The document summarizes key concepts from chapters 6-14 of a finance textbook on risk and return, time value of money, bonds, stock and their valuation, cost of capital, capital budgeting, and cash flow estimation. It defines terms like expected rate of return, risk measures like standard deviation and beta, bond and stock valuation models, weighted average cost of capital, net present value, internal rate of return, modified internal rate of return, and cash flow terms like operating cash flow, free cash flow, EBIT, and more. Formulas and calculator instructions are provided for computing many of these concepts.
The document describes the transform and quantization processes used in H.264 video compression. It discusses how the discrete cosine transform is approximated using integer arithmetic. The forward and inverse processes are derived from each other. Scaling matrices are incorporated to normalize values and minimize computational complexity while maintaining good compression performance. Quantization values are specified in the standard through scaling matrices.
This document describes research on identifying extract method refactoring opportunities through program analysis and tool support. It discusses limitations of early work, such as not supporting extraction of objects or composite variables. It presents techniques to address these limitations, including handling behavior preservation issues and ensuring the complete computation of extracted variables. Evaluation results of tools are provided, showing improvements in precision and recall over time. The document also discusses how the work influenced the researcher's career and other researchers.
This document proposes a self-adaptive version of simulated binary crossover (SBX) for real-parameter optimization. SBX is commonly used in evolutionary algorithms but its distribution index parameter is typically fixed, which can limit performance. The proposed method adapts the distribution index each generation based on how offspring compare to parents in terms of fitness. It derives an equation to update the index value based on whether offspring outperform parents. The goal is to improve SBX's ability to solve complex optimization problems by dynamically adjusting its behavior during a run.
This document appears to be an exam question paper for a Digital Logic Circuits course. It contains 15 multiple choice and long answer questions covering various topics in digital logic design including:
- Logic simplification using K-maps
- Half adder and full adder circuit design
- Flip flop circuit design including JK, T and binary counter circuits
- Finite state machine design and state reduction
- Programmable logic array and read only memory circuit design
- Hardware description language modeling of digital circuits
The document discusses attribute-based encryption (ABE) schemes, including Key-Policy ABE (KP-ABE) and Ciphertext-Policy ABE (CP-ABE). It defines the components of KP-ABE and CP-ABE, including setup, encryption, key generation, and decryption algorithms. It also describes the security models and proves the selective security of the GPSW KP-ABE scheme and correctness of the Waters CP-ABE scheme under the decisional bilinear Diffie-Hellman assumption. The document outlines the KP-ABE and CP-ABE constructions and security proofs in detail.
The document discusses quantization in analog-to-digital conversion. It describes the three processes of A/D conversion as sampling, quantization, and binary encoding. Quantization involves mapping amplitude values into a set of discrete values using a quantization interval or step size. The document discusses uniform quantization and how the range is divided into equal intervals. It also discusses non-uniform quantization which has smaller intervals near zero to better match real audio signals. Examples and MATLAB code demonstrations are provided to illustrate quantization of audio signals at different bit rates.
This document shows how to compute and graph the Fourier series coefficients for a square wave signal using a TI-89 calculator. It defines the Fourier series and integral used to calculate the complex coefficients. For a square wave example, it evaluates the integral to find the coefficients, plots the coefficients, and reconstructs the original square wave signal from the coefficients. Increasing the number of terms in the summation improves the approximation of the square wave.
The document discusses advanced topics in sorting algorithms, including selection, handling duplicate keys, comparators, and applications. It describes quick-select, an efficient linear-time algorithm for selection, and notes that mergesort handles duplicate keys better than quicksort, which can have quadratic time when there are many duplicate keys if partitioning does not stop on equal keys.
The document describes the transform and quantization processes used in H.264 video compression. It discusses how the discrete cosine transform is approximated using integer arithmetic. The forward and inverse processes are derived from each other. Scaling matrices are incorporated to normalize values and minimize computational complexity while maintaining good compression performance. Quantization values are specified in the standard through scaling matrices.
This document describes research on identifying extract method refactoring opportunities through program analysis and tool support. It discusses limitations of early work, such as not supporting extraction of objects or composite variables. It presents techniques to address these limitations, including handling behavior preservation issues and ensuring the complete computation of extracted variables. Evaluation results of tools are provided, showing improvements in precision and recall over time. The document also discusses how the work influenced the researcher's career and other researchers.
