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

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

Download "Compounding Assumptions. Compounding Assumptions. Financial Calculations on the Texas Instruments BAII Plus. Compounding Assumptions."

## Transcription

1 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 about compounding and payment frequencies. Compounding and Payment frequencies are controlled with the [P/Y] key Copyright 22, Alan Marshall 1 Copyright 22, Alan Marshall 2 Compounding Assumptions Compounding Assumptions Press the [P/Y] key ([2nd][I/Y] Unless the settings have been changed, you will see the default, preset payment frequency: P/Y = payments/year Using the down arrow [^] or up arrow [v] will scroll you to the next window, the number of times per year the interest is compounded: C/Y = times/year Copyright 22, Alan Marshall 3 For the first part of the Time Value of Money slides, we are dealing with annual compounding and annual payments, so these values need to be changed: [P/Y] = 1 [ENTER] [C/Y] will automatically be changed to 1 [^] [C/Y] Display = 1 To return to the calculator mode press [QUIT] or [2nd][CPT] Copyright 22, Alan Marshall 4 An Alternative One way to make the BAII Plus work very much like the Sharp EL-733A is to set the [P/Y] and [C/Y] to 1 and leave it there all the time. If you do this, some of the directions that follow will not work if the values of [P/Y] and [C/Y] are changed Clearing It is also very important to clear the Time Value worksheet before doing a new set of calculations [CLR][TVM] Copyright 22, Alan Marshall 5 Copyright 22, Alan Marshall 6 1

2 A Word on Rounding I set my BA II Plus to an artificially large number of decimals - usually 7 - which will rarely all be displayed. The BA II Plus will display the answer rounded correctly to the number of decimals available or as set by you, whichever is less. In these notes, 1/7 = may be written as.1428, where the simply means that I have stopped writing down the decimals, but I have not rounded. FV 5 Future Values = PV (1+ = \$44,651.6(1.6 n = \$44,651.6( = \$59, Copyright 22, Alan Marshall 7 Copyright 22, Alan Marshall [PV]; 6 [I/Y]; 5 [N] [CPT][FV] Display = -59, To get the FV k,n, simply use PV = 1 1 [PV]; 6 [I/Y]; 5 [N] [CPT][FV] Display = Present Values A contract that promised to pay you v59, in 5 years would be worth today, at 6% interest: PV = = = ( FV5 ( PVIF6%,5 5 \$59,753.19( 1.6 \$59,753.19( = \$44,651.6 Copyright 22, Alan Marshall 9 Copyright 22, Alan Marshall [FV]; 6 [I/Y]; 5 [N] [CPT][PV] Display = -44,651.6 To get the PV k,n, simply use FV = 1 1 [FV]; 6 [I/Y]; 5 [N] [CPT][PV] Display = Perpetuities Perpetuities, growing perpetuities and growing finite annuities must be done using the formulae as financial calculators do not have special functions for these cash flows Copyright 22, Alan Marshall 11 Copyright 22, Alan Marshall 12 2

3 PV of Annuity Example PV 1 (1+ = \$1,6 k 5 1 (1.6 = \$1,6.6 = \$1,6( = \$44,651.6 n 1,6 [PMT]; 6 [I/Y]; 5 [N] [CPT][PV] Display = -44,651.6 To get the PVA k,n, simply use PMT = 1 1 [PMT]; 6 [I/Y]; 5 [N] [CPT][PV] Display = Copyright 22, Alan Marshall 13 Copyright 22, Alan Marshall 14 FV of Annuity Example FV 5 (1+ = \$1,6 k 5 (1.6 1 = \$1,6.6 = \$1,6( = \$59, n 1 1,6 [PMT]; 6 [I/Y]; 5 [N] [CPT][FV] Display = -59, To get the FVA k,n, simply use PMT = 1 1 [PMT]; 6 [I/Y]; 5 [N] [CPT][FV] Display = Copyright 22, Alan Marshall 15 Copyright 22, Alan Marshall 16 Annuities Due To access the toggle that switches the annuity payments between regular (END and due (BGN you use the [BGN] key ([2nd][PMT] To toggle between the BGN and END setting, use [SET] ([2nd][ENTER] and [QUIT] to return to the calculator mode If set for annuities due, you will see BGN in the display Copyright 22, Alan Marshall 17 PV PV of an Annuity Due 1 (1+ = \$1, k 5 1 (1.6 = \$1,.6 = \$1,( = \$44,651.6 n ( 1+ ( 1.6 Copyright 22, Alan Marshall 18 3

