# BEFORE YOU CAN DO ANYTHING WITH THIS CALCULATOR YOU MUST LEARN THE RITUAL OF CALCULATOR PURIFICATION.

Size: px
Start display at page:

Download "BEFORE YOU CAN DO ANYTHING WITH THIS CALCULATOR YOU MUST LEARN THE RITUAL OF CALCULATOR PURIFICATION."

Transcription

6 2 Using the Cash Flow Keys Not all investments have nice even cash flows. Consider a proposal to open a gold mine. The size and timing of the cash flows are shown below: Year 0 Year 1 Year 2 Year 3 \$800,000 \$500,000 \$1,000,000 \$500,000 Opening the mine costs \$800,000. In one year we make \$500,000, the year after that we make a million dollars and in year three we have to shut down the mine and pay reclamation costs of half a million dollars. If we undertake this investment, what is our rate of return? We could algebrate our way solving this for r: \$500,000 \$1,000,000 \$500,000 \$800,000 = (1 + r ) (1 + r) (1 + r) That looks like work, being a third degree polynomial and all. Instead let s use the cash flow keys. Find the CF key next to the 2nd key. The calculator display shows CF0 = Type 800,000 +/ and push ENTER. Use the down arrow key,, (next to ON/OFF) to enter the next three cash flows. 500,000 ENTER C01 = 500,000, F01 = 1.00, (by the way, this means the frequency of the first cash flow is just once) 1,000,000 ENTER C02 = 1,000,000, F02 = 1.00, +/ 500,000 ENTER C03 = 500,000, F03 = 1.00, To find the rate of return, hit the IRR key then CPT The display should read IRR = If you don t believe me, evaluate the right hand side of this equation: \$500,000 \$1,000,000 \$500,000 \$ 800,000 = (1.2284) (1.2284) (1.2284) The great thing about this calculator is that when you re in the cash flow menu you can use the... keys to navigate up and down through the cash flows to double check your data entry. 6

7 Suppose on the same problem, your interest rate is 15 percent. What is the Net Present Value of the project? Find the NPV key. Enter 15 for the interest rate. 15 ENTER The display should show I = Hit the. key. The display should show NPV = Hit the CPT key to compute net present value. The display should show NPV = 62, To convince yourself, you could check the following: \$500,000 \$1,000,000 \$500,000 \$ 62, = \$800, (1.15) (1.15) (1.15) By the way, one more thing about the cash flow menu. It is not on the same payments per year plan as the time value of money keys. That is you did not have to set P/Y = 1 to get the results on the last page. That s fine if the cash flows are annual, but what if the cash flows are monthly? We just have to use the right discount rate. The right discount rate is the monthly rate. Suppose your friendly furniture dealer offers to sell you a \$5,000 bedroom suite on the following terms: Make no payment for six months, then pay \$450 per month for 12 months. What rate of interest (APR) is being extended? Then enter the cash flows CF0 5,000 CF1 0 F01 5 (see the time line) CF2 450 F02 12 When you compute the IRR the result is 0.67 the correct interpretation is that this is a loan with a MONTHLY interest rate of The APR = = 8.09% \$5, \$450 \$450 \$450 \$450 \$450 \$ \$450 \$450 \$450 \$450 \$450 \$ To clear out the cash flow registers without resetting your calculator use [CLR WORK], (behind CE/C ). 7

8 3. Interest Rate Conversion Menu [ICONV] First some background: Suppose you are offered an investment that costs \$1,000 today and promises to pay \$2,000 in 5 years. What rate of return are you earning? If your calculator is in 12 payments per year you would enter N 60 CPT I/Y PV 1,000 PMT 0 FV 2,000 Now if you hit CPT and I/Y the calculator will display I/Y = But if you were in 1 payment per year your results would be different: N 5 CPT I/Y PV 1,000 PMT 0 FV 2,000 Now if you hit CPT and I/Y the calculator will display I/Y = What s going on here? Well percent and percent are both the right answers the right answers to different questions, that is percent is the Annual Percentage Rate (APR) of this loan (if the loan has monthly compounding) percent is the Effective Annual Rate (EAR). The Effective Annual Rate has economic significance, the APR has legal significance. In the U.S., lenders are required by law to disclose the APR of any loan. APRs are handy and easy. That s why you see them in TV commercials. As financial economists, we should be interested in economic significance. If you know the number of compounding periods you can easily go back and forth between APR and EAR. In fact, your calculator has a special menu to convert between these interest rates it s called the Interest Rate Conversion Menu [ICONV]. Open up the [ICONV] menu (it s hiding out under the number 2). The display shows NOM = Enter Now use the down arrow key,, (next to the ON/OFF key). The display now shows EFF = Hit the CPT key to see EFF = Consider a loan with monthly compounding and an APR of 12%. This is really a loan with a monthly rate of 1%. If you borrowed \$1,000 in one year you would owe \$1, N 12 I/Y 12 PV 1,000 PMT 0 FV 1,

