# FINANCIAL CALCULATIONS

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 number of periods I periodic interest rate PV present value PMT payment FV Future value These are all at the top row of the HB10bII and HB10bII+ calculator 2 Determine which variable you would like to solve for. You will need four out of the five variables to start, keeping in mind that PMT, PV or FV may be zero Know when to use zero PMT invest a lump sum or owe all of your money at the end of the term PV when you are receiving or making payments FV when a loan or annuity is paid off finished paying out 3 1

2 Keep in mind that the number of periods is usually listed in the same increment as the interest rate, i.e a 30 year mortgage bond would have 360 periods (30 years) If you are uncertain, always use Shift N function. 4 Annually 1 NACA Semi Annually 2 NACSA Quarterly 4 NACQ Monthly 12 NACM Daily 365 NACD 5 Number of periods per year Number of decimals used Begin/end mode Always clear the calculator (Shift C All) before you start any calculation Always practice your calculations well Watch these YouTube training videos:

3 Mrs.BassonwantstotakeherfamilytoDisneyWorld10yearsfromnow. The travel agent has estimated that such a trip would currently cost R150,000.Inflationisexpectedtoaverage8%peryearoverthenext10 years. Mrs. Basson has the following investments available to fund this trip: R20000inasavingsaccount,investedataneffectiverateof7%p.a. AnendowmentpolicywithacurrentvalueofR10000.Mrs.Basson investsalevelamountofr1000permonthintothispolicy.thepolicy willmatureoneyearbeforetheplannedtripandshehasindicated that she will merely reinvest the maturity value for another year without making any further payments. The expected growth rate in this portfolio is 9% per annum, compounded monthly. Mrs.Bassonwouldliketoknowhowmuchshehastoinvestperannumin ordertoensurethatshewouldhaveenoughmoneyfortheholiday,taking into account her current investments earmarked for this purpose. She indicates that she can escalate her annual investment by 5% per year, and thatshebelievesthatanewinvestmentcangrowataneffectiverateof 9% per year. Calculate the annual investment required to make up the shortfall. 7 Brackets Others (indices and integers) Division Multiplication Addition Subtraction Multiplication and division are performed whichever comes first from left to right Addition and subtraction are performed whichever comes first from left to right 8 A number that is anything from 0 to 1 Therefore a fraction is less than 1, but greater than 0 ¼ 1 divide by 4 (Long Division) 9 3

4 2/10 6/10 55/100 73/80 60/ / or rdg Converting a fraction to a percentage requires multiplying by 100/1 Therefore: x = = 25% 11 Examples: 32/50 75/100 12/71 25/ /200 64% 75% 16.91% 25% 60% 12 4

5 Bob invests R2,000 at 10%p.a. simple interest for 4 years Amortisation table Year Start 2000 Interest Year End 13 Bob invests R2,000 at 10%p.a. simple interest for 4 years Year Start Intere st Year End Bob invests R2,000 at 10%p.a. simple interest for 4 years Therefore: 2000 X 10% = x 4 yrs = = 2800 Year Start Interest Year End

6 For how many years does one have to invest a lump sum of R at 15% pa simple interest in order to receive R at the end of the term? 16 26,600 10,000 = 16,600 15% of 10,000 = 1,500 simple interest per year. 16,600 / 1,500 = (26,600 10,000) / 1,500 = years 10 15% pa annum = R Capital invested = Growth = x years = R R = R Bob Invests R2,000 at 10% p.a. compounding annually for 4 Years 2000 x (1+0.1) = 2200 x 1.1 = 2420 x 1.1 = 2662 x 1.1 = Year Start Int End

7 Bob Invests R2,000 at 10% p.a. compounding Monthly for 1 Year x (1+(0.1/12)) = 2000 x (1+(0.0083)) = x = x = x = Therefore: 2000 x (1.0083) 4 = x (1.0083) 12 = PV x (1 + (I/PY / P/YR) N = FV Future Value = Present Value x (1 + (Int rate / Comp Periods per year)) Power of Total Compounding periods 20 N = TOTAL number of compounding periods in the calculation. I/YR = Nominal per annum interest / growth rate applicable PV = Present Value PMT = Any Regular payment (same as periods per year) 2 nd F P/YR= Number of compounding periods in 1 Year. FV = Future Value PV x (1 + (I/PY / P/YR) N = FV 21 7

