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Financing effects are special kinds of considerations made for the companies or individuals who are weaker in terms of finances and may find it hard to obtain debt from the markets. The intention of financial effects is to help companies and individuals mitigate the financial burdens that may arise from time to time.Here are some prominent forms of financing effects.Subsidized LoansIn case of a subsidized loan, the lender pays the interest portion of the loan, reducing the burden of the borrower who may find it hard to pay back the interests on a loan taken for a certain reason, such ... Read More
Risk-free Debt is HypotheticalRisk-free debt is a hypothetical condition where the risk associated with the debt is zero. In general, there is no such thing as risk-free debt. While the risk of debt may go up and down in comparison, it can never be zero in any condition. This is apparent from the government bonds which carry minimum risk but not risk-free.Even when a collateral is issued against the debt resourced, the debt does not become risk-free. Investors should be aware that the company may be unable to provide the debt back in case of bankruptcy.It is notable that the ... Read More
The Free Cash Flow of a company depends on the following factors −Sales ProjectionExpense EstimationDepreciationCapital ExpenditureChanges in Net Working CapitalInterest ExpensesTax RatesInflationLet us discuss each of these factors in detail and see how they affect the Free Cash Flows of a company.Sales ProjectionTo determine the Free Cash Flow of a company, the first step is to determine its projected sales.Sales depend upon many factors, such as market share, growth, and demand of products in the market.A company cannot remain at one stage in terms of sales. There are normal, super-normal, and declining growth phases of a company.An analyst dealing with ... Read More
Debt rebalancing is a process of rebalancing the debt while calculating the Weighted Average Cost of Capital (WACC). The concept of WACC is based on the assumption that WACC remains constant throughout the lifetime of a project. It also depends on the fact that debt proportionality remains the same over the course of years of a project.As WACC remains constant throughout the lifetime of a project, the debt will go down each year according to WACC.As WACC remains constant over the years, to keep the debt proportionality constant, debt has to be rebalanced to keep the WACC constant.This change in ... Read More
Autocorrelation FunctionThe autocorrelation function defines the measure of similarity or coherence between a signal and its time delayed version. The autocorrelation function of a real energy signal $\mathit{x}\mathrm{(\mathit{t})}$ is given by, $$\mathit{R}\mathrm{(\mathit{\tau})} \:\mathrm{=}\: \int_{-\infty}^{\infty}\mathit{x\mathrm(\mathit{t})}\:\mathit{x}\mathrm{(\mathit{t-\tau})}\:\mathit{dt}$$Energy Spectral Density (ESD) FunctionThe distribution of the energy of a signal in the frequency domain is called the energy spectral density.The ESD function of a signal is given by, $$\mathit{\psi}\mathrm{(\mathit{\omega})}\: \mathrm{=}\: \mathrm{|\mathit{X}\mathrm{(\mathit{\omega})}|}^\mathrm{2} \:\mathrm{=}\: \mathit{X}\mathrm{(\mathit{\omega})} \mathit{X}\mathrm{(\mathit{-\omega})}$$Autocorrelation TheoremStatement − The autocorrelation theorem states that the autocorrelation function $\mathit{R}\mathrm{(\mathrm{\tau})}$ and the ESD (Energy Spectral Density) function $\mathit{\psi}\mathrm{(\mathit{\omega})}$ of an energy signal $\mathit{x}\mathrm{(\mathit{t})}$ form a Fourier transform pair, i.e., $$\mathit{R}\mathrm{(\mathit{\tau})} ... Read More
To compute the condition number of a matrix with respect to a matrix norm, we could apply torch.linalg.cond() method. It returns a new tensor with computed condition number. It accepts a matrix, a batch of matrices and also batches of matrices. A matrix is a 2D torch Tensor. It supports input of float, double, cfloat, and cdouble data typesSyntaxtorch.linalg.cond(M, p=None)ParametersM – A matrix or batch of matrices.p – A type of matrix norm to be used in computation of condition number. Default matrix norm is 2-norm.It returns a real-valued tensor of condition number.StepsWe could use the following steps to compute the ... Read More
To compute the pseudoinverse of a square matrix, we could apply torch.linalg.pinv() method. It returns a new tensor with pseudoinverse of the given matrix. It accepts a matrix, a batch of matrices and also batches of matrices. A matrix is a 2D torch Tensor. It supports input of float, double, cfloat, and cdouble data types.Syntaxtorch.linalg.pinv(M)Where M is a matrix or batches of matrices.StepsWe could use the following steps to compute the pseudoinverse of a matrix −Import the required library. In all the following examples, the required Python library is torch. Make sure you have already installed it.import torchDefine a matrix. ... Read More
To compute the inverse of a square matrix, we could apply torch.linalg.inv() method. It returns a new tensor with inverse of the given matrix. It accepts a square matrix, a batch of square matrices, and also batches of square matrices.A matrix is a 2D torch Tensor. It supports input of float, double, cfloat, and cdouble data types. The inverse matrix exists if and only if the square matrix is invertible.Syntaxtorch.linalg.inv(M)Where M is a square matrix or a batch of square matrices. It returns the inverse matrix.StepsWe could use the following steps to compute the inverse of a square matrix −Import ... Read More
To compute the norm of a vector or a matrix, we could apply torch.linalg.norm() method. It returns a new tensor with computed norm. It accepts a vector, matrix, a batch of matrices and also batches of matrices.A vector is a 1D torch Tensor where a matrix is a 2D torch Tensor. It supports input of float, double, cfloat, and cdouble data types. We can compute the norm of the matrix or batch/es of matrices along the different dimensions. For example, we could compute the norm of a matrix along dimension 0 or along dimension1.Syntaxtorch.linalg.norm(A)A is a vector, matrix or batch/s ... Read More
To solve a square system of linear equations with unique solution, we could apply the torch.linalg.solve() method. This method takes two parameters −first, the coefficient matrix A, andsecond, the right-hand tensor b.Where A is a square matrix and b is a vector. The solution is unique if A invertible. We can solve a number of systems of linear equations. In this case, A is a batch of square matrices and b is a batch of vectors.Syntaxtorch.linalg.solve(A, b)ParametersA – Square matrix or batch of square matrices. It is the coefficient matrix of system of linear equations.b – Vector or a batch ... Read More