9 If this was an economically identical loan with annual compounding, the interest rate would obviously be % since r = % solves the equation: \$1, = \$1,000 (1 + r) Another way of finding r = % is to solve the following: (1.01) 12 = 1 + r An APR of 12% with monthly compounding is another way of saying a 12-month loan with interest charged at 1% per month. Open up the [ICONV] menu. The display shows NOM = Enter 12. Now use the down arrow key,. The display now shows EFF=0.00. Hit CPT to see EFF = Hit again. The display shows C/Y = That is the default setting for the number of compounding periods per year. Since most loans in the U.S. have monthly payments the engineers at Texas Instruments must have decided to make all the defaults work with the type of loan that we see a lot of. We can change to C/Y = 2 if we had a loan with semi-annual payments or C/Y = 52 if we had a loan with weekly payments When do you use APR and EAR? Well if you re comparing two loans that are identical in terms of the number of payments per year, you can use either. But if you re comparing loans with different numbers of payments per year, you really have to go with EAR. Which loan is the better deal? Borrow \$1,000,000 for one year at 10% APR with monthly compounding or borrow \$1,000,000 at 9.98% APR with weekly compounding? The 9.98% APR is actually the more expensive: [ICONV] since the default is 12 payments per year, let s do this one first. NOM = 10.00, EFF = To evaluate the effective annual rate on the second loan [ICONV] First, change to 52 payments per year by hitting the up arrow,. C/Y = 52, NOM = 9.98, EFF = The payment at the end of the year is only \$1,104, with the 10 percent loan with monthly compounding but is \$1,104, with the 9.98 percent APR loan with weekly compounding: N 12 N 52 I/Y 10 I/Y 9.98 PV 1,000,000 PV 1,000,000 PMT 0 PMT 0 FV 1,104, FV 1,104,

10 4. AMORT menu Most consumer loans in the U.S. are amortizing. The level payment that you commit yourself to has an interesting feature: while the size of the payment is constant, the amount of each payment that is interest and principal varies with each payment. Consider the following loan: You borrow \$1,000 and agree to repay \$87.92 at the end of each of the next 12 months. Your interest rate is 10% APR. N 12 I/Y 10 PV 1,000 PMT 0 CPT FV Month Payment Interest Principal Loan Balance 1 \$87.92 = \$ \$79.59 \$ = \$1, \$ \$87.92 = \$ \$80.25 \$ = \$ \$ \$87.92 = \$ \$80.92 \$ = \$ \$ \$87.92 = \$ \$81.59 \$ = \$ \$ \$87.92 = \$ \$82.27 \$ = \$ \$ \$87.92 = \$ \$82.96 \$ = \$ \$ \$87.92 = \$ \$83.65 \$ = \$ \$ \$87.92 = \$ \$84.35 \$ = \$ \$ \$87.92 = \$ \$85.05 \$ = \$ \$ \$87.92 = \$ \$85.76 \$ = \$ \$ \$87.92 = \$ \$86.47 \$87.14 = \$ \$ \$87.87 = \$ \$87.14 \$0.00 = \$87.14 \$87.14 The calculations are straightforward applications of our earlier work. Consider the first payment The interest expense is \$8.33 = \$1, This result can also be found using the time value of money menu: N 1 I/Y 10 PV 1,000 PMT 0 CPT FV 1, Now if our payment is \$87.92 and \$8.33 of that first payment is interest, then the difference is the amount of the principal repaid in the first payment: \$79.59 = \$87.92 \$8.33 Since we retired \$79.59 in principal with the first payment, our outstanding balance is now only \$ = \$1,000 \$79.59 And so on for 12 months. Notice that our last payment is a nickel lower than others. That s because we truncate the payments at pennies in the U.S. (since the smallest decimal division of money in the U.S. is the cent). If we had something smaller than a penny then our payment would be something like \$ and we would have perfect amortization. By the way we can truncate numbers on our calculator with the [ROUND] key. Try it on the loan payment to see that the total sum of payments in the real world is \$1, and not \$1, OK, even I admit that this is kind of trivial: \$1, = 12 \$87.92 and \$1, = 12 \$