This document proposes a self-adaptive version of simulated binary crossover (SBX) for real-parameter optimization. SBX is commonly used in evolutionary algorithms but its distribution index parameter is typically fixed, which can limit performance. The proposed method adapts the distribution index each generation based on how offspring compare to parents in terms of fitness. It derives an equation to update the index value based on whether offspring outperform parents. The goal is to improve SBX's ability to solve complex optimization problems by dynamically adjusting its behavior during a run.
This document appears to be an exam question paper for a Digital Logic Circuits course. It contains 15 multiple choice and long answer questions covering various topics in digital logic design including:
- Logic simplification using K-maps
- Half adder and full adder circuit design
- Flip flop circuit design including JK, T and binary counter circuits
- Finite state machine design and state reduction
- Programmable logic array and read only memory circuit design
- Hardware description language modeling of digital circuits
The document discusses attribute-based encryption (ABE) schemes, including Key-Policy ABE (KP-ABE) and Ciphertext-Policy ABE (CP-ABE). It defines the components of KP-ABE and CP-ABE, including setup, encryption, key generation, and decryption algorithms. It also describes the security models and proves the selective security of the GPSW KP-ABE scheme and correctness of the Waters CP-ABE scheme under the decisional bilinear Diffie-Hellman assumption. The document outlines the KP-ABE and CP-ABE constructions and security proofs in detail.
The document discusses quantization in analog-to-digital conversion. It describes the three processes of A/D conversion as sampling, quantization, and binary encoding. Quantization involves mapping amplitude values into a set of discrete values using a quantization interval or step size. The document discusses uniform quantization and how the range is divided into equal intervals. It also discusses non-uniform quantization which has smaller intervals near zero to better match real audio signals. Examples and MATLAB code demonstrations are provided to illustrate quantization of audio signals at different bit rates.
This document shows how to compute and graph the Fourier series coefficients for a square wave signal using a TI-89 calculator. It defines the Fourier series and integral used to calculate the complex coefficients. For a square wave example, it evaluates the integral to find the coefficients, plots the coefficients, and reconstructs the original square wave signal from the coefficients. Increasing the number of terms in the summation improves the approximation of the square wave.
The document discusses advanced topics in sorting algorithms, including selection, handling duplicate keys, comparators, and applications. It describes quick-select, an efficient linear-time algorithm for selection, and notes that mergesort handles duplicate keys better than quicksort, which can have quadratic time when there are many duplicate keys if partitioning does not stop on equal keys.
The document summarizes key concepts from chapters 6-14 of a finance textbook on risk and return, time value of money, bonds, stock and their valuation, cost of capital, capital budgeting, and cash flow estimation. It defines terms like expected rate of return, risk measures like standard deviation and beta, bond and stock valuation models, weighted average cost of capital (WACC), net present value (NPV), internal rate of return (IRR), modified IRR, free cash flow, and operating cash flow. Formulas for concepts like time value of money, yield to maturity, dividend discount model, security market line, and cost of debt are also presented.
This document summarizes key concepts from chapters 6-13 of a finance textbook on risk and return, bonds, stocks, and capital budgeting. It defines rate of return, expected rate of return, risk/standard deviation, beta coefficient, correlation, security market line, time value of money, yield to maturity, dividend discount model for stocks, weighted average cost of capital (WACC), net present value (NPV), internal rate of return (IRR), and modified IRR (MIRR). Formulas are provided for calculating these concepts.
Webinar: MS and MBA programs from Embry-Riddle Aeronautical University in Day...Web2Present
MBA programs are available from nearly every institution of higher education that offers graduate degrees, so your choices are vast. But, at Embry-Riddle, you’ll be pursuing your Master degree already aligned with an industry. Students have followed their career path in companies like American Airlines, Boieng, British Airways, Federal Aviation Administration, amongst other consultancies and commercial firms.
This document discusses financial ratio analysis, which involves establishing quantitative relationships between financial statement items to analyze a company's financial position, performance, and trends over time. It provides definitions and formulas for various types of ratios, including liquidity, solvency, activity, and profitability ratios. Examples are given to demonstrate how to calculate and interpret common ratios like current ratio, acid test ratio, debt-to-equity ratio, and return on assets. The document aims to explain ratio analysis as a tool for evaluating the strengths and weaknesses of a business.