8 Nominal interest rate Simply the stated interest rate of a given bond, loan or investment E.g. if nominal rate on a loan is 5%, then borrowers can expect to pay R5 on every R100 loaned to them Effective interest rate Take the power of compounding into consideration The difference between nominal and effective rates increases with the number of compounding periods within a specific time period 22 A Bank advises you can earn 15% pa on a one year fixed deposit interest accumulates once a year: Capital Invested R 100 Plus interest R 15 Nominal and effective the same as there is no interest on interest. 23 A Bank advises you can earn 15% pa on a one year fixed deposit interest accumulates monthly: Capital invested R100 Plus interest R P/YR 15 Shift Nom % Shift EFF% = 16.08% 24 8

9 R1000 invested over a 5 year period with growth at 10%. What will I get at the end? 25 Billy wins the lotto and invest the money for 10 years at an interest rate of 11% per annum. After the 10 years he receives R What is the capital sum that Billy invested?

10 If I invest R1000 a month for the next 5 years at 10%, what will the maturity value be? 28 Mr P invested R years ago and receives R now. What is the rate of return on the investment? Show all steps

11 Elizabeth invests a lump sum amount of R for a period of 5 years. The interest rate is 6.5% per annum which will be credited to the account on a monthly basis. Ignore income tax. At the end of the term she will receive an amount of? Mr A invests R550 at the beginning of each month for 10 years. What is the maturity value if the investment has an 8% effective interest rate? [3] 33 11

12 34 Tish signed an investment contract where she will invest R a further R1000 pa at beginning of each year for next 5 years at 12% interest: Maturity value will be? 35 Alma buys a house & takes a bond of R at an interest rate of 12% for 20 years calculate monthly instalment: 36 12

13 Mr N s investment receives an annuity income of R pa in advance for 15 years as well as R at the end of the term. The interest rate is 10% calculated in advance. How much did Mr N invest initially? [4] Bond of R at an interest rate of 11% and term is 20 yrs. Calculate the monthly instalment: End Mode 12 Shift P/YR PV 11 I/YR 20 Shift N PMT? DO NOT CLEAR THE CALCULATOR!! 39 13

14 SHIFT AMORT PRESS = prin - capital amount paid ( ) = int - interest portion paid ( ) = bal balance ( INPUT 24 Shift Amort Capital = R Interest = R Balance = R At beg of year 3 rates increase to 12% a) what is new monthly instalments? b) what is the balance at end of year 2? End Mode 12 Shift P/YR PV 12 I/YR 18 Shift N (remaining years) PMT? -R What if after 2 yrs bond holder wants to reduce term by 2 yrs? Use same example as above Answer? 42 14

15 43 Mr Nkosi has a mortgage bond of R repayable over 20 years at an interest rate of 13% 1.1 Calculate monthly repayments [2] 1.2 The interest rate drops from 13% to 11% at the beg of the 2 nd year. Mr Nkosi elects not to reduce his monthly payments. Calculate how long it will now take Mr Nkosi to repay his bond? [4]

16 46 Frans buys a new car for R He pays a deposit of R and takes a loan from the bank for the balance for a period of 3 years. His monthly instalment is R What is the percentage interest that he pays on the loan?

17 Scenario Annual premium pd to an investment must increase each year by 7% and the investment s growth is 10% Can we account for 2 growth factors? Only 1 I/YR key no escalation key. Can t add them together! ie can t do a FV calc. Can deduct and get a net effect and thereby do an equivalent PV calc 49 Brad wants to invest 100 per year, escalating at 7% p.a. for 3 years. Growth on the investment is 10% 50 PV FV % for 3 yrs 10% for 2 yrs % for 1 yr 51 17

18 Incorporates both interest and escalation rate: I = interest or growth rate E = escalation Alternative method: Interest 12% Escalation rate 10% / 1,10 = 1,81818% = resultant rate NB: I AM BEFORE E IS 52 PMT PV Resultant Rate Interest Rate PV FV 53 Brad invests R100 pa at the beginning of each year, escalating at 7% pa for 5 years at an interest of 9%. What is the FV? 54 18

19 12mth pmt PMT PV Nominal (Eff Rate) Nominal Interest Resultant Interest Rate Rate Rate 12 P/YR Or 1/py with eff rate PV of annual PV of FV of Payment escalating invest annuity itself! 55 Mr J wants to invest R2 500 pm for the next 5 years at an interest rate of 7.5% and wants to increase his premiums by 6% every year. How much will he receive after 5 years if he invests the R2 500 at the beg of each month? [6] 56 Step 1: Calculate PV of the annual contributions 57 19

