Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
A pure-equity or an unlevered firm obtains all its funds internally and does not require to obtain any debt from the market. In other words, pure-equity firms are debt-free. Therefore, in case of an investment, a pure-equity firm doesn’t have to pay any interest for the debt the company may acquire from the market.Debt-free companies may use retained earnings or revenues generated from their existing projects to fund an investment project, so they do not need to acquire financing externally.Pure-equity firms use the asset cost of capital instead of the cost of equity to fund their investment projects. It is ... Read More
Asset cost of capital refers to the capital of a firm when the financing of a project is purely done by equity without any form of debt. It is the expected rate of return on the company's assets in a hypothetical debt-free method. Asset cost of capital is also known as the unlevered cost of capital because it is done without any financial leverage of debt. It is completely a financial position where a company can finance without taking care of any debt.The cost of executing a project in a completely debt-free manner is the asset cost of capital. As ... Read More
Like Free Cash Flow (FCF) and Capital Cash Flow (CCF), Adjusted Present value (APV) is another way of evaluating an investment project. However, it is completely different from FCF and CCF approaches.FCF and CCF are primarily related to interest tax shields and they do not consider the various financing effects that may affect the value of the investment project. In fact, most of the investment projects contain some form of financing effects and so Adjusted Present Value approach is a more utilized approach in practice.It is known that FCF approach of evaluating a project is good when the debt-to-value ratio ... Read More
What are Issue Costs?When companies raise money from the market, it needs to distribute securities in the market which requires the company to incur some cost. These one-time costs are called issue costs that have to be considered while the project begins. It is a preliminary cost all companies must spend to raise money from the investors in the market.How to Handle Issue Costs?Issue costs are handled at the outset of a project. The best way to manage the issue cost is to use the APV model to evaluate an investment project. In APV approach, the issue cost is discounted ... Read More
The levered cost of equity represents the risk components of the financial structure of a firm. To finance the projects of a firm, companies often need to resort to debt that is collected from the market. The market offers the debt by the resources of the investors.In case of levered cost of equity, the firms have larger debt proportions, and hence the firms must convince the investors that it is capable to provide the business and financial risk premiums.In general, when a company uses unlevered cost of equity, it does not go for debts from the market. It uses the ... Read More
Laplace TransformThe Laplace transform is a mathematical tool which is used to convert the differential equations in time domain into the algebraic equations in the frequency domain or s-domain.Mathematically, the Laplace transform of a time-domain function $\mathit{x}\mathrm{\left(\mathit{t}\right)}$ is defined as −$$\mathrm{\mathit{L}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{t}\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{s}\right)}\:\mathrm{=}\:\int_{\mathrm{0} }^{\mathrm{\infty} }\mathit{x}\mathrm{\left(\mathit{t}\right)}\mathit{e^{-\mathit{st}}\:\mathit{dt}}}$$Where, s is a complex variable and it is given by, $$\mathrm{\mathit{s}\:\mathrm{=}\:\sigma \:\mathrm{+}\:\mathit{j\omega}}$$And the operator L is called the Laplace transform operator which transforms the domain function $\mathit{x}\mathrm{\left(\mathit{t}\right)}$ into the frequency domain function X(s).Properties