12 Other Menus: Bond Pricing (chapter 5 material) Pricing a bond is a straightforward application of our earlier work. Consider a Treasury bond that pays a \$45 coupon payment twice a year on January 1 and July 1. The bond has a remaining maturity of exactly 5 years (today is January 2 of 2008). If the par value is \$1,000 and the yield to maturity is 6 percent APR (effective rate of 6.09%--use the ICONV menu) we can value the bond as the present value of the coupons and principal discounted back at 6 percent: \$45 \$45 \$45 \$45 \$45 \$45 \$45 \$45 \$45 \$1,045 0 ½ \$43.69= \$ \$42.42 \$45 1 1½ \$41.18 \$45 \$39.98 \$45 \$38.82 \$45 \$37.69 \$ \$36.59 \$45 \$35.52 \$ \$34.49 \$45 2½ ½ ½ \$ \$1,045 \$1, Consider how much work that would be to manually price a 30-year bond with semiannual coupon payments. 5 12

13 While it s tempting to use the cash flow menu here, the caution is that you have to be sure to correctly specify the periodic rate, which is easy to forget. Here s how: 2nd [RESET] ENTER CF0 0 CF1 45 F01 9 (see the time line) CF2 1,045 F02 1 I 3 (the periodic rate (6 month period) is ½ the stated APR) CPT NPV \$1, There s a much easier way to find \$1, using the time value of money keys. [ P/Y] N Remaining Years to Maturity Payments per Year [P/Y] 2 times per year for Treasury Bonds, 1 or 2 times per I/Y Yield to Maturity year for corporate bonds [AMORT] PV Price [BGN] PMT [CLR TVM] FV [Coupon Rate Par Value] Payments per Year Par Value N 10 = 5 years 2 payments per year. Try this: enter 5 then [ P/Y] to get 10 then hit N. I/Y 6 CPT PV 1, PMT 45 FV 1,000 (a common mistake is 1,045 but your calculator is programmed to expect 1,000) The other advantage of using the time value of money menu is that we could solve for a coupon rate if we were given a price and a yield to maturity, but we could never do that with the cash flow menu. Why show you those two hard ways at all? In my experience of teaching this material to over 4,000 students over the years, there s always somebody every semester who doesn t want to buy a financial calculator. He has his calculator from high school and wants to save \$30 by doing every problem by hand. There is also the student who is infatuated with the cash flow menu and who then misses almost all of the bond pricing questions. Don t be those guys this semester. 13

17 The Depreciation Menu DEPR : We will need this in chapter 8. If you ve had an accounting class you know that there are a lot of different types of depreciation choices out there: Straight-line, Sum-of-Years-Digits, Declining Balance, Double-Declining-Balance-with crossover. There s even more (e.g. the French do straightline depreciation differently that we do and your calculator will do that if you first change your formatting to the European way then your last choice in this menu is SLF straight line French) but for now in this class let s stay in straight-line depreciation (SL). To understand how to use this menu, let s depreciate a \$60,000 piece of equipment straight-line to a salvage value of \$6,000 over 3 years. From our accounting prerequisites we know that the depreciation \$60, 000 \$6, 000 charge in each year will be \$18, 000 = 3 And if this were an accounting class we could come up the following worksheet YEAR 0 YEAR 1 YEAR 2 YEAR 3 Book Value \$60,000 Depreciation Charge \$18,000 \$18,000 \$18,000 Remaining Book Value \$60,000 \$18,000 \$42,000 \$42,000 \$18,000 \$24,000 \$24,000 \$18,000 \$6,000 Remaining Depreciable Value \$36,000 \$18,000 \$0 Let s do this with our calculator: please enter 2nd [RESET] ENTER 2nd [QUIT] 2nd DEPR. The display shows SL leave that alone and use the down arrow key,. The display now shows LIF= 1.00 Enter 3. The display shows LIF = 3.00 Now use the down arrow key,. The display now shows M01= 1.00 leave that alone and use the down arrow key,. (In the real world, if we had put an asset into service on Valentine s Day we would only be entitled to a partial depreciation charge in the first year, entering M01 =2.5 means February 14.) The display now shows CST= 0.00 Enter 60,000 The display shows CST= 60, Use the down arrow key:. The display now shows SAL= 0.00 Enter 6,000 The display shows SAL = 6, Use the down arrow key:. The display now shows YR= 1.00 leave that alone and to view our results: DEP = 18, RBV = 42, RDV = 36, ENTER YR = 2 DEP = 18, RBV = 24, RDV = 18, ENTER YR = 3 DEP = 18, RBV = 6, RDV =