20 Step 2 calculate resultant rate Step 3 calculate PV of the escalating annual investment 58 Step 4 Calculate the FV of the investment using the interest rate 59 Ann wants to invest R100 per month for 5 years. This monthly investment must increase by 6% per annum. The investment will earn 8%. What will the future value of this monthly investment be? We want to know the FV of an investment if we are investing MONTHLY

21 Step 1 determine the annual equivalent iro the monthly instalments discounted at the nominal rate. 61 Step 2 change to effective rate and calculate resultant rate. Resultant rate 62 Step 3 discount the annual equivalent to PV using resultant rate

22 Step 4 calculate the FV of the instalment using the nominal rate. 64 Tom pays out an amount of R and receives monthly payments of R3000, R6000, R6000, R22000 and R15000 Calculate internal rate of return If discounted at 12% what will the net present value be?

23 Calculate NPV if discounted at 12% 67 Your client has been making uneven adhoc contributions into her investment for the past year. Contributions made as follows: March R1000 April R2000 June R1750 September R350 October R900 December R175 January R1000 February R 250 The current value is R8 587 Calculate the annual rate of return, assuming the fund compounds monthly:

24 Mr Nel has just taken cession of a life assurance contract. The policy is due to mature in 4 years time. Premiums of R750 pa are payable towards the policy. The estimated maturity value of the policy in 4 years time is R The growth rate is assumed to be 10%. What is the PV of this policy? Mrs Waterman invests R The nominal rate of interest is 10% and the interest is compounded half-annually. What is her FV after 2 years? 72 24

25 73 Mrs Van Wyk wants to invest R500 at the beginning of each year for 10 years. The interest payable on this investment will be 15% What will the future value of this investment be? Still using the same figures above, how much capital would she need to buy an annuity of R 500 per annum payable at beg of each year- for 10 years, if the life assurer pays 15% on her investment? What is the FV if we take the result from the previous calculation if she invests a lump sum of R for 10 years at 15% 74 FV of the investment will be: 75 25

26 Capital needed to buy an annuity? 76 FV OF R2886? 77 Mr Verwey wants to invest R800 pm for the next 5 years at an interest rate of 8% and wants to increase his premiums by 5% every year. How much will he receive after 5 years if he invests the R800 at the beginning of each month? 78 26

27 STEP 1 PV OF ANNUAL CONTRIBUTIONS 79 STEP 2 CALCULATE RESULTANT RATE 80 STEP 3 PV OF ESCALATING PAYMENTS 81 27

28 STEP 4 CALCULATE FV 82 Susan has R in a fixed deposit which earns interest of 15%. The inflation rate is 6%. Sue s marginal tax rate is 40%. What effect will this have on her real rate of return?

29 Mpho owns a house. The interest she pays on the bond is 12%. She won R from the lotto. Her marginal tax rate is 40% What taxable rate of interest must she earn on the R to equal the 12% interest rate she is paying on her bond? Mr Greedy would like to double his inheritance of R within 5 years by speculation on the stock market. He is aware that he will have to give up approximately 40% to tax annually. Calculate the annual pre-tax yield rate he will have to achieve in order to reach his goal

30 88 Mr R needs R in 5 years time. He will invest by way of annual installments. He will start with an amount Of R8 500 and then increase the Installment by a fixed %. He will earn interest at 7.5% pa. Calculate the % by which he has to increase his installments every year? 89 STEP 1 - WHAT IS THE PV OF WHAT I WANT? 90 30

31 STEP 2 DETERMINE THE RESULTANT RATE 91 STEP 3 CALCULATE ESCALATION RATE 92 Calculation of Retirement Needs: Mr G who is currently 45 years of age would like to retire at the age of 65. His current salary is R pa and he will be happy to receive 75% of his salary. He believes that his salary will increase with 8% pa. What is the first year s income that he will need at the age of 65? 93 31

32 94 Mr G would like this income (75% of his salary ) for at least until his age of 85 but the income he receives must be increased by 6% every year. The capital will be invested and will attract 8% growth. How much Capital will Mr G need to have at the age of 65 to address his needs?

