of a written contract at the expense of a specific party.

Relational intangible assets refer to the economic resources formed by the non-contractual trust relationship between the subject and the relevant business parties, which are established by the subject through the improvement of the enterprise’s management level, product quality, service quality and business reputation. Although there is no contractual guarantee for relational intangible assets, the relationship of trust between a specific subject and relevant business parties can generate economic benefits for a specific holding.The relationship that continues to bring economic benefits forms a business reputation, without a contractual relationship, which constitutes the basic content of a relational intangible asset.

The scope of other types of intangible assets is more ambiguous. Quantitatively speaking, other intangible assets are equivalent to the value of the enterprise minus the value of the so recognizable assets, which are usually considered as goodwill, i.e., they contain so intangible assets that are difficult to exist or recognize individually and that cannot be categorized as the above types.

Cost method refers to the use of current market prices to re-estimate the value of the target company’s assets minus the loss of various types of intangible assets, this calculation is based on the book value of the enterprise, through the re-assessment of the current value of intangible assets. The calculation of the cost method is shown in formula (1): (1) V=C−D1−D2−D3\[V=C-{{D}_{1}}-{{D}_{2}}-{{D}_{3}}\]

In Eq:

V, the value of the target company’s intangible assets.

D₁, mainly for such enterprises in the production process of machine tools in the long term after the use of wear and tear brought about by the depreciation. D₂ mainly because of the market competition between enterprises in the same industry has developed or access to new technologies, resulting in the original technology of the enterprise lags behind, production efficiency, production quality and so on have been reduced, and finally caused the reduction of enterprise value. D3 This devaluation mainly originates from outside the enterprise. The cost method formula can also be expressed as formula (3): (3) V=C×t\[V=C\times t\]

In Eq:

V, the value of the target company’s intangible assets.

The common valuation of t is generally based on the following three ways:

1) Value assessment of intangible assets by experts.

The main idea of the market approach can be divided into three items, the first item is to find one or several companies in the same industry that are almost always in the same situation as the target company to carry out the assessment, the second item is to obtain the company’s value multiplier based on the results obtained in the first item as a reference, and the third item is to make corrections to the previous calculations to obtain the final value, which is mainly based on the market value of the target company.

The market method of valuation is shown in formula (6): (6) V1X1=V2X2\[{}^{{{V}_{1}}}\!\!\diagup\!\!{}_{{{X}_{1}}}\;={}^{{{V}_{2}}}\!\!\diagup\!\!{}_{{{X}_{2}}}\;\]

In Eq:

V₁, the enterprise value of the target company being evaluated.

The income approach relies on the basic parameters of income, discount rate, and income period, which must be available in order to calculate the value of an intangible asset.

This paper uses the direct estimation method, which is mainly used to determine the value of intangible assets by comparing and analyzing the revenues from used and unused intangible assets. After determining the revenue of the intangible asset, the results are categorized into two types: one is the revenue growth type and the other is the cost saving type. For the first type of revenue growth path includes the first is the production of products at a higher price than the price of other companies in the same industry to produce this product, to get the amount of revenue as formula (7): (7) R=(P2−P1)×Q×(1−t)\[R=\left( {{P}_{2}}-{{P}_{1}} \right)\times Q\times \left( 1-t \right)\]

In Eq:

R, Amount of revenue.

For the first category in the earnings growth path included in the second is in the same industry, the same product, the enterprise uses the same sales price case, sales volume of a substantial increase in order to quickly capture the market, the amount of revenue as formula (8): (8) R=(Q2−Q1)×(P−C)×(1−t)\[R=\left( {{Q}_{2}}-{{Q}_{1}} \right)\times \left( P-C \right)\times \left( 1-t \right)\]

In Eq:

Q₁, the sales obtained by the enterprise under the condition of not using the intangible asset.