4 [BGN][SET] to set to BGN 1, [PMT]; 6 [I/Y]; 5 [N] [CPT][PV] Display = -44,651.6 To get the PVA k,n, simply use PMT = 1 1 [PMT]; 6 [I/Y]; 5 [N] [CPT][PV] Display = FV of an Annuity Due FVA n,k ( Due (1+ = PMT k = PMT FV 1 ( ( 1+ k,n n ( 1+ Copyright 22, Alan Marshall 19 Copyright 22, Alan Marshall 2 [BGN][SET] to set to BGN 1, [PMT]; 6 [I/Y]; 5 [N] [CPT][FV] Display = -59, To get the FVA k,n, simply use PMT = 1 1 [PMT]; 6 [I/Y]; 5 [N] [CPT][FV] Display = Example, Uneven Cash Flows Valued at 6% \$2, \$15, \$25, \$3, \$1, \$18, \$13, \$2,99.48 \$23, \$7, \$84, Copyright 22, Alan Marshall 21 Copyright 22, Alan Marshall 22 We use the [CF] key, Initially, we see the Display: Cf =. The down arrow [v] and up arrow [^] allow us to scroll through the displays Each Cnn is followed by Fnn to allow the user to enter multiple occurrences of a value After the cash flows are entered, we use the [NPV] key The first display is I = and is asking us to enter the interest or discount rate. After entering the rate the [v] gives us the NPV = display. [CPT] will give us the net present value of the cash flows. Copyright 22, Alan Marshall 23 Copyright 22, Alan Marshall 24 4

5 Example on the TI BAII Plus Look for hidden annuities CF =. [v] C1 = 2 [ENTER] [v] F1 = 1 [v] C2 = 2 [ENTER] [v] F2 = 1 [v] C3 = 2 [ENTER] [v] F3 = 1 [v] C4 = 2 [ENTER] [v] F4 = 1 [v] C5 = 2 [ENTER] [v] F5 = 1 [v] [NPV] Display: I = 6 [ENTER] [v] Display: NPV = [CPT] Display: NPV = 84, Copyright 22, Alan Marshall 25 Sometimes there will be annuities to simplify your calculations that are not so obvious \$15, \$15, \$2, \$2, \$2, \$27,5.89 \$47, \$53,46.24 \$75,8.31 A 3 Yr \$2, annuity Copyright 22, Alan Marshall 26 Example on the TI BAII Plus CF =. [v] C1 = 15 [ENTER] [v] F1 = 2 [ENTER] [v] C2 = 2 [ENTER] [v] F2 = 3 [ENTER] [v] [NPV] Display: I = 6 [ENTER] [v] Display: NPV = [CPT] Display: NPV = 75,8.31 Example Suppose that Consolidated Moose Pasture (CMP borrowed \$466,5 and promised to repay \$1,, eight years from now. There will be no intermediate interest payments. What is the implied rate of interest? Copyright 22, Alan Marshall 27 Copyright 22, Alan Marshall [PV]; 1 [+/-] [FV]; 8 [N] [CPT][I/Y] Display = 1. Example - Annuities Suppose you have the choice to receive \$1, now or \$15, per year at the start of each of the next 1 years. [BGN][SET] (to toggle to BGN 15 [PMT]; 1 [+/-][PV], 1 [N] [CPT][I/Y] Display: 1.49 Copyright 22, Alan Marshall 29 Copyright 22, Alan Marshall 3 5

6 Converting from APR to EAR Consider \$1 for 1 year 6% compounded quarterly: 1.5% every quarter for 4 quarters monthly:.5% every month for 12 months daily: (6/365% every day for 365 days Effective Annual Rate Quarterly FV = \$1* Monthly FV = \$1* ( 1.15 EAR = 6.136% ( 1.5 EAR = % 4 12 = \$ = \$ Daily FV = \$1* EAR = % ( 1+ ( 6 / = \$ Copyright 22, Alan Marshall 31 Copyright 22, Alan Marshall 32 To convert from a nominal (APR to EAR You can do it by using the formulaic approach from the previous slide, or You can use the [ICONV] worksheet (above the numeral [2] The first screen is NOM = The second screen is EFF = The third screen is C/Y = Using the [ICONV] worksheet NOM = 6 [ENTER], [^] C/Y = 4 [ENTER], [^] EFF = [CPT] Display = NOM = 6 [ENTER], [^] C/Y = 12 [ENTER], [^] EFF = [CPT] Display = NOM = 6 [ENTER], [^] C/Y = 365 [ENTER], [^] EFF = [CPT] Display = Copyright 22, Alan Marshall 33 Copyright 22, Alan Marshall 34 Converting from EAR to APR Example The account earns an EAR of 6% If the account compounds interest quarterly, what is the APR? If the account compounds interest monthly, what is the APR? If the account compounds interest daily, what is the APR? Quarterly Monthly Daily q = q = q = q = ( 1 m ( 1+ EAR ( 1.6 ( ( = % ( 1 12 ( 1.6 = % ( ( = % m 365 Copyright 22, Alan Marshall 35 Copyright 22, Alan Marshall 36 6