33 Mr G is very concerned as he will under no circumstances have this type of money! He would like to know: - with an investment growth of 12%. a) How much does he have to invest annually assuming it will be a level premium? b) What if he decides to increase the premium by 10% every year? 97 Level Annual Investment Amount 98 Step 1 Equivalent Lump Sum (PV) 99 33

34 Step 2 Discounted PMT at Esc 10% 100 Mrs.BassonwantstotakeherfamilytoDisneyWorld10yearsfromnow. The travel agent has estimated that such a trip would currently cost R150,000.Inflationisexpectedtoaverage8%peryearoverthenext10 years. Mrs. Basson has the following investments available to fund this trip: R20000inasavingsaccount,investedataneffectiverateof7% p.a. AnendowmentpolicywithacurrentvalueofR10000.Mrs.Basson investsalevelamountofr1000permonthintothispolicy.thepolicy willmatureoneyearbeforetheplannedtripandshehasindicated that she will merely reinvest the maturity value for another year without making any further payments. The expected growth rate in this portfolio is 9% per annum, compounded monthly. Mrs.Bassonwouldliketoknowhowmuchshehastoinvestperannumin ordertoensurethatshewouldhaveenoughmoneyfortheholiday,taking into account her current investments earmarked for this purpose. She indicates that she can escalate her annual investment by 5% per year, and thatshebelievesthatanewinvestmentcangrowataneffectiverateof 9% per year. Calculate the annual investment required to make up the shortfall. 101 Need Provision Surplus / Shortfall

35

36

37 Step 2 Equivalent escalating annual cash flow for PV Lump Sum Mr Makhensa, born 20 January Wants to receive a monthly income of at least R35,000 (after tax 40%) in today s value, when he retires at the age of 60. The monthly income should last for 25 years from the date of retirement and escalate by the rate of inflation per annum. (Given as 6% currently) His Current retirement savings only consist of a pension preservation fund at R350,000 current value. Growth on all investments 10%

38 Q Calculate the capital required at retirement to meet Makhensa s retirement goals. (5) Calculate the capital available at retirement (2) Calculate the shortfall at retirement. (2) Calculate the increasing monthly investment that Makhensa should make/save at the beginning of each month, in his retirement annuity fund to make up for the shortfall. He wants to increase the premium at 6% p.a. (3) 112 Calculate the pre-tax income required monthly Then grow from now to retirement (30 years) 113 Effective rate for monthly conversion to annual Resultant rate (use effective)

39

40 118 Step 1 convert shortfall to current day equivalent lump sum (Monthly, so use Nominal rate and 12 P/YR) 119 Step 2 convert current lump sum value needed to an equivalent annual escalating premium

41 Step 3 convert first year s annual premium to an equivalent monthly premium

### CARMEN VENTER COPYRIGHT www.futurefinance.co.za 0828807192 1

Carmen Venter CFP WORKSHOPS FINANCIAL CALCULATIONS presented by Geoff Brittain Q 5.3.1 Calculate the capital required at retirement to meet Makhensa s retirement goals. (5) 5.3.2 Calculate the capital

### 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

### 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

### 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

### 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.

### 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

### 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

### 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,

### 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

### E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is

E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =

### 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

### 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

### 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

### 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 Present Value

Chapter 3 Present Value MULTIPLE CHOICE 1. Which of the following cannot be calculated? a. Present value of an annuity. b. Future value of an annuity. c. Present value of a perpetuity. d. Future value

### 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

### 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

### 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 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

### 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

### 3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction.

Spring 2012 Finance 3130 Sample Exam 1A Questions for Review 1. The form of organization for a business is an important issue, as this decision has very significant effect on the income and wealth of the

### 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

### Excel Financial Functions

Excel Financial Functions PV() Effect() Nominal() FV() PMT() Payment Amortization Table Payment Array Table NPer() Rate() NPV() IRR() MIRR() Yield() Price() Accrint() Future Value How much will your money

### 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

### 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

### 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

### Learning Objectives. Learning Objectives. Learning Objectives. Principles Used in this Chapter. Simple Interest. Principle 2:

Learning Objectives Chapter 5 The Time Value of Money Explain the mechanics of compounding, which is how money grows over a time when it is invested. Be able to move money through time using time value

### 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

### 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

### 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

### Statistical Models for Forecasting and Planning

Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information

### Value of Money Concept\$

Value of Money Concept\$ Time, not timing is the key to investing 2 Introduction Time Value of Money Application of TVM in financial planning : - determine capital needs for retirement plan - determine

### 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

### MAT116 Project 2 Chapters 8 & 9

MAT116 Project 2 Chapters 8 & 9 1 8-1: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the