For the cost-saving type, the amount of revenue when the cost of production is lowered while the revenue and the price remain the same is shown in Equation (9): (9) R=(C2−C1)×Q×(1−t)\[R=\left( {{C}_{2}}-{{C}_{1}} \right)\times Q\times \left( 1-t \right)\]

In Eq:

R, the amount of revenue.

The B-S model uses the no-arbitrage principle, which states that there are no risk-free arbitrage opportunities in the market [20-21]: if there exist two assets with the same cash flows at any point in the future, then the current prices of the two assets should be the same. The basic formula for the B-S option pricing model is: (10) C=S[ N(d1) ]−Xe−rT[ N(d2) ]\[C=S\left[ N\left( {{d}_{1}} \right) \right]-X{{e}^{-rT}}\left[ N\left( {{d}_{2}} \right) \right]\] where d1=[ ln(s/x)+(r+σ2/2)T ]/σT${{d}_{1}}={\left[ \ln (s/x)+\left( r+{{{\sigma }^{2}}}/{2}\; \right)T \right]}/{\sigma \sqrt{T}}\;$, d2=d1−σT${{d}_{2}}={{d}_{1}}-\sigma \sqrt{T}$. in the public C is the value of the option, S is the value of the underlying asset, X is the strike price, r is the risk-free rate of return, T is the time to expiration, σ is the volatility, and N(d) is the probability distribution function of the normal distribution.

The B-P neural network adds an error back propagation process compared to the general neural network, and the structure of the more widely used neural networks generally includes at least three layers. An input layer, one or more hidden layers and an output layer, the role of the input layer is mainly to receive the input signal, while the hidden layer is responsible for the signal from the input layer through the activation function to process and transmit the signal to the output layer, the signal from the output layer will be compared with the real signal, and then determine whether to output the final result or enter the process of back propagation. In the process of propagation, each layer of neurons affects the state of the next layer of neurons by changing the weights.The data flow in the B-P neural network structure is divided into two parts: forward computation and back propagation.The principle of B-P neural network is shown in Fig. 1.

Figure 1.

Schematic diagram of neural network

Positive computation of the input signals: initial processed signals x are fed from the input layer, and then these signals are given a weight v. Next, they are processed through the computation of one or more hidden layers to obtain y, which is ultimately adjusted by the connection weights w and transmitted to the output layer to obtain the result o. The output result is compared with the reference metric d, which is usually subtracted from both to find the sum of the squares of the errors. In this process, the connection weights between the layers in the neural network use initial values and remain temporarily unchanged. If the final output of the learning result is more different from the expected value, then the weights need to be adjusted by entering the error backpropagation.

Error backpropagation: the error generated by the output result o and the reference metric d is discriminated, and if the error is lower than the threshold, the error signal will be backpropagated from the output layer to the upper layer of the B-P neural network, and in the process of backpropagation, the computer will adjust the threshold value of the neurons and the weights w between the hidden layers according to a predetermined rule, so as to make the output result close to the real value.

In the continuous uninterrupted propagation process, the B-P neural network will automatically adjust and update the weights according to the error in real time to ensure that the error will be reduced every time, so that the output results are more and more close to the reference metric.

Let the input layer of the model be X = (x₁,x₂,⋯,x_d)^T, i.e., the relevant attribute variables of the data assets, the number of nodes in the hidden layer be q, the output information of a certain hidden layer Y = (y₁,y₂,⋯,y_q)^T, the final output of the model O = (o₁,o₂,⋯,o_t)^T, i.e., the predicted value of the data assets, the true value of the sample D = (d₁,d₂,⋯,d_t)^T, i.e., the price of the data assets that are actually traded on the UEI data network, the weights between the input layer and the hidden layer V = (v₁,v₂,⋯,v_d)^T, and the weights between the hidden layer and the output layer W = (w₁,w₂,⋯,w_q)T.

