ü 6.3 The Net Present Value Investment Rule ü 4.6 Annuities


 Louisa Jenkins
 1 years ago
 Views:
Transcription
1 4.6 Annuities PV and FV of Annuities Cash flows of the same amount is called "annuity". Paying 10,000 yen per month for gift certificate of the department store constitutes an annuity. If cash flows start immediately, it is called an "immediate annuity." If the cash flows start at the end of the current period, rather than immediately, it is call an "ordinary annuity." Let r be interest rate per month. Suppose you keep paying amount $A each month for a year. Starting today, you pay twelve times. Apply monthly compounding. This is an immediate annuity. FV is given by FV 12 A Next suppose that you will receive amount $A per month 12 times for a year. The first payment is a month from now. What is PV of this ordinary annuity? Apply monthly compounding. PV of the annuity is expressed as a sum of geometric sequence. PV of the first cash flow = A 1 r PV of the second cash flow = ª PV of the last cash flow = A 1 r 2 A 1 r 12 Then PV of this annuity is given by. 1 r t Example Suppose that you will receive amount $100 per month 12 times for a year. Interest rate per month is 1 percent. Then PV of this annuity is $1, as shown below. In terms of PV, having $1, today is equivalent to receiving $100 each month for a year. In[92]:= Clear A, r ; A 0; r 0.01; Print " ", Mathematica Print[ expression you want to show] For example command if you input Print[ variable name ] then you will see value of variable name. Print[ "expression as you see ", expression to be calculated] You have comma here. You use comma to differentiate the end of one expression from the next one. Chapter 6. How to Analyze Investment Projects 6.3 The Net Present Value Investment Rule Invest if the proposed project's NPV is positive. 1
2 6.5 Cost of Capital Cost of Capital is the riskadjusted discount rate to use in computing a project's NPV. It depends on riskiness of the project. It can vary from project to project. 6.8 Projects with Different Lives When the lives of projects are different, we can compare their annualized capital costs. Annualized capital cost: an annual cash payment that has a present value equal to the initial outlay. In other words, annualized capital cost is a constant payment per year over the investment period which is calculated so that total of their present values is equal to the cost. Decision rule based on annualized capital cost: We choose the project with smaller annualized capital cost. Example: Two types of machines with different lives Suppose that we are considering to install a machine to filter water from the hot spring. Two types of machines are available. Which machine type to choose? Type A works 5 years. Type B works 10 years. Type B lasts longer and costs more. Suppose that interest rate to borrow is 10%. machine type life year price yen Type A 5 years 2 6 Type B 10 years 4 6 Let ca be annual cash payment for type A machine. Then annualized capital cost is value of ca which solves the following equation. 5 ca 2 1 r t 106 (1) Let cb be annualized capital cost of type B. It satisfies the following equation. 10 cb 4 6 (2) 1 r t Finding value of annualized capital cost of Type A We are going to solve equation (1). In[93]:= 5 ca Clear ca, r, ansa ;r 0.1; ansa NSolve 2 6,ca Out[93]= ca In[94]:= ca ca. ansa 1 ; Print "ca ", ca ca Annualized cost of capital of type A is $527,595. 2