18 The Profit Menu 2nd PROFIT CST = The cost of an item SEL = The selling price MAR = The profit margin Enter values for any two variables and the calculator will solve for the third. The Break Even Menu This menu calculates accounting break even price or quantity. 2nd BRKEVN FC VC P PFT Q = Fixed cost = Variable cost = The selling price per unit = Total profit = The accounting break-even quantity Enter values for any four variables and the calculator will solve for the remaining one. Most often we set profit equal to zero and either solve for break-even quantity or break-even price. The Percentage Change Menu This menu is kind of embarrassing. 2nd Δ% OLD = The original value NEW = The new value %CH = The percentage change per period #PD = Number of periods Enter values for any three variables and the calculator will solve for the fourth. 18

19 The Memory Menu This menu shows the values that we have entered into our calculator s memory. We can have our calculator remember any number that we like and it will remember as many as ten different numbers for us. Our ten memory registers are the numbers 0 through 9. We store a number in a memory register by entering STO and we can recall a number by using the RCL key and then the number of the register. So for example, let s store the number 105 in memory register 5: 2nd [RESET] ENTER 2nd [QUIT] Enter 105 STO 5 Now clear the display with the CE/C key. We can recall our stored data by using the RCL key: enter RCL 5 and our display shows To see all of the stored values 2nd MEM M0 = 0.00 M1 = 0.00 M2 = 0.00 M3 = 0.00 M4 = 0.00 M5 = M6 = 0.00 M7 = 0.00 M8 = 0.00 M9 = 0.00 You will really save yourself a lot of existential angst if you get in the habit of using your calculator s memories. Your calculator saves the number out to 24 decimal places (even if the display only shows you two). Your calculator also doesn t have fat fingers that thinks it s entering 105 but is really entering 150 by mistake. That s about it for the kinds of menus that you will need in a finance class. There s a lot of other menus: trigonometry, statistics, transcendental functions, factorials, combinations and permutations, the thing even can do five different kinds of regression, but we re just not about that kind of fun in this course. If you ever need to know the answers to life s persistent questions, try the ANS. key (under the = key). 19

### Course FM / Exam 2. Calculator advice

Course FM / Exam 2 Introduction It wasn t very long ago that the square root key was the most advanced function of the only calculator approved by the SOA/CAS for use during an actuarial exam. Now students

### Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e

Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,

### substantially more powerful. The internal rate of return feature is one of the most useful of the additions. Using the TI BA II Plus

for Actuarial Finance Calculations Introduction. This manual is being written to help actuarial students become more efficient problem solvers for the Part II examination of the Casualty Actuarial Society

### Introduction. Turning the Calculator On and Off

Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction

### Compounding Assumptions. Compounding Assumptions. Financial Calculations on the Texas Instruments BAII Plus. Compounding Assumptions.

Compounding Assumptions Financial Calculations on the Texas Instruments BAII Plus This is a first draft, and may contain errors. Feedback is appreciated The TI BAII Plus has built-in preset assumptions

### Using Financial Calculators

Chapter 4 Discounted Cash Flow Valuation 4B-1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your Hewlett-Packard or Texas Instruments BA II Plus financial calculator

### Texas Instruments BA II Plus. Calculator tutorial

Chartered Financial Analyst Program Texas Instruments BA II Plus calculator tutorial Nicholas J Blain, CFA Chief Executive Quartic Training 1 outline 0. Calculator setup and introduction 1. Basic algebra

### HANDBOOK: HOW TO USE YOUR TI BA II PLUS CALCULATOR

HANDBOOK: HOW TO USE YOUR TI BA II PLUS CALCULATOR This document is designed to provide you with (1) the basics of how your TI BA II Plus financial calculator operates, and (2) the typical keystrokes that

### In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.

Section 4: Using a Financial Calculator Tab 1: Introduction and Objectives Introduction In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.