7 To convert from EAR to APR You can do it by using the formulaic approach from the previous slide, or You can use the same [ICONV] worksheet with the nominal being the value to be computed Using the [ICONV] worksheet EFF = 6 [ENTER], [^] C/Y = 4 [ENTER], [^] NOM = [CPT] Display = EFF = 6 [ENTER], [^] C/Y = 12 [ENTER], [^] NOM = [CPT] Display = EFF = 6 [ENTER], [^] C/Y = 365 [ENTER], [^] NOM = [CPT] Display = Copyright 22, Alan Marshall 37 Copyright 22, Alan Marshall 38 Example Your older sister just had a baby. If she opens an RESP and puts \$125/month into it for 18 years, how much will be available for the child if the rate of return is 8% per annum, 2/3% per month? [P/Y] = 12 [ENTER] [QUIT] 8 [I/Y]; 125 [PMT]; 216 [N] (or 18[2nd][N] [CPT][FV] Display: -6,1.77 Continuous Compounding With continuous compounding, you must solve using the formula and the [e x ] key (or [2nd][ln] Suppose you want to have \$1,, in your retirement account when you reach 65, 44 years from now. If a financial institution is offering you 7% compounded continuously, how much would you have to deposit now, while you re 21?.7 [x] 44[+/-][=] Display: -3.8[e x ] Display: [x] 1 [=] Display: 45, Copyright 22, Alan Marshall 39 Copyright 22, Alan Marshall 4 Mortgage Example \$12, principal (=PV 25 year amortization (n=3 months 8% five year term EAR=8.16% APR=7.87% monthly= % PV = C(PVA 12, = C(PVA C = = Solution k mon,n 12, PVA %, %,3 12, = \$ Copyright 22, Alan Marshall 41 Copyright 22, Alan Marshall 42 7

8 Renewal Balance 1. Enter the the payment frequency, [P/Y] 12 [ENTER] and compounding frequency, [^] [C/Y] 2 [ENTER] 2. Enter the mortgage parameters: The principal: 12 [PV], nominal rate 8 [I/Y] and amortization term 3 [N] 3. Compute the payment [CPT][PMT] Display: PMT = MORE TO COME, DO NOT CLEAR Copyright 22, Alan Marshall 43 The principal of a mortgage is always the PV of the payments that remain on the amortization After 5 years: BAL6 = \$915.86(PVA %, 24 = \$915.86( = \$11, Copyright 22, Alan Marshall 44 Other Questions Principal \$12,. At Renewal 11, Principal Paid 9, Interest Paid 45, Total Paid 54,951.6 Copyright 22, Alan Marshall 45 The AMORT key gives us access to the amortization worksheet Once you have accessed the AMORT worksheet, the display should say P1 = 1 This is the first payment in the range Pressing the down arrow will give you P2 = something and you can specify the last payment in the range If you want to see each payment sequentially, use P1 = 1, P2 = 1; then P1 = 2, P2 = 2; and so on. Copyright 22, Alan Marshall 46 Using the [AMORT] worksheet: First Payment P1 = 1 [ENTER], [v] P2 = 1 [ENTER], [v] BAL = 119,987.13, [v] PRN = ,[v] INT = Second Payment P1 = 2 [ENTER], [v] P2 = 2 [ENTER], [v] BAL = 119,741.41, [v] PRN = ,[v] INT = We can jump to any payment This is one of the situations where the calculator takes its time - and appears to die - to do the calculation Copyright 22, Alan Marshall 47 Copyright 22, Alan Marshall 48 8