3 Finding value of annualized capital cost of Type B Annualized cost of capital of type B is solution to equation (2). In[95]:= 10 cb Clear ansb, cb ; ansb NSolve cb cb. ansb 1 ; Print "cb ", cb 4 6,cb ; cb Annualized cost of capital of type B is $650,982. In[97]:= Print "ca cb ", ca cb ca cb Conclusion: Type A has lower annualized capital cost. We choose type A. Mathematically, finding value of annualized capital cost is the same the following: Interest rate is given. Value of annuaity is given. You find value of value of constant payment. 6.9 Ranking Mutually Exclusive Projects If projects under consideration require exclusive use of unique asset, we call them mutually exclusive projects. "Internal Rate of Return" may not be a good measure for ranking such mutually exclusive projects. You should use NPV method. Example: Plans with different scales for the same parcel of land Suppose you have a peace of land. You have two choices. building office building and making parking lot. 1. office building: initial outlay $ You can sell it for $ 10 6 in one year. 2. parking lot: initial outlay $10,000. You can expect $10,000 per year forever. We like to compare these two alternatives and choose by using IRR and NPV methods. Comparison by Using IRR Net present value of the project of the office building is NPV 20. Internal rate of return is an interest rate which 1 x make NPV equal to zero. We solve an equation; x In[98]:= office building Clear x, ansx, IRRx ; ansx NSolve 20 1 x, x ; IRRx x. ansx 1 ; Print " IRRx ", IRRx IRRx 0.2 IRR for the office building is 20%. NPV of the parking lot is equal to 1 y t. We solve an equation; 0. 1 y t 3
4 In[101]:= parking lot Clear y, IRRy, ansy ; ansy NSolve 0, y ; t 1 y IRRy y. ansy 1 ; Print "IRRy ", IRRy IRRy 1. IRR of Parking lot is 100%. So parking lot has higher IRR. Comparison by Using NPV We want to choose the one which has higher NPV. Suppose that cost of capital is 15%. In[104]:= office building Clear NPVx, r ; r 0.15; NPVx 1 r 20 6 ; Print "NPV of the office building is ", NPVx NPV of the office building is In[107]:= Parking lot Clear NPVy NPVy N 103 ; Print " NPV of the parking lot is ", NPVy, ", NPVx NPVy ", NPVx NPVy NPV of the parking lot is , NPVx NPVy As shown above, if cost of capital is 15%, then the office building has higher NPV. You should choose office building. Result can be reversed However, if cost of capital is higher than 20%, the result is reversed. The result depends on cost of capital. For example, suppose cost of capital is 21%. Cost of Capital = 21% In[110]:= Clear r, NPV1, NPV2 ; r 0.21; NPV1 1 r 20 6 ; Print "NPV of office building when r 0.21 : NPV1 ", NPV1 NPV of office building when r 0.21 : NPV In[112]:= NPV2 N 103 ; Print "NPV of parking lot ", NPV2 Print "Comparison: NPV1 NPV2 ", NPV1 NPV2, " 0" 4
5 NPV of parking lot Comparison: NPV1 NPV If the cost of capital is 21%, then the parking lot is the project to choose. Switchover Point When is the result reversed? Where is "switchover point"? It is % as shown below. In[115]:= Clear r ; NSolve 20 1 r 6 3 0, r Out[115]= r , r How can such a reversal happen? One of the reasons is different lives of the projects. Consider NPV as a function of cost of capital. It is denoted as r in our example. If cost of capital is below %, then parking lot has higher NPV again. NPV as a function of cost of capital Let's draw graphs and see how NPV's changeas cost of capital changes. In[116]:= NPV of Office Building Clear f1,r,g1 f1 r_ : 1 r 20 6 ; In[118]:= g1 Plot f1 r, r, 0, 0.22, ImageSize 200, PlotLabel "NPV of office building" 4 μ 10 6 NPV of office building 3 μ 10 6 Out[118]= 2 μ μ In[119]:= NPV of Parking Lot Clear f2, g2 f2 r_ : 103 ; 5
6 In[121]:= g2 Plot f2 r, r, 0, 0.22, ImageSize 200, PlotLabel "NPV of parking lot" NPV of parking lot Out[121]= In[122]:= Show g1, g2, PlotLabel "comparison of NPV's" 4 μ 10 6 comparison of NPV's 3 μ 10 6 Out[122]= 2 μ μ Homework No. 2, Due next class Q1. p.146, Problem 36. Hint: interest rate per month = APR. Consider initially there were 13 loans. Sammy paid back 12 of 12 them in a year. Q2. Suppose cost of capital is 18%. At what scale would the NPV of the parking lot be equal to the office building? Hint: Quick Check 68. Q3. p190, Problem 1. Also calculate IRR. Q4. p.193, Problem 18. Q5. p.194, Problem 23. 6
Bank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later.