### Texas Instruments BAII PLUS Tutorial

To begin, look at the face of the calculator. Almost every key on the BAII PLUS has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in

### Key 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

### Continue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not.

Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two

### Using Financial And Business Calculators. Daniel J. Borgia

Using Financial And Business Calculators Daniel J. Borgia August 2000 Table of Contents I. Texas Instruments BA-35 SOLAR II. Texas Instruments BAII PLUS III. Hewlett Packard 12C IV. Hewlett Packard 17BII..

### The explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.

USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas

BA II Plus Advanced Business Analyst Calculator Quick Guide to Settings and Concepts Purpose of Guide This Quick Guide is a supplement to the BA II Plus Guidebook. It includes brief examples of commonly

### Main TVM functions of a BAII Plus Financial Calculator

Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there

### The Time Value of Money

The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time

### Texas Instruments BAII PLUS Tutorial

Omar M. Al Nasser, Ph.D., MBA. Visiting Assistant Professor of Finance School of Business Administration University of Houston-Victoria Email: alnassero@uhv.edu Texas Instruments BAII PLUS Tutorial To

### Oklahoma 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 sign-in bonus for your new job? 1. \$15,000 cash upon signing the

### Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.

### Module 5: Interest concepts of future and present value

file:///f /Courses/2010-11/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present

### Chapter 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

### Time-Value-of-Money and Amortization Worksheets

2 Time-Value-of-Money and Amortization Worksheets The Time-Value-of-Money and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or

### How To Read The Book \"Financial Planning\"

Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value

### Key Concepts and Skills

McGraw-Hill/Irwin Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash

### Note: In the authors opinion the Ativa AT 10 is not recommended as a college financial calculator at any level of study

Appendix 1: Ativa AT 10 Instructions Note: DNS = Does Not Calculate Note: Loan and Savings Calculations Automatically round to two decimals. -Clear -Store Data in Memory -Recall Stored Data in Memory [CE]

### Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations

Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the Hewlett-Packard

### Sharp EL-733A Tutorial

To begin, look at the face of the calculator. Almost every key on the EL-733A has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in

### CHAPTER 4 DISCOUNTED CASH FLOW VALUATION

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value

### Chapter 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

### BEST INTEREST RATE. To convert a nominal rate to an effective rate, press

FINANCIAL COMPUTATIONS George A. Jahn Chairman, Dept. of Mathematics Palm Beach Community College Palm Beach Gardens Location http://www.pbcc.edu/faculty/jahng/ The TI-83 Plus and TI-84 Plus have a wonderful

### Hewlett-Packard 10BII Tutorial

This tutorial has been developed to be used in conjunction with Brigham and Houston s Fundamentals of Financial Management 11 th edition and Fundamentals of Financial Management: Concise Edition. In particular,

### Chapter 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

### CALCULATOR 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

### Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The

### Module 5: Interest concepts of future and present value

Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities

### TIME VALUE OF MONEY. Hewlett-Packard HP-12C Calculator

SECTION 1, CHAPTER 6 TIME VALUE OF MONEY CHAPTER OUTLINE Clues, Hints, and Tips Present Value Future Value Texas Instruments BA II+ Calculator Hewlett-Packard HP-12C Calculator CLUES, HINTS, AND TIPS Present

### Discounted 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

### Hewlett-Packard 10B Tutorial

To begin, look at the face of the calculator. Every key (except one, the gold shift key) on the 10B has two functions: each key's primary function is noted in white on the key itself, while each key's

### Integrated Case. 5-42 First National Bank Time Value of Money Analysis

Integrated Case 5-42 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

### Calculator (Hewlett-Packard 10BII) Tutorial

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT Calculator (Hewlett-Packard 10BII) Tutorial To begin, look at the face of the calculator. Most keys (except a few) have two functions: Each key s primary function

### CHAPTER 6 DISCOUNTED CASH FLOW VALUATION

CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and

### BA II PLUS Calculator

BA II PLUS Calculator 1997, 2002 Texas Instruments Incorporated Important Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability

### DISCOUNTED 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

### 5. 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

### appendix B COMPOUND SUM OF AN ANNUITY OF \$1 appendix C PRESENT VALUE OF \$1 appendix D PRESENT VALUE OF AN ANNUITY OF \$1

appendices appendix A COMPOUND SUM OF \$1 appendix B COMPOUND SUM OF AN ANNUITY OF \$1 appendix C PRESENT VALUE OF \$1 appendix D PRESENT VALUE OF AN ANNUITY OF \$1 appendix E TIME VALUE OF MONEY AND INVESTMENT

### This 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 by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/

### BA II PLUS PROFESSIONAL Calculator

BA II PLUS PROFESSIONAL Calculator Important Information Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness

### BA II PLUS Calculator

BA II PLUS Calculator Important Information Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular

### CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount

### CHAPTER 1. Compound Interest

CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.

### Chapter 8. Present Value Mathematics for Real Estate

Chapter 8 Present Value Mathematics for Real Estate Real estate deals almost always involve cash amounts at different points in time. Examples: Buy a property now, sell it later. Sign a lease now, pay

### Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction...2 2. Interest Rates: Interpretation...2 3. The Future Value of a Single Cash Flow...4 4. The

### REVIEW MATERIALS FOR REAL ESTATE ANALYSIS

REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS

### Finance 197. Simple One-time Interest

Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for

### Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS

Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS 7-1 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 \$10,000(1.10) 5 \$10,000(FVIF 10%, 5 ) \$10,000(1.6105) \$16,105. Alternatively, with a financial calculator enter the

### The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)

The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-738 Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

### Discounted Cash Flow Valuation

6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

### CHAPTER 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)

### Key Concepts and Skills. Chapter Outline. Basic Definitions. Future Values. Future Values: General Formula 1-1. Chapter 4

Key Concepts and Skills Chapter 4 Introduction to Valuation: The Time Value of Money Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received

### CHAPTER 2. Time Value of Money 2-1

CHAPTER 2 Time Value of Money 2-1 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 2-2 Time lines 0 1 2 3

### 1.4 Interest-Rate calculations and returns

.4 Interest-Rate calculations and returns Effective Annual Rate (EAR) The Effective Annual Rate (EAR) is the actual rate paid (or received) after accounting for compounding that occurs during the year

### CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: \$5,000.08 = \$400 So after 10 years you will have: \$400 10 = \$4,000 in interest. The total balance will be

### CHAPTER 4 DISCOUNTED CASH FLOW VALUATION

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability

### EXAM 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

### HP 12C Calculations. 2. If you are given the following set of cash flows and discount rates, can you calculate the PV? (pg.

HP 12C Calculations This handout has examples for calculations on the HP12C: 1. Present Value (PV) 2. Present Value with cash flows and discount rate constant over time 3. Present Value with uneven cash

### TVM Appendix B: Using the TI-83/84. Time Value of Money Problems on a Texas Instruments TI-83 1

Before you start: Time Value of Money Problems on a Texas Instruments TI-83 1 To calculate problems on a TI-83, you have to go into the applications menu, the blue APPS key on the calculator. Several applications

### Casio Financial Consultant A Supplementary Reader - Part 2

Casio Financial Consultant A Supplementary Reader - Part 2 An Electronic Publication By Contents i CASIO Financial Consultant: A Supplementary Reader - Part 2 CONTENTS Page Introduction ii Compound Interest

### Fixed Income: Practice Problems with Solutions

Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semi-annual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.

### CHAPTER 8 INTEREST RATES AND BOND VALUATION

CHAPTER 8 INTEREST RATES AND BOND VALUATION Answers to Concept Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury securities have substantial

### Topics. Chapter 5. Future Value. Future Value - Compounding. Time Value of Money. 0 r = 5% 1

Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series

### TVM Applications Chapter

Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (long-term receivables) 7 Long-term assets 10

### 3. 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

### Finding 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.

### 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%?

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

### Activity 3.1 Annuities & Installment Payments

Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.

### Ehrhardt Chapter 8 Page 1

Chapter 2 Time Value of Money 1 Time Value Topics Future value Present value Rates of return Amortization 2 Time lines show timing of cash flows. 0 1 2 3 I% CF 0 CF 1 CF 2 CF 3 Tick marks at ends of periods,

### Time Value of Money. If you deposit \$100 in an account that pays 6% annual interest, what amount will you expect to have in

Time Value of Money Future value Present value Rates of return 1 If you deposit \$100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.