9 Sixtieth Payment (just before the five-year renewal P1 = 6 [ENTER], [v] P2 = 6 [ENTER], [v] BAL = 11,562.91, [v] PRN = ,[v] INT = Accumulated Values The [AMORT] worksheet will also allow us to determine how much principal and interest has been paid over a range of periods by specifying ranges for P1 = and P2 = Copyright 22, Alan Marshall 49 Copyright 22, Alan Marshall 5 Over the first five years: P1 = 1 [ENTER], [v] P2 = 6 [ENTER], [v] BAL = 11,562.91, [v] PRN = -9,437.9,[v] INT = Car Buying or Leasing Suppose you have decided on a new Bolero from National Motors. Its total cost before sales taxes (15% is \$23,5. You plan to put \$3,5 down regardless whether you lease or buy. The buyback at the end of the 48 month lease is \$9,. The dealer is offering 4.8% APR financing and lease rates, both compounded monthly. Copyright 22, Alan Marshall 51 Copyright 22, Alan Marshall 52 Buying - Loan \$23,5 + 15%(v23,5-3,5 = \$23, % APR, r MON =.4% Assume a 48 month loan PVIFA.4,48 = 43, PMT = Principal PVIFA 23, 525 = = \$ r MON,N The [P/Y] and [C/Y] should both be set to 12 - this is what you get when you [CLR_WORK] the [P/Y] key 48 [N], [PV], 4.8 [I/Y] [CPT] [PMT] Display: Copyright 22, Alan Marshall 53 Copyright 22, Alan Marshall 54 9

10 Lease On the lease, the sales tax does not get financed, but the payments are subject to sales taxes The present value of the lease payments, plus the present value of the buyback on the car must equal the cash price of the car Lease payments are made in advance, or at the beginning of each month = PMT = PMT 12, = PMT Lease 9, 2, = PMT( PVIFAD \$ %, ( ( ( , PMT = = ( , ,43.61 Copyright 22, Alan Marshall 55 Copyright 22, Alan Marshall 56 The [P/Y] and [C/Y] should both be set to 12 - this is what you get when you [CLRiWORK] the [P/Y] key You also need to set the calculator to BGN: [BGN][SET]; BGN will display 48 [N], 2 [PV], 4.8 [I/Y], -9 [FV] [CPT] [PMT] Display: Bonds With Bonds, you can approach them two ways: Using the Time Value functions, OR Using the [BOND] worksheet Copyright 22, Alan Marshall 57 Copyright 22, Alan Marshall 58 Regular Fixed Coupon Bond PV B B B = I ( PVA M + (1+ k Consider a 9%,12 yr kb,n 1 = 45( (1.35 = = \$1,16.58 b 24 n Using the Time Value Functions [P/Y] = 2 [ENTER] [N] = 24; [FV] = 1; [PMT] = 45; [I/Y] = 7 [CPT][PV] = -1,16.58 Copyright 22, Alan Marshall 59 Copyright 22, Alan Marshall 6 1

11 Using the [BOND] Worksheet The [BOND] worksheet requires starting and maturity dates If none are given, make them up dates are entered in the form mm.ddyy Jan 1, 21 would be 1.11 The maturity value [RV] defaults to 1 and is fine if you keep the coupon as a percent You will also get a price that is a percent of par Copyright 22, Alan Marshall 61 Using the [BOND] Worksheet Using the Default Value of RV = 1 SDT = 1.11 [ENTER] [v] CPN = 9 [ENTER] [v] RTD = [ENTER] [v] (Maturity Date RV = 1 [ENTER] [v] (Maturity Value ACT [v] (Actual day count 2/Y [v] (2 coupons/yr YLD = 7 [ENTER] [v] PRI = [CPT] Display: Copyright 22, Alan Marshall 62 Using the [BOND] Worksheet Using the Value of RV = 1 SDT = 1.11 [ENTER] [v] CPN = 9 [ENTER] [v] RTD = [ENTER] [v] (Maturity Date RV = 1 [ENTER] [v] (Maturity Value ACT [v] (Actual day count 2/Y [v] (2 coupons/yr YLD = 7 [ENTER] [v] PRI = [CPT] Display: 1, Copyright 22, Alan Marshall 63 11

### 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

### 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

### 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 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,

### Future Value. Basic TVM Concepts. Chapter 2 Time Value of Money. \$500 cash flow. On a time line for 3 years: \$100. FV 15%, 10 yr.

Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated

### 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

### 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

### 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

### 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

### 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 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

### 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

### 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

### 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.

### FinQuiz Notes 2 0 1 4

Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

### Chapter 4 Discounted Cash Flow Valuation

University of Science and Technology Beijing Dongling School of Economics and management Chapter 4 Discounted Cash Flow Valuation Sep. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Be able to compute

### 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

### 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

### Chapter 28 Time Value of Money

Chapter 28 Time Value of Money Lump sum cash flows 1. For example, how much would I get if I deposit \$100 in a bank account for 5 years at an annual interest rate of 10%? Let s try using our calculator:

### 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

### Chapter 4. The Time Value of Money

Chapter 4 The Time Value of Money 4-2 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest

### Chapter 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

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

### 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

### 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

### Time Value of Money Problems

Time Value of Money Problems 1. What will a deposit of \$4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. \$8,020.22 b. \$7,959.55 c. \$8,081.55 d. \$8,181.55 2. What will

### 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 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

### 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

### Time Value of Money. Reading 5. IFT Notes for the 2015 Level 1 CFA exam

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

### 2. How many months will it take to pay off a \$9,000 loan with monthly payments of \$225? The APR is 18%.

Lesson 1: The Time Value of Money Study Questions 1. Your mother, who gave you life (and therefore everything), has encouraged you to borrow \$65,000 in student loans. The interest rate is a record-low

### Problem Set: Annuities and Perpetuities (Solutions Below)

Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save \$300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years

### FinQuiz Notes 2 0 1 5

Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

### CHAPTER 9 Time Value Analysis

Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 9-1 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams

### Chapter 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

### 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,

### 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

### 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

### Chapter 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

### 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

### Chapter. Discounted Cash Flow Valuation. CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG.

Chapter 6 Discounted Cash Flow Valuation CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG. Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute

### 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.

### 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

### 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

### 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

### 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

### The 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

### Chapter 2 Applying Time Value Concepts

Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the

Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 4 work problems. Questions in the multiple choice section will be either concept or calculation

### 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

### 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

### 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..

### 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

### 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

### 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

### Key Concepts and Skills

Chapters 5 and 6 Calculators Time Value of Money and Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Key Concepts and Skills Be able

### Financial Management

Just Published! 206 Financial Management Principles & Practice 7e By Timothy Gallagher Colorado State University Changes to the new Seventh Edition: Updating of all time sensitive material and some new

### USING THE SHARP EL 738 FINANCIAL CALCULATOR

USING THE SHARP EL 738 FINANCIAL CALCULATOR Basic financial examples with financial calculator steps Prepared by Colin C Smith 2010 Some important things to consider 1. These notes cover basic financial

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

Brief Tutorial for the Texas Instruments BAII PLUS Part One By John Stansfield, CFA, Ph D, MBA, and calculator enthusiast. The Texas Instruments BAII PLUS is the only calculator for the well-dressed finance

### 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

### A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%

1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.

### 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

### 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

### Solutions to Problems: Chapter 5

Solutions to Problems: Chapter 5 P5-1. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start

### TIME VALUE OF MONEY (TVM)

TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate

### 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

### Chapter 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

### 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.

Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

### Chapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)

Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

### 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,

### 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

### 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

### PRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.

PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values

### 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

### 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

### 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

### 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

### 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

### 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

### Discounted 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?

### 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

### Week 4. Chonga Zangpo, DFB

Week 4 Time Value of Money Chonga Zangpo, DFB What is time value of money? It is based on the belief that people have a positive time preference for consumption. It reflects the notion that people prefer

### Chapter 5 Discounted Cash Flow Valuation

Chapter Discounted Cash Flow Valuation Compounding Periods Other Than Annual Let s examine monthly compounding problems. Future Value Suppose you invest \$9,000 today and get an interest rate of 9 percent

### 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

### FNCE 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

### FINANCIAL CALCULATIONS

FINANCIAL CALCULATIONS 1 Main function is to calculate payments, determine interest rates and to solve for the present or future value of a loan or an annuity 5 common keys on financial calculators: N

### HOW TO CALCULATE PRESENT VALUES

Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGraw-Hill/Irwin Copyright 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

### Chapter 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)

### Time Value of Money. Background

Time Value of Money (Text reference: Chapter 4) Topics Background One period case - single cash flow Multi-period case - single cash flow Multi-period case - compounding periods Multi-period case - multiple

### How 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

### You 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

### 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

### 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

### 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

### The values in the TVM Solver are quantities involved in compound interest and annuities.

Texas Instruments Graphing Calculators have a built in app that may be used to compute quantities involved in compound interest, annuities, and amortization. For the examples below, we ll utilize the screens

### The Interest Rate: A loan, expressed as a percentage of the amount loaned per year.

Interest Rates Time Value of Money The Interest Rate Simple Interest Amortizing a Loan The Interest Rate: A loan, expressed as a percentage of the amount loaned per year. Interest rate is the "price" of