ü 4.4 lternative Discounted Cash Flow Decision Rules ü Three Decision Rules (1) Net Present Value (2) Future Value (3) Internal Rate of Return, IRR ü (3) Internal Rate of Return, IRR Internal Rate of Return
More informationChapter 4: Time Value of Money
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)
More informationEXAM 2 OVERVIEW. Binay Adhikari
EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing
More informationThe Time Value of Money
The Time Value of Money Future Value  Amount to which an investment will grow after earning interest. Compound Interest  Interest earned on interest. Simple Interest  Interest earned only on the original
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationSolutions to Chapter 8. Net Present Value and Other Investment Criteria
Solutions to Chapter 8 Net Present Value and Other Investment Criteria. NPV A = $00 + [$80 annuity factor (%, periods)] = $00 $80 $8. 0 0. 0. (.) NPV B = $00 + [$00 annuity factor (%, periods)] = $00 $00
More information5. Time value of money
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More information( ) ( )( ) ( ) 2 ( ) 3. n n = 100 000 1+ 0.10 = 100 000 1.331 = 133100
Mariusz Próchniak Chair of Economics II Warsaw School of Economics CAPITAL BUDGETING Managerial Economics 1 2 1 Future value (FV) r annual interest rate B the amount of money held today Interest is compounded
More informationHOW TO CALCULATE PRESENT VALUES
Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGrawHill/Irwin Copyright 2014 by The McGrawHill Companies, Inc. All rights reserved.
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
More information3. Time value of money. We will review some tools for discounting cash flows.
1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationSolutions to Time value of money practice problems
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
More information$1,300 + 1,500 + 1,900 = $4,700. in cash flows. The project still needs to create another: $5,500 4,700 = $800
1. To calculate the payback period, we need to find the time that the project has recovered its initial investment. After three years, the project has created: $1,300 + 1,500 + 1,900 = $4,700 in cash flows.
More informationPowerPoint. to accompany. Chapter 5. Interest Rates
PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When
More informationDiscounted Cash Flow Valuation
BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?
More informationInternational Financial Strategies Time Value of Money
International Financial Strategies 1 Future Value and Compounding Future value = cash value of the investment at some point in the future Investing for single period: FV. Future Value PV. Present Value
More informationChapter 2 Present Value
Chapter 2 Present Value Road Map Part A Introduction to finance. Financial decisions and financial markets. Present value. Part B Valuation of assets, given discount rates. Part C Determination of riskadjusted
More informationChapter 02 How to Calculate Present Values
Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00
More informationCHAPTER 9 Time Value Analysis
Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 91 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams
More informationYou just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
More informationBENEFITCOST ANALYSIS Financial and Economic Appraisal using Spreadsheets
BENEFITCOST ANALYSIS Financial and Economic Appraisal using Spreadsheets Ch. 3: Decision Rules Harry Campbell & Richard Brown School of Economics The University of Queensland Applied Investment Appraisal
More informationNet Present Value (NPV)
Investment Criteria 208 Net Present Value (NPV) What: NPV is a measure of how much value is created or added today by undertaking an investment (the difference between the investment s market value and
More informationThis is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1).
This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons byncsa 3.0 (http://creativecommons.org/licenses/byncsa/
More informationCHAPTER 4. The Time Value of Money. Chapter Synopsis
CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money
More informationCALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
More informationKey Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued
6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More information1. Annuity a sequence of payments, each made at equally spaced time intervals.
Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology
More informationDiscounted Cash Flow Valuation
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationIntegrated Case. 542 First National Bank Time Value of Money Analysis
Integrated Case 542 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money
More informationChapter 8. 48 Financial Planning Handbook PDP
Chapter 8 48 Financial Planning Handbook PDP The Financial Planner's Toolkit As a financial planner, you will be doing a lot of mathematical calculations for your clients. Doing these calculations for
More informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in
More informationChapter 5 & 6 Financial Calculator and Examples
Chapter 5 & 6 Financial Calculator and Examples Konan Chan Financial Management, Spring 2016 Five Factors in TVM Present value: PV Future value: FV Discount rate: r Payment: PMT Number of periods: N Get
More informationWhy Use Net Present Value? The Payback Period Method The Discounted Payback Period Method The Average Accounting Return Method The Internal Rate of
1 Why Use Net Present Value? The Payback Period Method The Discounted Payback Period Method The Average Accounting Return Method The Internal Rate of Return Problems with the IRR Approach The Profitability
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More informationThe Time Value of Money
The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future
More informationFinancial Management Spring 2012
31 Financial Management Spring 2012 Week 4 How to Calculate Present Values III 41 32 Topics Covered More Shortcuts Growing Perpetuities and Annuities How Interest Is Paid and Quoted 42 Example 33
More information2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?
CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equalsized
More informationFI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY
FI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY 1. (3 points) BS16 What is a 401k plan Most U.S. households single largest lifetime source of savings is
More informationrate nper pmt pv Interest Number of Payment Present Future Rate Periods Amount Value Value 12.00% 1 0 $100.00 $112.00
In Excel language, if the initial cash flow is an inflow (positive), then the future value must be an outflow (negative). Therefore you must add a negative sign before the FV (and PV) function. The inputs
More informationChapter 3. Present Value. Answers to Concept Review Questions
Chapter 3 Present Value Answers to Concept Review Questions 1. Will a deposit made in an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one
More informationICASL  Business School Programme
ICASL  Business School Programme Quantitative Techniques for Business (Module 3) Financial Mathematics TUTORIAL 2A This chapter deals with problems related to investing money or capital in a business
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More informationCAPITAL BUDGETING. Net Present Value and Other Investment Criteria
CAPITAL BUDGETING Net Present Value and Other Investment Criteria Net Present Value (NPV) Net present value is the difference between an investment s market value (in today s dollars) and its cost (also
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More informationChapter 1: Time Value of Money
1 Chapter 1: Time Value of Money Study Unit 1: Time Value of Money Concepts Basic Concepts Cash Flows A cash flow has 2 components: 1. The receipt or payment of money: This differs from the accounting
More informationInvestment, Time, and Present Value
Investment, Time, and Present Value Contents: Introduction Future Value (FV) Present Value (PV) Net Present Value (NPV) Optional: The Capital Asset Pricing Model (CAPM) Introduction Decisions made by a
More informationInvestment Appraisal
Investment Appraisal Article relevant to F1 Business Mathematics and Quantitative Methods Author: Pat McGillion, current Examiner. Questions 1 and 6 often relate to Investment Appraisal, which is underpinned
More informationHO23: METHODS OF INVESTMENT APPRAISAL
HO23: METHODS OF INVESTMENT APPRAISAL After completing this exercise you will be able to: Calculate and compare the different returns on an investment using the ROI, NPV, IRR functions. Investments: Discounting,
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More informationHow to calculate present values
How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance
More informationChapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS 41 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
More informationFIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1
FIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1 Solutions to Problems  Chapter 3 Mortgage Loan Foundations: The Time Value of Money Problem 31 a) Future Value = FV(n,i,PV,PMT)
More informationBusiness 2019. Fundamentals of Finance, Chapter 6 Solution to Selected Problems
Business 209 Fundamentals of Finance, Chapter 6 Solution to Selected Problems 8. Calculating Annuity Values You want to have $50,000 in your savings account five years from now, and you re prepared to
More informationSpring 2012. True/False Indicate whether the statement is true or false.
Corporation Finance Spring 2012 Sample Exam 2B True/False Indicate whether the statement is true or false. 1. The total return on a share of stock refers to the dividend yield less any commissions paid
More informationHOW TO CALCULATE PRESENT VALUES
Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11 th Global Edition McGrawHill Education Copyright 2014 by The McGrawHill Companies, Inc. All rights
More informationChapter 7. Net Present Value and Other Investment Criteria
Chapter 7 Net Present Value and Other Investment Criteria 72 Topics Covered Net Present Value Other Investment Criteria Mutually Exclusive Projects Capital Rationing 73 Net Present Value Net Present
More informationHOW TO USE YOUR HP 12 C CALCULATOR
HOW TO USE YOUR HP 12 C CALCULATOR This document is designed to provide you with (1) the basics of how your HP 12C financial calculator operates, and (2) the typical keystrokes that will be required on
More informationNet Present Value and Other Investment Criteria
Net Present Value and Other Investment Criteria Topics Covered Net Present Value Other Investment Criteria Mutually Exclusive Projects Capital Rationing Net Present Value Net Present Value  Present value
More informationHow to Calculate Present Values
How to Calculate Present Values Michael Frantz, 20100922 Present Value What is the Present Value The Present Value is the value today of tomorrow s cash flows. It is based on the fact that a Euro tomorrow