The document summarizes a presentation given at EMC Zurich Munich 2007 about circuit extraction for transmission lines. It discusses developing transmission line models using DFF and DFFz polynomials to represent voltages and currents. It presents the half-T ladder network representation and describes extracting poles and residues in closed form to develop the model's two-port representation. It also covers model order reduction techniques to select a reduced set of poles within a fixed bandwidth.
The document discusses the unified charge control model (UCCM) for MOSFET modeling. It presents the equations that define the UCCM and approximations used. Threshold voltage VT0 is defined as the gate voltage when the pinch-off voltage VP is 0. An example calculates VT0 for an n-channel MOSFET as 0.1V given parameters like flat-band voltage and oxide thickness. The relationship between pinch-off voltage VP and gate voltage VG is also examined.
The document summarizes key concepts from chapters 6-14 of a finance textbook on risk and return, time value of money, bonds, stock and their valuation, cost of capital, capital budgeting, and cash flow estimation. It defines terms like expected rate of return, risk measures like standard deviation and beta, bond and stock valuation models, weighted average cost of capital (WACC), net present value (NPV), internal rate of return (IRR), modified IRR, free cash flow, and operating cash flow. Formulas for concepts like time value of money, yield to maturity, dividend discount model, security market line, and cost of debt are also presented.
This document summarizes key concepts from chapters 6-13 of a finance textbook on risk and return, bonds, stocks, and capital budgeting. It defines rate of return, expected rate of return, risk/standard deviation, beta coefficient, correlation, security market line, time value of money, yield to maturity, dividend discount model for stocks, weighted average cost of capital (WACC), net present value (NPV), internal rate of return (IRR), and modified IRR (MIRR). Formulas are provided for calculating these concepts.
Webinar: MS and MBA programs from Embry-Riddle Aeronautical University in Day...Web2Present
MBA programs are available from nearly every institution of higher education that offers graduate degrees, so your choices are vast. But, at Embry-Riddle, you’ll be pursuing your Master degree already aligned with an industry. Students have followed their career path in companies like American Airlines, Boieng, British Airways, Federal Aviation Administration, amongst other consultancies and commercial firms.
This document discusses financial ratio analysis, which involves establishing quantitative relationships between financial statement items to analyze a company's financial position, performance, and trends over time. It provides definitions and formulas for various types of ratios, including liquidity, solvency, activity, and profitability ratios. Examples are given to demonstrate how to calculate and interpret common ratios like current ratio, acid test ratio, debt-to-equity ratio, and return on assets. The document aims to explain ratio analysis as a tool for evaluating the strengths and weaknesses of a business.
The document summarizes a presentation given at EMC Zurich Munich 2007 about circuit extraction for transmission lines. It discusses developing transmission line models using DFF and DFFz polynomials to represent voltages and currents. It presents the half-T ladder network representation and describes extracting poles and residues in closed form to develop the model's two-port representation. It also covers model order reduction techniques to select a reduced set of poles within a fixed bandwidth.
The document discusses the unified charge control model (UCCM) for MOSFET modeling. It presents the equations that define the UCCM and approximations used. Threshold voltage VT0 is defined as the gate voltage when the pinch-off voltage VP is 0. An example calculates VT0 for an n-channel MOSFET as 0.1V given parameters like flat-band voltage and oxide thickness. The relationship between pinch-off voltage VP and gate voltage VG is also examined.
The document provides formulas related to physics. It includes formulas for radioactivity, exponential decay, capacitors, harmonic oscillators, gravitation, Doppler shift, ideal gases, electromagnetic machines, electric and magnetic fields, quantum mechanics, ionizing radiation, and general physics. Key formulas include the half-life equation, capacitance equation, period of a pendulum, ideal gas law, transformer equations, Coulomb's law, De Broglie wavelength, exponential attenuation of gamma radiation, and density equation.
This document discusses efficient algorithms for computing the discrete Fourier transform (DFT), specifically the fast Fourier transform (FFT). It covers several FFT algorithms including decimation-in-time, decimation-in-frequency, and the Goertzel algorithm. The decimation-in-time algorithm recursively breaks down the DFT computation into smaller DFTs by decomposing the input sequence. This allows the computation to be performed in O(NlogN) time rather than O(N^2) time for a direct DFT computation. The document also discusses optimizations like in-place computation to reduce memory usage.
