...MBA/MFM 253 TVM Practice Problems 2 Fall 2011 1. You are considering buying a new car. The current price of the car is $25,000. The dealer has offered you a special nominal interest rate of 3% each year for the next 3 years if you finance through the dealership. a) What is your monthly car payment? PV = 25,000 I = 0.25 N = 36 FV = 0 PMT =? = $727.03 25,000 = PMT (1-(1/(1.0025)36))/.0025 b) You are considering putting a $5,000 down payment on the car, what would your payment be if you did this assuming you could still get the special interest rate? $581.62 c) In either case what is the effective rate of interest you paid on the car? 1.002512=1.030416 3.0416% 2. A given rate is quoted at an effective annual rate of 12.55%. If you know that the interest compounds quarterly, what is the nominal annual rate? 12% Need to find the rate that when compounded four periods will equal .1255 solve for r in the following equation (1+(r/4))4=1.125 3. What is the PV of an annuity that pays 10,000 a year at the end of each of the next 15 years assuming a 5% return? $103,796.58PMT = 10,000 N=15 I = 5 FV = ) PV = ? What is the PV of an annuity that pays 10,000 a year at the beginning of each of the next 12 years assuming a rate of 7%? $84,986.743 3. PV and FV problems that are a little harder ( you need to figure out the pieces, the final answers are there – but you need to figure out how it set it up – the set up is usually the trickier part and the...
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...points) Solve the following initial value problems. (a) y + t3 y = t3 y(0) = 0. (b) y = − (1+x) y y(−1) = 1. Question 2 (40 points) Solve the second-order initial value problem 2y − 3y − 5y = 0 y(0) = 0 2 y (0) = 1. Question 3 (40 points) For each equation below, first determine whether the equation is exact or not exact. If the equation is exact, find the solution. (a) cos(y) + (2y − x sin(y)) dy = 0. dx (b) 3xy 2 + (y 3 + 3x2 ) 3 dy = 0. dx Question 4 (40 points) Consider the following first-order differential equation y = (y 2 − 1)(4 − y 2 ). Find all critical (equilibrium) solutions and classify their stability. 4 Question 5 (40 points) (True/False) In each of the following, determine whether the given function solves the given differential equation or initial value problem. (a) If k > 0 denotes any real constant, then the function y(t) = e−kt solves the initial value problem y = −ky y(0) = 1. (b) The function y(t) = (1 − t)−1 = 1/(1 − t) solves the initial value problem y = y2 y(0) = 1. (c) The function y(t) = e2t solves the second-order initial value problem y = 2y y(0) = 1 y (0) = 2. (d) Any function y(x) defined by the implicit equation x4 + 2x2 y 2 + y 4 = C solves the differential equation x3 + xy 2 + (x2 y + y 3 )y = 0. 5 Question 6 (Extra Credit, 10 points) An object with mass m is thrown vertically upward with initial velocity 20m (i.e. 20 times the mass m) meters per second. Assume...
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...pore. The transported and di®used solute par- ticles undergo the in¯nite adsorption rate reactions at the lateral tube boundary. At the inlet boundary we suppose Danckwerts' boundary conditions. The transport and reaction pa- rameters are such that we have dominant Peclet number. Our analysis uses the anisotropic singular perturbation technique, the small characteristic parameter " being the ratio between the thickness and the longitudinal observation length. Our goal is to obtain error estimates for the approximation of the physical solution by the upscaled one. They are presented in the energy norm. They give the approximation error as a power of " and guarantee the validity of the upscaled model. We use the Laplace transform in time to get better estimates than in our previous article [20] and to undertake the study of important Danckwerts' boundary conditions. Keywords: Taylor's dispersion; large Peclet number; singular perturbation; Laplace's transform; adsorption chemical reaction; Danckwerts' boundary conditions. AMS Subject...