More information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationFIN 3000. Chapter 6. Annuities. Liuren Wu
FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
More informationUNIVERSITY OF WAH Department of Management Sciences
BBA330: FINANCIAL MANAGEMENT UNIVERSITY OF WAH COURSE DESCRIPTION/OBJECTIVES The module aims at building competence in corporate finance further by extending the coverage in Business Finance module to
More informationUNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed. Time Value Analysis
This is a sample of the instructor resources for Understanding Healthcare Financial Management, Fifth Edition, by Louis Gapenski. This sample contains the chapter models, endofchapter problems, and endofchapter
More informationTIME VALUE OF MONEY PROBLEM #8: NET PRESENT VALUE Professor Peter Harris Mathematics by Sharon Petrushka
TIME VALUE OF MONEY PROBLEM #8: NET PRESENT VALUE Professor Peter Harris Mathematics by Sharon Petrushka Introduction Creativity Unlimited Corporation is contemplating buying a machine for $100,000, which
More informationEXERCISE 64 (15 20 minutes)
EXERCISE 64 (15 20 minutes) (a) (b) (c) (d) Future value of an ordinary annuity of $4,000 a period for 20 periods at 8% $183,047.84 ($4,000 X 45.76196) Factor (1 +.08) X 1.08 Future value of an annuity
More information1 Interest rates, and riskfree investments
Interest rates, and riskfree investments Copyright c 2005 by Karl Sigman. Interest and compounded interest Suppose that you place x 0 ($) in an account that offers a fixed (never to change over time)
More informationCHAPTER 2. Time Value of Money 21
CHAPTER 2 Time Value of Money 21 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 22 Time lines 0 1 2 3
More informationChapter 5 Capital Budgeting
Chapter 5 Capital Budgeting Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. FixedIncome securities. Common stocks. Real assets (capital budgeting). Part C Determination
More informationCapital Budgeting OVERVIEW
WSG12 7/7/03 4:25 PM Page 191 12 Capital Budgeting OVERVIEW This chapter concentrates on the longterm, strategic considerations and focuses primarily on the firm s investment opportunities. The discussions
More informationChapter 10. What is capital budgeting? Topics. The Basics of Capital Budgeting: Evaluating Cash Flows
Chapter 10 The Basics of Capital Budgeting: Evaluating Cash Flows 1 Topics Overview and vocabulary Methods NPV IRR, MIRR Profitability Index Payback, discounted payback Unequal lives Economic life 2 What
More informationCHAPTER 7 MAKING CAPITAL INVESTMENT DECISIONS
CHAPTER 7 MAKING CAPITAL INVESTMENT DECISIONS Answers to Concepts Review and Critical Thinking Questions 1. In this context, an opportunity cost refers to the value of an asset or other input that will
More informationPrepared by: Dalia A. Marafi Version 2.0
Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version
More informationOklahoma State University Spears School of Business. Time Value of Money
Oklahoma State University Spears School of Business Time Value of Money Slide 2 Time Value of Money Which would you rather receive as a signin bonus for your new job? 1. $15,000 cash upon signing the
More informationTopics Covered. Compounding and Discounting Single Sums. Ch. 4  The Time Value of Money. The Time Value of Money
Ch. 4  The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate For now, we will omit the section 4.5 on inflation
More informationCHAPTER 7: NPV AND CAPITAL BUDGETING
CHAPTER 7: NPV AND CAPITAL BUDGETING I. Introduction Assigned problems are 3, 7, 34, 36, and 41. Read Appendix A. The key to analyzing a new project is to think incrementally. We calculate the incremental
More informationChapter 10 The Basics of Capital Budgeting: Evaluating Cash Flows ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 10 The Basics of Capital Budgeting: Evaluating Cash Flows ANSWERS TO ENDOFCHAPTER QUESTIONS 101 a. Capital budgeting is the whole process of analyzing projects and deciding whether they should
More informationCHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA
CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Answers to Concepts Review and Critical Thinking Questions 1. A payback period less than the project s life means that the NPV is positive for
More informationMODULE: PRINCIPLES OF FINANCE
Programme: BSc (Hons) Financial Services with Law BSc (Hons) Accounting with Finance BSc (Hons) Banking and International Finance BSc (Hons) Management Cohort: BFSL/13/FT Aug BACF/13/PT Aug BACF/13/FT
More informationReview Solutions FV = 4000*(1+.08/4) 5 = $4416.32
Review Solutions 1. Planning to use the money to finish your last year in school, you deposit $4,000 into a savings account with a quoted annual interest rate (APR) of 8% and quarterly compounding. Fifteen
More informationChapter 11. Bond Pricing  1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions.