This document provides an overview of MOSFET modeling concepts including:
1. Symmetry properties and normalization of the drain current equation.
2. Definitions of the forward and reverse currents, and the specific (normalization) current.
3. Description of the pinch-off voltage, slope factor, and their determination as functions of gate voltage.
The document is an exam for the Caribbean Examinations Council's Secondary Education Certificate in Mathematics. It contains 8 questions testing various math skills like algebra, geometry, trigonometry, and statistics. The exam is 2 hours and 40 minutes long and students must answer all questions in Section I and any two questions in Section II. Working must be shown clearly and formulas are provided.
The document discusses production functions in the long run. It defines production functions as tools that express the relationship between production inputs like capital and labor, and the resulting output. In the long run, production functions assume that both capital and labor are variable inputs that firms can adjust. Isoquant curves illustrate combinations of capital and labor that produce the same output level. The slopes of isoquant curves indicate the marginal rate of technical substitution between inputs. Returns to scale refer to how output changes proportionally with changes in all inputs, and can exhibit increasing, constant, or diminishing patterns.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document summarizes an article from the International Journal of Engineering Research and Development that presents a design for a highly linear Operational Transconductance Amplifier (OTA). The OTA combines two linearization techniques: 1) adaptive biasing of the differential pairs using a circuit that biases the tail current based on the quadratic input voltage to cancel non-linearity, and 2) resistive source degeneration to account for mobility reduction in short channel devices. Simulation results using a 0.18um CMOS technology show that the third order harmonic distortion remains below -60dB for a 300mV peak-to-peak differential input at 3MHz frequency, demonstrating high linearity. The design aims to provide distortion-free and interference-
The document summarizes a lecture on packet routing algorithms for hypercubes, including analyzing the expected time for a random routing algorithm to route packets from source to destination in two phases. It then discusses primal-dual algorithms for solving multi-commodity flow problems on networks and how they maintain constraints for both the primal and dual optimization problems through an iterative process of adjusting primal and dual variables.
This document proposes a Mahalanobis kernel for hyperspectral image classification based on probabilistic principal component analysis (PPCA). The PPCA model captures the cluster structure of each class in a lower-dimensional subspace. This model is used to define the hyperparameters for the Mahalanobis kernel. Experimental results on simulated and real hyperspectral images show the PPCA-based Mahalanobis kernel achieves better classification accuracy than Gaussian and PCA-based kernels. Future work includes optimizing the hyperparameters and estimating the number of principal components.
This document discusses various techniques for reducing power consumption at different levels of digital design. At the gate level, power can be reduced by optimizing device sizing and fanout. Multiple supply voltages can be used within the same design to lower voltage in non-critical paths. At the architecture level, clock gating is introduced to power gate idle components. Clock gating finite state machines can reduce power based on the current state. Tradeoffs between power and delay can be achieved by adjusting the supply voltage.
The convenience yield implied by quadratic volatility smiles presentation [...yigalbt
This document discusses the implied convenience yield from quadratic volatility smiles in options. It presents formulas to calculate the implied convenience yield for illiquid options based on using liquid at-the-money options as hedging instruments. The formulas depend on observable market parameters like volatility and are meant to provide a simple way to compute the implied convenience yield without historical data assumptions. However, the model relies on several undefined expressions and economic assumptions that are not fully clear.
This document discusses real option valuation techniques for technology projects. It begins by providing examples of real options like options to abandon or expand a project. It then covers various valuation models like decision trees, binomial models, and Monte Carlo simulations. These models can value flexibility and account for uncertainty. The document concludes by discussing Captum Capital which provides valuation and consulting services, including upcoming events on their valuation masterclass and workshop on technology evaluation.
This document summarizes research on developing an efficient higher-order accurate unstructured finite volume algorithm for inviscid compressible fluid flows. The algorithm uses an ILU preconditioned GMRES method to solve the Euler equations on unstructured meshes. Higher-order solutions of up to fourth-order accuracy were obtained. Results show the third-order solution was 1.3-1.5 times more expensive than second-order, while fourth-order was 3.5-5 times more expensive, demonstrating the efficiency of the higher-order approach. Test cases included supersonic and transonic flows, with results agreeing well with structured solvers.
Robust adaptive integral backstepping control and its implementation onShubhobrata Rudra
The document presents a robust adaptive integral backstepping control scheme for motion control systems. It describes the state model of the system and control objective of tracking a reference signal. An integral backstepping control design is developed using error variables and a control Lyapunov function. An adaptation scheme estimates parameter variations using a parameter update law. To improve robustness, a continuous switching function is used to prevent abnormal variation of the adaptation rates. Simulation results show the proposed robust adaptive controller has better tracking performance and reduces parameter estimation error compared to a standard adaptive controller.