### 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

### 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

### 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

### Practice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.

PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor

### Math 120 Basic finance percent problems from prior courses (amount = % X base)

Math 120 Basic finance percent problems from prior courses (amount = % X base) 1) Given a sales tax rate of 8%, a) find the tax on an item priced at \$250, b) find the total amount due (which includes both

### 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

### 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)

### 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

### 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

### 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

### 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

### 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.

### Exercise 1 for Time Value of Money

Exercise 1 for Time Value of Money MULTIPLE CHOICE 1. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing

### 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

### 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

### Compounding Quarterly, Monthly, and Daily

126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,

### 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

### 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

### 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.

### 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

### 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

### 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,

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 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,

### 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

### 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

### 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:

### 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

### Present Value and Annuities. Chapter 3 Cont d

Present Value and Annuities Chapter 3 Cont d Present Value Helps us answer the question: What s the value in today s dollars of a sum of money to be received in the future? It lets us strip away the effects

### 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

### 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. 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

### 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.

### The Institute of Chartered Accountants of India

CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY- APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able

### 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

### Section 8.1. I. Percent per hundred

1 Section 8.1 I. Percent per hundred a. Fractions to Percents: 1. Write the fraction as an improper fraction 2. Divide the numerator by the denominator 3. Multiply by 100 (Move the decimal two times Right)

### 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

### 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

### Solutions Manual. Corporate Finance. Ross, Westerfield, and Jaffe 9 th edition

Solutions Manual Corporate Finance Ross, Westerfield, and Jaffe 9 th edition 1 CHAPTER 1 INTRODUCTION TO CORPORATE FINANCE Answers to Concept Questions 1. In the corporate form of ownership, the shareholders

### 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

### hp calculators HP 20b Time value of money basics The time value of money The time value of money application Special settings

The time value of money The time value of money application Special settings Clearing the time value of money registers Begin / End mode Periods per year Cash flow diagrams and sign conventions Practice

### SUPPLEMENTARY NOTES. For examination purposes, the following amendments shall take effect from 3 June 2011: 1. Chapter 12, Page 329, Chapter Outline

SUPPLEMENTARY NOTES ChFC01 Fundamentals Of Financial Planning And Investments Date Of Issue : 3 May 2011 [Applicable to 1 st Edition (2003), Re-printed March 2006 version and earlier] The following amendments

### 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.

### Appendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition

C- 1 Time Value of Money C- 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future

### 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

### Purpose EL-773A HP-10B BA-II PLUS Clear memory 0 n registers

D-How to Use a Financial Calculator* Most personal finance decisions involve calculations of the time value of money. Three methods are used to compute this value: time value of money tables (such as those

### Time Value of Money. Nature of Interest. appendix. study objectives

2918T_appC_C01-C20.qxd 8/28/08 9:57 PM Page C-1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.

### 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)

### Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of

### Time Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)

Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for

### 300 Chapter 5 Finance

300 Chapter 5 Finance 17. House Mortgage A couple wish to purchase a house for \$200,000 with a down payment of \$40,000. They can amortize the balance either at 8% for 20 years or at 9% for 25 years. Which

### PowerPoint. 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

### INSTITUTE OF ACTUARIES OF INDIA

INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 15 th November 2010 Subject CT1 Financial Mathematics Time allowed: Three Hours (15.00 18.00 Hrs) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1. Please

### Time Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology

Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations

### 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.

### FI 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

### Hewlett Packard (HP) 10BII

Hewlett Packard (HP) 10BII The HP10BII is programmed to perform two basic types of operations: statistical operations and financial operations. Various types of computations are activated by depressing

### 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

FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin-534/fin-534-week-4-quiz-3- str/ For more course tutorials visit www.tutorialoutlet.com Which of the following

### Financial Math on Spreadsheet and Calculator Version 4.0

Financial Math on Spreadsheet and Calculator Version 4.0 2002 Kent L. Womack and Andrew Brownell Tuck School of Business Dartmouth College Table of Contents INTRODUCTION...1 PERFORMING TVM CALCULATIONS

### 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

### FIN 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

### Sample problems from Chapter 10.1

Sample problems from Chapter 10.1 This is the annuities sinking funds formula. This formula is used in most cases for annuities. The payments for this formula are made at the end of a period. Your book

### TIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!

TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest \$1,000 it becomes \$1,050 \$1,000 return of \$50 return on Factors to consider when assessing Return on

### Finance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization

CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need