Bond Pricing  1 Chapter 11 Several Assumptions: To simplify the analysis, we make the following assumptions. 1. The coupon payments are made every six months. 2. The next coupon payment for the bond is
More informationGordon Guides For the MT Exam. Financial Math
Financial Math For the IMT Exam, candidates are expected to have a high degree of understanding of time value of money principles, security valuation and basic statistics. Formulas are provided on at the
More informationAnswers to WarmUp Exercises
Answers to WarmUp Exercises E101. Answer: E102. Answer: Payback period The payback period for Project Hydrogen is 4.29 years. The payback period for Project Helium is 5.75 years. Both projects are acceptable
More informationWhich projects should the corporation undertake
Which projects should the corporation undertake Investment criteria 1. Investment into a new project generates a flow of cash and, therefore, a standard DPV rule should be the first choice under consideration.
More informationTIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction
TIME VALUE OF MONEY #6: TREASURY BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This problem assumes that you have mastered problems 15, which are prerequisites. In this
More informationSession #5 Capital Budgeting  II Damodaran  Chapter 9: 6,12,16,18 Chapter 10: 2,10,16(a&b) Chapter 11: 6,12,14
Session #5 Capital Budgeting  II Damodaran  Chapter 9: 6,12,16,18 Chapter 10: 2,10,16(a&b) Chapter 11: 6,12,14 I. Additional Issues in Capital Budgeting. A. Capital rationing: Use profitability index
More informationYour Name: UVa Id:
University of Virginia  math1140: Financial Mathematics Fall 2011 Exam 1 7:009:00 pm, 26 Sep 2011 Honor Policy. For this exam, you must work alone. No resources may be used during the quiz. The only
More informationFNCE 301, Financial Management H Guy Williams, 2006
Review In the first class we looked at the value today of future payments (introduction), how to value projects and investments. Present Value = Future Payment * 1 Discount Factor. The discount factor
More informationExercise 6 8. Exercise 6 12 PVA = $5,000 x 4.35526* = $21,776
CHAPTER 6: EXERCISES Exercise 6 2 1. FV = $10,000 (2.65330 * ) = $26,533 * Future value of $1: n = 20, i = 5% (from Table 1) 2. FV = $10,000 (1.80611 * ) = $18,061 * Future value of $1: n = 20, i = 3%
More informationTime Value of Money (TVM)
BUSI Financial Management Time Value of Money 1 Time Value of Money (TVM) Present value and future value how much is $1 now worth in the future? how much is $1 in the future worth now? Business planning
More informationChapter 13 The Basics of Capital Budgeting Evaluating Cash Flows
Chapter 13 The Basics of Capital Budgeting Evaluating Cash Flows ANSWERS TO SELECTED ENDOFCHAPTER QUESTIONS 131 a. The capital budget outlines the planned expenditures on fixed assets. Capital budgeting
More informationNet Present Value and Capital Budgeting. What to Discount
Net Present Value and Capital Budgeting (Text reference: Chapter 7) Topics what to discount the CCA system total project cash flow vs. tax shield approach detailed CCA calculations and examples project
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More informationfirst complete "prior knowlegde"  to refresh knowledge of Simple and Compound Interest.
ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde"  to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: Allendof chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
More information6: Financial Calculations
: Financial Calculations The Time Value of Money Growth of Money I Growth of Money II The FV Function Amortisation of a Loan Annuity Calculation Comparing Investments Worked examples Other Financial Functions
More informationCHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA
CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Basic 1. To calculate the payback period, we need to find the time that the project has recovered its initial investment. After two years, the
More informationTime Value of Money. Background
Time Value of Money (Text reference: Chapter 4) Topics Background One period case  single cash flow Multiperiod case  single cash flow Multiperiod case  compounding periods Multiperiod case  multiple
More information