The document discusses basic concepts related to electrical power systems including:
1) Definitions of average power, RMS value, power factor, and reactive power for sinusoidal voltage and current signals in single-phase and three-phase systems.
2) Fourier series representation of periodic signals and definition of total harmonic distortion.
3) Concepts of average power, apparent power, and power factor under nonsinusoidal waveforms.
4) Brief overview of the roles of transformers and inductors in power electronics systems and how airgap influences transformer design.
This document discusses cocos2d and some of its features. It mentions cocos2d version 1.0.0 rc and provides contact information for the developer. It also briefly describes CCSprite, CCNode, OpenGL drawing, reordering child nodes, vertexZ values, and setting the projection to 2D. Actions like CCMoveTo and sequences are mentioned. Tiled map support, vertexZ, and layers are covered.
State equations model based on modulo 2 arithmetic and its applciation on rec...Anax Fotopoulos
1) The document discusses state equations that can model digital control systems based on modulo-2 arithmetic and their application to recursive convolutional coding.
2) State equations can be derived from the transfer function of a discrete-time controller and expressed using modulo-2 arithmetic.
3) A recursive convolutional encoder can be modeled by state equations in modulo-2 algebra, where the state at each time step is a function of the previous states and the input bit.
The document summarizes key concepts from chapters 6-14 of a finance textbook on risk and return, time value of money, bonds, stock and their valuation, cost of capital, capital budgeting, and cash flow estimation. It defines terms like expected rate of return, risk measures like standard deviation and beta, bond and stock valuation models, weighted average cost of capital, net present value, internal rate of return, modified internal rate of return, and cash flow terms like operating cash flow, free cash flow, EBIT, and more. Formulas and calculator instructions are provided for computing many of these concepts.
The document summarizes key concepts from chapters 6-14 of a finance textbook relating to risk and return, time value of money, bonds, stock valuation, cost of capital, capital budgeting, and cash flow estimation. It defines terms like expected rate of return, risk measures like standard deviation and beta, bond and stock valuation methods, weighted average cost of capital (WACC), net present value (NPV), internal rate of return (IRR), modified IRR, payback period, and cash flow items like net operating working capital, operating cash flow, and free cash flow. Formulas and calculator instructions are provided for computing many of these concepts.
The document discusses the cost of capital and components used to calculate the weighted average cost of capital (WACC). It covers sources of long-term capital firms use, after-tax costs of different components, and whether the analysis should focus on historical or current marginal costs. The key points are:
1) Firms use long-term debt, preferred stock, common stock, retained earnings, and new common stock as sources of long-term capital.
2) WACC is calculated using the costs of each capital component weighted by the firm's target capital structure.
3) The analysis should focus on current marginal costs, like today's costs, for decisions involving raising new capital.
Southwest Airlines' mission is to provide high quality customer service with warmth, friendliness and company spirit. The airline was founded to take advantage of deregulation and provide low-cost intrastate service in Texas. Over time, Southwest expanded its routes and grew rapidly while maintaining low fares and a focus on customer satisfaction. The airline industry is highly competitive, with airlines competing on factors like fares, service, flight frequency and reacting quickly to competitors. The future holds both opportunities for Southwest to continue growing but also challenges from rising fuel costs and more competition.
Top mailing list providers in the USA.pptxJeremyPeirce1
Discover the top mailing list providers in the USA, offering targeted lists, segmentation, and analytics to optimize your marketing campaigns and drive engagement.
Understanding User Needs and Satisfying ThemAggregage
https://www.productmanagementtoday.com/frs/26903918/understanding-user-needs-and-satisfying-them
We know we want to create products which our customers find to be valuable. Whether we label it as customer-centric or product-led depends on how long we've been doing product management. There are three challenges we face when doing this. The obvious challenge is figuring out what our users need; the non-obvious challenges are in creating a shared understanding of those needs and in sensing if what we're doing is meeting those needs.
In this webinar, we won't focus on the research methods for discovering user-needs. We will focus on synthesis of the needs we discover, communication and alignment tools, and how we operationalize addressing those needs.