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...fight against the old establishment and the revolution which physics experienced after Newton's subsequent synthesis. At the beginning of the last century, mathematical ideas and techniques were spread to theoretical and applied physics by the influence of two of the greatest mathematicians of all times, D. Hilbert and H. Poincar6, being then at the zenith of their careers. Their ability to establish very deep at first glance often hidden connections between a priori separated branches of science convinced physicists to adopt and work with the most powerful existing mathematical tools. Whereas the 20th century really was the century of physics, mathematics enjoyed a well deserved reputation from its very beginning, so facilitating the huge impact it had subsequently on humanity. This reputation has been crucial for the tremendous development of science and technology. Although mathematics supported the development of weapons of mass destruction, it simultaneously promoted the advancement of computers and high technology, without which the substantial improvement of the living conditions humanity as a whole has experienced, could not have been realized. In no previous time the world has seen such a spectacular growth of scientific knowledge as during the last century, with mathematics playing a central role in most scientific and technological successes. But, not surprisingly, the extraordinary development of mathematics and science politics created an impressive number...
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...| Lab 1: 1D Cellular Automaton | ECE 5760 | | Lucas Ackerman (lba36) Weiqing Li (wl336) | 9/16/2011 | Introduction The purpose of this lab was to design a hardware implementation of an elementary cellular automaton and display the evolving state of that automaton on a VGA screen (with a minimum resolution of 320x240). In the implementation, there was to be a way for the user to set the evolution rule which defined how each new generation formed from the previous generation. Additionally, the user should be able to press a button and display another screen with the next set of evolved states. The initial condition was to be selectable and either a single white cell in the center of the first generation or a random cellular automaton. In the proceeding sections we will discuss our implementation, the results, comparisons with natural phenomena and possible improvements to the design. Design and Testing Overview As mentioned above, the implementation of the 1D cellular automaton was completed in hardware and no software was designed. We used the Altera DE2 development board and the Cyclone II E2C35 FPGA. Since each cell of a new generation of the 1D cellular automaton is calculated by three cells from the previous generation and we wanted to generate the cellular automaton with hardware, a state machine running at 27Mhz was implemented to read from the memory, generate the new cell and store it back into memory. We also implemented a separate VGA interface...
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...ME3291 NATIONAL UNIVERSITY OF SINGAPORE ME3291 – NUMERICAL METHODS IN ENGINEERING (Semester 2 : AY2013/2014) Time Allowed : 2 Hours INSTRUCTIONS TO STUDENTS: 1. Please write your Student Number only. Do not write your name. 2. This assessment paper contains FOUR (4) questions and comprises FOUR (4) printed pages. 3. Students are required to answer ALL FOUR (4) questions. 4. Students should write the answers for each question on a new page. 5. This is a CLOSED-BOOK ASSESSMENT with authorized materials. Students are allowed to bring two A4 size sheets of notes/formulae written on both sides. 6. All questions carry equal marks. PAGE 2 ME3291 QUESTION 1 The heat conduction equation in 1D is given by T/ t = b 2 T/ x2. Here T is the temperature and b is the thermal conductivity. You are interested to use the DuFort & Frankel discretization scheme to obtain the finite difference equation of the governing equation because you have heard of its inherent stable properties. The DuFort & Frankel scheme is given as: (Tpq+1 - Tpq-1)/(2 t) = (b / ( x)2) [Tp+1q – (Tpq-1 + Tpq+1) + Tp-1q]. where Tpq = T (p x, q t) is the finite difference representation. You are interested to use the von Neumann (Fourier) stability analysis to determine if it is inherently stable or otherwise. If otherwise, then you show the criterion for the limit of stability. You may assume that Tpq = q ei ph where is the amplification factor,...
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...your text or other resources. Cite all resources consistent with APA guidelines. Term Definition Resource you used Time value of money Is the idea that money available at a present time is worth a lot more then the amount that its is in the future due to the “potential earning capacity”. The core principle of finance is provided money is able to earn interest and any money received sooner is worth more. Investopedia - Time Value of Money - TVM. (2014). Retrieved from http://www.investopedia.com/terms/t/timevalueofmoney.asp Efficient market Is a market that prices will quicky respond when there is an announcement of any kind of new information. Textbook. Primary versus secondary market Risk-return tradeoff Agency (principal and agent problems) Market information and security prices and information asymmetry Agile and lean principles Return on investment Cash flow and a source of value Project management Outsourcing and offshoring Inventory turnover Just-in-time inventory (JIT) Vender managed inventory (VMI) Forecasting and demand management University of Phoenix Material Definitions Define the following terms using your text or other resources. Cite all resources consistent with APA guidelines. Term Definition Resource you used Time value of money Is the idea that money available at a present time is worth a lot more then the amount that its is in the future due to the “potential earning capacity”. The core principle...