### BA-35 Solar Quick Reference Guide

BA-35 Solar Quick Reference Guide Table of Contents General Information... 2 The Display... 4 Arithmetic Operations... 6 Correcting Errors... 7 Display Formats... 8 Memory Operations... 9 Math Operations...

### Interest Theory. Richard C. Penney Purdue University

Interest Theory Richard C. Penney Purdue University Contents Chapter 1. Compound Interest 5 1. The TI BA II Plus Calculator 5 2. Compound Interest 6 3. Rate of Return 18 4. Discount and Force of Interest

### How To Calculate A Balance On A Savings Account

319 CHAPTER 4 Personal Finance The following is an article from a Marlboro, Massachusetts newspaper. NEWSPAPER ARTICLE 4.1: LET S TEACH FINANCIAL LITERACY STEPHEN LEDUC WED JAN 16, 2008 Boston - Last week

### FINA 351 Managerial Finance, Ch.4-5, Time-Value-of-Money (TVM), Notes

FINA 351 Managerial Finance, Ch.4-5, Time-Value-of-Money (TVM), Notes The concept of time-value-of-money is important to know, not only for this class, but for your own financial planning. It is a critical

### LOS 56.a: Explain steps in the bond valuation process.

The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Introduction

### Real Estate. Refinancing

Introduction This Solutions Handbook has been designed to supplement the HP-2C Owner's Handbook by providing a variety of applications in the financial area. Programs and/or step-by-step keystroke procedures

### hp calculators HP 17bII+ Discounting & Discounted Cash Flow Analysis It's About Time The Financial Registers versus Discounted Cash Flow

HP 17bII+ Discounting & Discounted Cash Flow Analysis It's About Time The Financial Registers versus Discounted Cash Flow Discounting a Single Sum Discounting and Compounding Discounting a Series of Sums

### BUSI 121 Foundations of Real Estate Mathematics

Real Estate Division BUSI 121 Foundations of Real Estate Mathematics SESSION 2 By Graham McIntosh Sauder School of Business University of British Columbia Outline Introduction Cash Flow Problems Cash Flow

### Mathematics. Rosella Castellano. Rome, University of Tor Vergata

and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings

### Prepared by: Dalia A. Marafi Version 2.0

Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC-200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version

### BA Finance Pro. 2010 Ernest Brock

BA Finance Pro 2010 Ernest Brock BA Finance Pro! 1 FAQ! 2 Sample Problems! 3 Setting up the calculator! 3 Time Value of Money (TVM) Computations! 3 Lump Sums! 3 Regular Annuities! 5 Calculator! 9 Time

### Chapter 4: Time Value of Money

Chapter 4: Time Value of Money BASIC KEYS USED IN FINANCE PROBLEMS The following two key sequences should be done before starting any "new" problem: ~ is used to separate key strokes (3~N: enter 3 then

### The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)

The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-733A Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

### Notes on the SHARP EL-738 calculator

Chapter 1 Notes on the SHARP EL-738 calculator General The SHARP EL-738 calculator is recommended for this module. The advantage of this calculator is that it can do basic calculations, financial calculations

### Math Workshop Algebra (Time Value of Money; TVM)

Math Workshop Algebra (Time Value of Money; TVM) FV 1 = PV+INT 1 = PV+PV*I = PV(1+I) = \$100(1+10%) = \$110.00 FV 2 = FV 1 (1+I) = PV(1+I)(1+I) = PV(1+I) 2 =\$100(1.10) 2 = \$121.00 FV 3 = FV 2 (1+I) = PV(1

### Chapter 3. Understanding The Time Value of Money. Prentice-Hall, Inc. 1

Chapter 3 Understanding The Time Value of Money Prentice-Hall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,

### 2. Determine the appropriate discount rate based on the risk of the security

Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the

### Casio Financial Consultant A Supplementary Reader - Part 4

Casio Financial Consultant A Supplementary Reader - Part 4 An Electronic Publication By Contents i CASIO Financial Consultant: A Supplementary Reader - Part 4 CONTENTS Page Introduction ii BOND Calculations

### Chapter F: Finance. Section F.1-F.4

Chapter F: Finance Section F.1-F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given