Industry expert Scott Sehlhorst will:
• Introduce a taxonomy for user goals with real world examples
• Present the Onion Diagram, a tool for contextualizing task-level goals
• Illustrate how customer journey maps capture activity-level and task-level goals
• Demonstrate the best approach to selection and prioritization of user-goals to address
• Highlight the crucial benchmarks, observable changes, in ensuring fulfillment of customer needs
Structural Design Process: Step-by-Step Guide for BuildingsChandresh Chudasama
The structural design process is explained: Follow our step-by-step guide to understand building design intricacies and ensure structural integrity. Learn how to build wonderful buildings with the help of our detailed information. Learn how to create structures with durability and reliability and also gain insights on ways of managing structures.
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Discover timeless style with the 2022 Vintage Roman Numerals Men's Ring. Crafted from premium stainless steel, this 6mm wide ring embodies elegance and durability. Perfect as a gift, it seamlessly blends classic Roman numeral detailing with modern sophistication, making it an ideal accessory for any occasion.
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B2B payments are rapidly changing. Find out the 5 key questions you need to be asking yourself to be sure you are mastering B2B payments today. Learn more at www.BlueSnap.com.
buy old yahoo accounts buy yahoo accountsSusan Laney
As a business owner, I understand the importance of having a strong online presence and leveraging various digital platforms to reach and engage with your target audience. One often overlooked yet highly valuable asset in this regard is the humble Yahoo account. While many may perceive Yahoo as a relic of the past, the truth is that these accounts still hold immense potential for businesses of all sizes.
At Techbox Square, in Singapore, we're not just creative web designers and developers, we're the driving force behind your brand identity. Contact us today.
Tata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s DholeraAvirahi City Dholera
The Tata Group, a titan of Indian industry, is making waves with its advanced talks with Taiwanese chipmakers Powerchip Semiconductor Manufacturing Corporation (PSMC) and UMC Group. The goal? Establishing a cutting-edge semiconductor fabrication unit (fab) in Dholera, Gujarat. This isn’t just any project; it’s a potential game changer for India’s chipmaking aspirations and a boon for investors seeking promising residential projects in dholera sir.
Visit : https://www.avirahi.com/blog/tata-group-dials-taiwan-for-its-chipmaking-ambition-in-gujarats-dholera/
Part 2 Deep Dive: Navigating the 2024 Slowdownjeffkluth1
Introduction
The global retail industry has weathered numerous storms, with the financial crisis of 2008 serving as a poignant reminder of the sector's resilience and adaptability. However, as we navigate the complex landscape of 2024, retailers face a unique set of challenges that demand innovative strategies and a fundamental shift in mindset. This white paper contrasts the impact of the 2008 recession on the retail sector with the current headwinds retailers are grappling with, while offering a comprehensive roadmap for success in this new paradigm.
Event Report - SAP Sapphire 2024 Orlando - lots of innovation and old challengesHolger Mueller
Holger Mueller of Constellation Research shares his key takeaways from SAP's Sapphire confernece, held in Orlando, June 3rd till 5th 2024, in the Orange Convention Center.
IMPACT Silver is a pure silver zinc producer with over $260 million in revenue since 2008 and a large 100% owned 210km Mexico land package - 2024 catalysts includes new 14% grade zinc Plomosas mine and 20,000m of fully funded exploration drilling.
1. BA 640 Formula Chapter 6 Risk and Return