The data transfer relation equation from the input layer to the hidden layer is: (11) { yj=f(μj),j=1,2,⋯,qμj=∑i=1dvijxi,j=1,2,⋯,q\[\left\{ \begin{array}{*{35}{l}} {{y}_{j}}=f\left( {{\mu }_{j}} \right),j=1,2,\cdots ,q \\ {{\mu }_{j}}=\sum\limits_{i=1}^{d}{{{v}_{ij}}}{{x}_{i}},j=1,2,\cdots ,q \\ \end{array} \right.\]

The data transfer relation equation from the hidden layer to the output layer is: (12) { ok=f(μk),k=1,2,⋯,lμk=∑j=1qwjkyj,k=1,2,⋯,l\[\left\{ \begin{array}{*{35}{l}} {{o}_{k}}=f\left( {{\mu }_{k}} \right),k=1,2,\cdots ,l \\ {{\mu }_{k}}=\sum\limits_{j=1}^{q}{{{w}_{jk}}}{{y}_{j}},k=1,2,\cdots ,l \\ \end{array} \right.\]

Where f(·) function is the activation function, among the commonly used activation functions, the Tanh function has a better performance because of its mean value of 0 and data-centered effect, so it is chosen as the activation function and its expression is: (13) f(x)=ex−e−xex+e−x\[f\left( x \right)=\frac{{{e}^{x}}-{{e}^{-x}}}{{{e}^{x}}+{{e}^{-x}}}\]

For training set (x_k,o_k), the mean square error of the model is: (14) Ek=12∑k=1l(ok−dk)2\[{{E}_{k}}=\frac{1}{2}\sum\limits_{k=1}^{l}{{{\left( {{o}_{k}}-{{d}_{k}} \right)}^{2}}}\]

Based on the gradient descent strategy, all connection weights between neurons from the input layer to the hidden layer to the output layer are subjected to adjustment, and this process is done automatically by the computer based on the error feedback, so that the value of the error E_k is constantly decreasing, and in terms of this principle, it should be made so that the gradient of the error descent is proportional to the amount of adjustment of the connection weights, i.e: (15) { Δwjk=η⋅δko⋅∂μk∂wjk=η⋅δko⋅yjΔvij=η⋅δjy⋅∂μk∂vij=η⋅δjy⋅xi\[\left\{ \begin{array}{*{35}{l}} \Delta {{w}_{jk}}=\eta \cdot \delta _{k}^{o}\cdot \frac{\partial {{\mu }_{k}}}{\partial {{w}_{jk}}}=\eta \cdot \delta _{k}^{o}\cdot {{y}_{j}} \\ \Delta {{v}_{ij}}=\eta \cdot \delta _{j}^{y}\cdot \frac{\partial {{\mu }_{k}}}{\partial {{v}_{ij}}}=\eta \cdot \delta _{j}^{y}\cdot {{x}_{i}} \\ \end{array} \right.\] where the learning rate η ∈ (0,1), which controls the step size of the gradient descent in each round of propagation, reflects the speed of the training process, if it is too large, it will be easy to oscillate, if it is too small, the convergence rate will be too slow again, and the error δko$\delta _{k}^{o}$, δjy$\delta _{j}^{y}$ unfolds as: (16) { δko=(Dk−Ok)⋅Ok⋅(1−Ok)δjy=[ ∑kl(Dk−Ok)⋅f′(μk)⋅wjk ]⋅f′(μj)=(∑k=1lδko⋅wjk)⋅yj⋅(1−yj)\[\left\{ \begin{matrix} \delta _{k}^{o}=\left( {{D}_{k}}-{{O}_{k}} \right)\cdot {{O}_{k}}\cdot \left( 1-{{O}_{k}} \right) \\ \begin{align} & \delta _{j}^{y}=\left[ \sum\limits_{k}^{l}{\left( {{D}_{k}}-{{O}_{k}} \right)}\cdot f\prime \left( {{\mu }_{k}} \right)\cdot {{w}_{jk}} \right]\cdot f\prime \left( {{\mu }_{j}} \right) \\ & =\left( \sum\limits_{k=1}^{l}{\delta _{k}^{o}}\cdot {{w}_{jk}} \right)\cdot {{y}_{j}}\cdot \left( 1-{{y}_{j}} \right) \end{align} \\ \end{matrix} \right.\]