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...Time Value of Money Terminology Terminology (AKA jargon) can be a major impediment to understanding the concepts of finance. Fortunately, the vocabulary of time value of money concepts is pretty straightforward. Here are the basic definitions that you will need to understand to get started (calculator key abbreviations are in parentheses where appropriate): Banker's Year A banker's year is 12 months, each of which contains 30 days. Therefore, there are 360 (not 365) days in a banker's year. This is a convention that goes back to the days when "calculator" and "computer" were job descriptions instead of electronic devices. Using 360 days for a year made calculations easier to do. This convention is still used today in some calculations such as the Bank Discount Rate that is used for discount (money market) securities. Compound Interest This refers to the situation where, in future periods, interest is earned not only on the original principal amount, but also on the previously earned interest. This is a very powerful concept that means money can grow at an exponential rate. Compounding Frequency This refers to how often interest is credited to the account. Once interest is credited it becomes, in effect, principal. Note that the compounding frequency and the frequency of cash flows are not always the same. In that case, the interest rate is typically adjusted to an effective rate that is of the same periodicity as the cash flows. For example, if we have quarterly cash flows...
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...Part 2 Valuation 3 The Time Value of Money Contents n n n Objectives After studying Chapter 3, you should be able to: n The Interest Rate Simple Interest Compound Interest Single Amounts • Annuities • Mixed Flows Understand what is meant by “the time value of money.” Understand the relationship between present and future value. Describe how the interest rate can be used to adjust the value of cash flows – both forward and backward – to a single point in time. Calculate both the future and present value of: (a) an amount invested today; (b) a stream of equal cash flows (an annuity); and (c) a stream of mixed cash flows. Distinguish between an “ordinary annuity” and an “annuity due.” Use interest factor tables and understand how they provide a shortcut to calculating present and future values. Use interest factor tables to find an unknown interest rate or growth rate when the number of time periods and future and present values are known. Build an “amortization schedule” for an installment-style loan. n n Compounding More Than Once a Year Semiannual and Other Compounding Periods • Continuous Compounding • Effective Annual Interest Rate n n n Amortizing a Loan Summary Table of Key Compound Interest Formulas Summary Questions Self-Correction Problems Problems Solutions to Self-Correction Problems Selected References n n n n n n n n n n n 39 Part 2 Valuation The chief value of money lies in the fact that one lives in a world...
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...1/ This problem is about determining the amount of monthly payment given the Present value, APR, and number of payments. Therefore, the only equation that I have to rely on is: And the result that I obtain from this equation is as follow: |Scenario: |Monthly Payment | |i. |$ 456.22 | |ii. |$ 478.06 | |iii. |$ 434.99 | |iv. |$ 405.53 | |v. |$ 481.56 | |vi. |$ 394.50 | |vii. |$ 549.29 | But while doing it on Excel, I think it’s easier to separate the formula into two parts: ➢ First: I calculate the PVIFA separately. ➢ Second: Divided the Present Value by the PVIFA just calculated Summary and Interpretation: Back to the problem, as the numbers show; the lower the APR, the lower the monthly payment will be. It’s because that you would not have to pay as much interest. Other Scenarios shows that the lower the present value (scenarios iv. and v.) the lower the monthly payment. The reason for that is; with the fixed number of payments, the less amount of debt that you have, the less you have to in each payment. Finally when the number of payments changes, it effects the amount that you’d have to pay in each payment as well. For example, if you decide to pay your debt in a longer period of time, obviously...
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...Chapter 6 Time Value of Money LEARNING OBJECTIVES After reading this chapter, students should be able to: • Convert time value of money (TVM) problems from words to time lines. • Explain the relationship between compounding and discounting, between future and present value. • Calculate the future value of some beginning amount, and find the present value of a single payment to be received in the future. • Solve for time or interest rate, given the other three variables in the TVM equation. • Find the future value of a series of equal, periodic payments (an annuity) as well as the present value of such an annuity. • Explain the difference between an ordinary annuity and an annuity due, and calculate the difference in their values. • Calculate the value of a perpetuity. • Demonstrate how to find the present and future values of an uneven series of cash flows. • Distinguish among the following interest rates: Nominal (or Quoted) rate, Periodic rate, and Effective (or Equivalent) Annual Rate; and properly choose between securities with different compounding periods. • Solve time value of money problems that involve fractional time periods. • Construct loan amortization schedules for both fully-amortized and partially-amortized loans. LECTURE SUGGESTIONS We regard Chapter 6 as the most important chapter in the book, so we spend a good bit of time on it. We approach time value in three...