1) Rate of return = Amount received - Amount invested
Amount invested
n
k = ∑ k i Pi
ˆ
2) Expected rate of return Pi = Probability , ki = Rate of return
i =1
Calculator 1) Selecting Mode LR : MODE 5
2) Clear Data : CST EXE AC
3) Insert return before : -22 ALFHA Nj 0.1 MAR …… SHIFT 1 EXE
; DT x
∑ (k )P
n 2
= −k
ˆ
σ = Variance = σ
2
3) Risk or Standard deviation i i
i =1
Calculator 1) Insert return before : -22 ALFHA Nj 0.1 MAR …… SHIFT 2 EXE
; DT xσ n
CV = Risk / Return = σ/x
4) Coefficient of variation
5) Beta coefficient ( β ) Calculator insert Mkt. before : 25.7 ALFHA CFj 40 MAR …… SHIFT 8 EXE
β
, DT
6) Correlation ( r ) Calculator insert Mkt. before : 25.7 ALFHA CFj 40 MAR …… SHIFT 9 EXE
( -1 < r < 1 ) , DT r
∑ (k )P
n 2
n
= − kp
ˆ
∑ wi kˆi σp
ˆ
7) Expected return on a portfolio k p = , Risk on a portfolio pi i
i =1
i =1
8) Security Market Line (SML) : ki = kRF + (RPM)bi
Required return = Risk-free return + Premium for risk
Required return on stock i = Risk-free rate of return + (Market risk premium)(Stock i ‘ s beta)
Chapter 9 Bonds and Their Valuation
CF
CF CF
+ + .....+ n
1 2
(1+ k) (1+ k) (1+ k)n
1) PV = Calculator 1) Selecting Mode FIN : MODE 4
1 2
SHIFT AC EXE AC
2) Clear Data :
3) PV = 10 n 10 i% 100 PMT 1000 FV COMP PV EXE
2) Yield to maturity (YTM) or kd = 10 n -887 PV 90 PMT 1000 FV COMP i% EXE
Chapter 10 Stock and Their Valuation
D1 D2 D3 D∞
P=
+ + +. . . +
ˆ
(1+ ks )1 (1+ ks )2 (1+ ks )3 (1+ ks )∞
1) Stock Value = PV of Dividends 0
ˆ D (1 + g ) = D1
P0 = 0 D1
3) k s = +g
ˆ
ks − g ks − g
2) If g is constant, then
P0
= Actual dividend yield + Actual capital gains yield
3) k s
D D ps
V ps = k ps =
ps
or
4)
V ps
k ps
kS = kRF + (kM - kRF) bFirm
5) Use the SML to calculate kS ;
1) After-tax component cost of debt = kd ( 1-T )
Chapter 11 The cost of Capital
D
=
ps
2) The cost of preferred stock k
;
ps
Pn
2. WACC = wdkd (1-T) + wpskps + wceks
3) Weighted Average Cost of Capital (WACC) ;
ˆ
ks = k s = kRF + RP = D1 / P0 + expected g
4)
5) ks = Bond yield + Risk premium
6) g = (Retention rate)(ROE) = (1.0 – Payout rate)(ROE) = b(ROE)
Chapter 13 The Basics of Capital Budgeting : Evaluating Cash Flows
1) Payback period = Year before full recovery + Unrecovered cost at start of year
Cash flow during year
2) Net Present Value (NPV) : Sum of PVs of inflows and Outflows = PV inflow – PV outflow
n n
CFt
CF t
∑ NPV = ∑
= − CF0
NPV
(1 + k )t (1 + k )t
or
t=0 t =1
Calculator -100 CFj 10 CFj 60 CFj 80 10 i% COMP NPV EXE
n
CF t
∑ (1 +
IRR = =0
)t
3) Internal Rate of Return (IRR) : NPV =0 ;
IRR
t=0
Calculator -100 CFj 10 CFj 60 CFj 80 10 i% COMP IRR EXE
TV
4) Modify Internal rate of return (MIRR) : PV costs = PV terminal value : PV costs =
(1 + MIRR ) n
Chapter 8 Time Value of Money
FVn = PV (1 + i )
n
⎛1⎞
n FV
⎜ ⎟
n
or PV = = FV
1)
(1 + i )n n
⎝1+ i⎠
mn
⎛ ⎞
mn
⎛ ⎞
i i
= PV ⎜ 1 + Nom ⎟ = ⎜ 1 + Nom ⎟ − 1 .0
FV or Effective annual rate
2) n
⎝ m⎠
⎝ m⎠
Chapter 14 Cash Flow Estimate and Risk Analysis
1) Net Proceeds from sales (NP) = MV + Tax ; MV = Market value
= MV + Tax rate ( MV-BV) ; BV = Book value
2) Net operating working capital (NOWC) = All current assets that _ All current liabilities that
do not pay interest do not pay interest
= Operating current assets – operating current liabilities
3) Operating capital = (Net operating working capital) – (Net plant and equipment)
4) NOPAT = Net operating profit after taxes = EBIT(1-Tax rate)
5) Operating cash flow (OCF) = NOPAT + Depreciation = EBIT(1-Tax) + Depreciation
= (Sales – CGS – Operating Expense – depreciation)(1-Tax) + Depreciation
= (Sales – CGS – Operating Expense)(1-Tax) + (Depreciation x Tax)
6) Free cash flow (FCF) = Operating cash flow - Gross investment in operating capital
= NOPAT – Net investment in operating capital
7) Free cash flow (FCF) = EBIT(1-Tax) + Depreciation + ∆NWC + ∆CAPEX
8) EBIT = Sales – CGS – Operating Expense – depreciation
= Sales – Variable Cost – Fixed Cost