Substituting Eq. (16) into Eq. (15), the formula for updating the weights of connections between neurons of the B-P neural network is obtained: (17) { Δwjk=η⋅δko⋅yj=η⋅(Dk−Ok)⋅Ok(1−Ok)⋅yjΔvij=η⋅δjy⋅xi=η⋅(∑k=1lδko⋅wjk)⋅yj⋅(1−yj)⋅xi\[\left\{ \begin{array}{*{35}{l}} \Delta {{w}_{jk}}=\eta \cdot \delta _{k}^{o}\cdot {{y}_{j}}=\eta \cdot \left( {{D}_{k}}-{{O}_{k}} \right)\cdot {{O}_{k}}\left( 1-{{O}_{k}} \right)\cdot {{y}_{j}} \\ \Delta {{v}_{ij}}=\eta \cdot \delta _{j}^{y}\cdot {{x}_{i}}=\eta \cdot \left( \sum\limits_{k=1}^{l}{\delta _{k}^{o}}\cdot {{w}_{jk}} \right)\cdot {{y}_{j}}\cdot \left( 1-{{y}_{j}} \right)\cdot {{x}_{i}} \\ \end{array} \right.\]

In order to predict the value of data assets, this section will construct a data asset value assessment model based on B-P neural network according to the method principle described in the previous section, and the process of constructing an enterprise intangible asset value assessment model based on B-P neural network is shown in Figure 2.

Figure 2.

Enterprise intangible asset value evaluation model construction process

Firstly, the full sample data is divided into two subsets, which are the training set and the test set, and the indicators of each influencing factor affecting the value of data assets are taken as the input vectors of the input layer of the neural network, and the value of the data assets is taken as the output of the neural network, in which the determination of the number of hidden layers and the number of neurons is determined by the characteristics of the trained historical data and the predicted values, and the specific values will be described in detail in the empirical section. This network is then trained with the training set, in which the input layer data is provided to the input layer neurons and the signals are forward propagated layer by layer, and different input vectors will get different output values in the output layer; this output value is further compared with the true value of the data asset value to find out the mean-square error, and the training is considered to be completed when the value is less than a certain given value, or else the error signals will be back-propagated again to each of the Otherwise, the error signal is back-propagated to each neuron in the hidden layer, and finally the weights and thresholds are adjusted according to the hidden layer neuron errors, and the process continues until the stopping condition is reached.

Finally, the test set data is used to verify the accuracy of the evaluation model that has just finished training, and if the accuracy is low, it is necessary to adjust the parameters and repeat the above process to retrain. Through the above procedure, the value of the unknown data assets can finally be assessed more accurately.

The main source of corporate transaction data for this paper is the “BVD-Zephyr - Global M&A Transaction Analysis Database”. The company reports come from the integrated BvD and BvD value-added software, and the data collection covers East and Southeast Asian countries including China. A sample of 300 publicly available corporate intangible asset data was identified, 210 of the sample data were selected for model training, and the remaining 90 samples were used to test the model, which was used to test whether the established model meets the objective requirements.

In order to improve the fitting effect of the B-P neural network model, the sample data is normalized. In order to improve the effect of model training and make the prediction results more accurate, the data need to be normalized. In this paper, the normalization of data is mainly used in the normalization method. The premnmx function and tramnmx function are used to normalize the training data and test data of the samples respectively, and the two functions are normalized in the same way, only the subject of the object is different. The main processing as the following formula: (18) Y=X−minXmaxX−X−1\[Y=\frac{X-\min X}{\max X-X}-1\]