of Laplace TransformThe following table highlights some of the important properties of Laplace transform −PropertyFunction $\mathit{x}\mathrm{\left(\mathit{t}\right)}$Laplace Transform $\mathit{X}\mathrm{\left(\mathit{s}\right)}$Notation$\mathrm{\mathit{x}_{\mathrm{1}}\mathrm{\left(\mathit{t}\right)}}$$\mathrm{\mathit{X}_{\mathrm{1}}\mathrm{\left(\mathit{s}\right)}}$$\mathrm{\mathit{x}_{\mathrm{2}}\mathrm{\left(\mathit{t}\right)}}$$\mathrm{\mathit{X}_{\mathrm{2}}\mathrm{\left(\mathit{s}\right)}}$Scalar Multiplication$\mathrm{\mathit{k}\mathit{x}\mathrm{\left(\mathit{t}\right)}}$$\mathrm{\mathit{k}\mathit{X}\mathrm{\left(\mathit{s}\right)}}$Linearity$\mathrm{\mathit{a}\mathit{x}_{\mathrm{1}}\mathrm{\left( \mathit{t}\right)}\:\mathrm{+}\:\mathit{b}\mathit{x}_{\mathrm{2}}\mathrm{\left( \mathit{t}\right)}}$$\mathrm{\mathit{a}\mathit{X}_{\mathrm{1}}\mathrm{\left( \mathit{s }\right)}\:\mathrm{+}\:\mathit{b}\mathit{X}_{\mathrm{2}}\mathrm{\left(\mathit{s}\right)}}$Time Shifting$\mathrm{\mathit{x}\mathrm{\left(\mathit{t-t_{\mathrm{0}}}\right)}}$$\mathrm{\mathit{e}^{- ... Read More
Z-TransformZ-transform is a mathematical tool which is used to convert the difference equations in time domain into the algebraic equations in the frequency domain.Mathematically, if $\mathrm{\mathit{x\left ( n \right )}}$ is a discrete-time sequence, then its Z-transform is defined as −$$\mathrm{\mathit{X\left ( z \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }-\infty }^{\infty }x\left ( n \right )z^{-n}\; \; \; \cdot \cdot \cdot \left ( \mathrm{1} \right )}}$$Where, z is a complex variable. The z-transform defined in eq. (1) is called bilateral or two-sided z-transform.The unilateral or one-sided z-transform is defined as −$$\mathrm{\mathit{X\left ( z \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }\mathrm{0}}^{\infty }x\left ( ... Read More
Laplace TransformThe Laplace transform is a mathematical tool which is used to convert the differential equation in time domain into the algebraic equations in the frequency domain or s-domain.Mathematically, if $\mathrm{\mathit{x\left ( t \right )}}$ is a time domain function, then its Laplace transform is defined as, $$\mathrm{\mathit{L\left [ x\left ( t \right ) \right ]\mathrm{\, =\, }X\left ( s \right )\mathrm{\, =\, }\int_{-\infty }^{\infty }x\left ( t \right )e^{-st}\:dt \; \; \cdot \cdot \cdot \left ( \mathrm{1} \right )}}$$Equation (1) gives the bilateral Laplace transform of the function $\mathrm{\mathit{x\left ( t \right )}}$. But for the causal signals, the ... Read More
Laplace TransformThe Laplace transform is a mathematical tool which is used to convert the differential equation in time domain into the algebraic equations in the frequency domain or s-domain.Mathematically, if $\mathrm{\mathit{x\left ( t \right )}}$ is a time domain function, then its Laplace transform is defined as −$$\mathrm{\mathit{L\left [ x\left ( t \right ) \right ]\mathrm{\, =\, }X\left ( s \right )\mathrm{\, =\, }\int_{-\infty }^{\infty }x\left ( t \right )e^{-st}\:dt }}$$Time Reversal Property of Laplace TransformStatement – The time reversal property of Laplace transform states that if a signal is reversed about the vertical axis at origin in the time ... Read More
The Inverse Z-TransformThe inverse Z-transform is defined as the process of finding the time domain signal $\mathrm{\mathit{x\left ( n \right )}}$ from its Z-transform $\mathrm{\mathit{X\left ( z \right )}}$. The inverse Z-transform is denoted as −$$\mathrm{\mathit{x\left ( n \right )\mathrm{\, =\, }Z^{-\mathrm{1}}\left [ X\left ( z \right ) \right ]}}$$Since the Z-transform is defined as, $$\mathrm{\mathit{X\left ( z \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }-\infty }^{\infty }x\left ( n \right )z^{-n}\; \; \; \cdot \cdot \cdot \left ( \mathrm{1} \right )}}$$Where, z is a complex variable and is given by, $$\mathrm{\mathit{z\mathrm{\, =\, }r\, e^{j\, \omega }}}$$Where, r is the radius of ... Read More