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...and Jimmy, with joy and pride. Craig CONTENTS Preface PART 1 TIME VALUE OF MONEY Chapter 1 Single Cash Flow 1.1 Present Value 1.2 Future Value Problems Chapter 2 Annuity 2.1 Present Value 2.2 Future Value 2.3 System of Four Annuity Variables Problems Chapter 3 Net Present Value 3.1 Constant Discount Rate 3.2 General Discount Rate Problems Chapter 4 Real and Inflation 4.1 Constant Discount Rate 4.2 General Discount Rate Problems Chapter 5 Loan Amortization 5.1 Basics 5.2 Sensitivity Analysis Problems PART 2 VALUATION Chapter 6 Bond Valuation 6.1 Basics 6.2 By Yield To Maturity 6.3 System Of Five Bond Variables 6.4 Dynamic Chart Problems Chapter 7 Stock Valuation 7.1 Two Stage 7.2 Dynamic Chart Problems Chapter 8 The Yield Curve 8.1 Obtaining It From Bond Listings 8.2 Using It To Price A Coupon Bond 8.3 Using It To Determine Forward Rates Problems Chapter 9 U.S. Yield Curve Dynamics 9.1 Dynamic Chart Problems PART 3 CAPITAL BUDGETING Chapter 10 Project NPV 10.1 Basics 10.2 Forecasting Cash Flows 10.3 Working Capital 10.4 Sensitivity Analysis Problems Chapter 11 Cost-Reducing Project 11.1 Basics 11.2 Sensitivity Analysis Problems Chapter 12 Break-Even Analysis 12.1 Based On Accounting Profit 12.2 Based On NPV Problems Chapter 13 Three Valuation Methods 13.1 Adjusted Present Value 13.2 Flows To Equity 13.3 Weighted Average Cost of Capital Problems PART 4 FINANCIAL PLANNING Chapter 14 Corporate Financial Planning ...
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...CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) | | |Brief Exercises | | | |Topics |Questions | |Exercises |Problems | | 1. |Present value concepts. |1, 2, 3, 4, | | | | | | |5, 9, 17 | | | | | 2. |Use of tables. |13, 14 |8 |1 | | | 3. |Present and future value problems: | | | | | | |a. Unknown future amount. |7, 19 |1, 5, 13 |2, 3, 4, 7 | | | |b. Unknown payments. |10, 11, 12 |6, 12, |8, 16, 17 |2, 6 | | | | |15, 17 | | | | ...
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......................................... xiii The Excel Modeling and Estimation Series .................................................. xiii Suggestions for Faculty Members ..................................................................xiv Acknowledgements ........................................................................................... xv About The Author ................................................................. xvi PART 1 TIME VALUE OF MONEY ..... 1 Chapter 1 Single Cash Flow ....................................................1 1.1 Present Value ............................................................................................... 1 1.2 Future Value ................................................................................................ 2 Problems .............................................................................................................. 3 Chapter 2 Annuity ...................................................................4 2.1 Present Value...
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...CHAPTER 20 CAPITAL BUDGETING DECISIONS I. Questions 1. A capital investment involves a current commitment of funds with the expectation of generating a satisfactory return on these funds over a relatively extended period of time in the future. 2. Cost of capital is the weighted minimum desired average rate that a company must pay for long-term capital while discounted rate of return is the maximum rate of interest that could be paid for the capital employed over the life of an investment without loss on the project. 3. The basic principles in capital budgeting are: 1. Capital investment models are focused on the future cash inflows and outflows - rather than on net income. 2. Investment proposals should be evaluated according to their differential effects on the company’s cash flows as a whole. 3. Financing costs associated with the project are excluded in the analysis of incremental cash flows in order to avoid the “double-counting” of the cost of money. 4. The concept of the time value of money recognizes that a peso of present return is worth more than a peso of future return. 5. Choose the investments that will maximize the total net present value of the projects subject to the capital availability constraint. 4. The major classifications as to purpose are: 1. Replacement projects - those involving replacements of worn-out assets to avoid disruption of normal operations, or to improve efficiency...
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