# The Time Value of Money

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 The Time Value of Money 1

2 Learning Objectives The time value of money and its importance to business. The future value and present value of a single amount. The future value and present value of an annuity. The present value of a series of uneven cash flows. 2

3 The Time Value of Money Money grows over time when it earns interest. Therefore, money that is to be received at some time in the future is worth less than the same dollar amount to be received today. Similarly, a debt of a given amount to be paid in the future are less burdensome than that debt to be paid now. 3

4 The Future Value of a Single Amount Suppose that you have \$100 today and plan to put it in a bank account that earns 8% per year. How much will you have after 1 year? 5 years? 15 years? After one year: \$100 + (.08 x \$100) = \$100 + \$8 = \$108 OR: \$100 x (1.08) 1 = \$108 4

5 The Future Value of a Single Amount Suppose that you have \$100 today and plan to put it in a bank account that earns 8% per year. How much will you have after 1 year? 5? 15? After one year: \$100 x (1.08) 1 = \$108 After five years: \$100 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 = \$100 x (1.08) 5 = \$ After fifteen years: Equation: \$100 x (1.08) 15 = \$ FV = PV (1 + k) n 5

6 The Future Value of a Single Amount Graphical Presentation Different Interest Rates \$ k = 8% k = 4% k = 0% Year 6

7 Present Value of a Single Amount Value today of an amount to be received or paid in the future. PV = FV n x 1 (1 + k) n Example: Expect to receive \$100 in one year. If can invest at 10%, what is it worth today? PV = (1.10) 1= \$100 7

8 Present Value of a Single Amount Value today of an amount to be received or paid in the future. PV = FV n x 1 (1 + k) n Example: Expect to receive \$100 in EIGHT years. If can invest at 10%, what is it worth today? PV = 100 (1+.10) 8 = \$100 8

9 Present Value of a Single Amount Graphical Presentation \$ k = 0% k = 5% k = 10% Year 9

10 Financial Calculator Solution - PV Previous Example: Expect to receive \$100 in EIGHT Using Formula: years. If can invest at 10%, what is it worth PV = 100 today? (1+.10) 8 = Calculator Enter: N = 8 I/YR = 10 FV = 100 CPT PV =? N I/YR PV PMT FV 8 10?

11 Financial Calculator Solution - FV Previous Example: You invest \$200 at 10%. How much is it worth after 5 years? Using Formula: FV = \$200 (1.10) 5 = \$

12 Financial Calculator Solution - FV Previous Example: Previous Example: You invest \$200 at 10%. How much is it worth after 5 years? Using Formula: FV = \$200 (1.10) 5 = \$ Calculator Enter: N = 5 I/YR = 10 PV = -200 CPT FV =? N I/YR PV PMT FV ?

13 Annuities An annuity is a series of equal cash flows spaced evenly over time. For example, you pay your landlord an annuity since your rent is the same amount, paid on the same day of the month for the entire year. Jan Feb Mar Dec \$500 \$500 \$500 \$500 \$500 13

14 Future Value of an Annuity \$0 \$100 \$100 \$100 You deposit \$100 each year (end of year) into a savings account. How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? 14

15 Future Value of an Annuity \$0 \$100 \$100 \$100 \$100(1.08) 2 \$100(1.08) 1 \$100(1.08) 0 \$ \$ \$ \$ You deposit \$100 each year (end of year) into a savings account. How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? 15

16 Future Value of an Annuity \$0 \$100 \$100 \$100 \$100(1.08) 2 \$100(1.08) 1 \$100(1.08) 0 \$ \$ \$ \$ How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? n = 100 ( (1+.08) 3-1) FVA = PMTx( (1+k) - 1 ).08 k = 100(3.2464) =

17 Future Value of an Annuity Calculator Solution \$0 \$100 \$100 \$100 Enter: N = 3 I/YR = 8 PMT = -100 CPT FV =? N I/YR PV PMT FV ? 17

18 Present Value of an Annuity How much would the following cash flows be worth to you today if you could earn 8% on your deposits? \$0 \$100 \$100 \$100 18

19 Present Value of an Annuity How much would the following cash flows be worth to you today if you could earn 8% on your deposits? \$100/(1.08) 1 \$100 / (1.08) 2 \$100 / (1.08) \$0 \$100 \$100 \$100 \$92.60 \$85.73 \$79.38 \$

20 Present Value of an Annuity How much would the following cash flows be worth to you today if you could earn 8% on your deposits? \$0 \$100 \$100 \$100 \$92.60 \$85.73 \$79.38 \$ PVA = PMTx( ) \$100/(1.08) 1 \$100 / (1.08) 2 \$100 / (1.08) (1+k) n k = (1.08) 3.08 ( ) = 100(2.5771) =

21 Present Value of an Annuity Calculator Solution \$0 \$100 \$100 \$100 PV=? Enter: N = 3 I/YR = 8 PMT = 100 CPT PV =? N I/YR PV PMT FV 3 8?

22 Annuities An annuity is a series of equal cash payments spaced evenly over time. Ordinary Annuity: The cash payments occur at the END of each time period. Annuity Due: The cash payments occur at the BEGINNING of each time period. 22

23 Future Value of an Annuity Due \$100 \$100 \$100 FVA=? You deposit \$100 each year (beginning of year) into a savings account. How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? 23

24 Future Value of an Annuity Due \$100 \$100 \$100 \$100(1.08) 2 \$100(1.08) 1 \$100(1.08) 3 \$108 \$ \$ \$ You deposit \$100 each year (beginning of year) into a savings account. How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? 24

25 Future Value of an Annuity Due \$100 \$100 \$100 \$100(1.08) 2 \$100(1.08) 1 \$100(1.08) 3 \$108 \$ \$ \$ How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? FVA = PMTx( (1+k) n -1 )(1+k) k (1+.08) 3-1 = 100 ( ) (1.08).08 =100(3.2464)(1.08)=

26 Present Value of an Annuity Due How much would the following cash flows be worth to you today if you could earn 8% on your deposits? \$100 \$100 \$100 PV=? 26

27 Present Value of an Annuity Due How much would the following cash flows be worth to you today if you could earn 8% on your deposits? \$100 \$100 \$100 \$100/(1.08) 0 \$100/(1.08) 1 \$100 / (1.08) 2 \$ \$92.60 \$85.73 \$

28 Present Value of an Annuity Due How much would the following cash flows be worth to you today if you could earn 8% on your deposits? \$100 \$100 \$100 \$100/(1.08) 0 \$100/(1.08) 1 \$100 / (1.08) 2 \$ \$92.60 \$85.73 \$ (1+k) PVA = PMTx( n )(1+k) k = 100( (1.08) 3 )(1.08).08 = 100(2.5771)(1.08) =

29 Amortized Loans A loan that is paid off in equal amounts that include principal as well as interest. Solving for loan payments. 29

30 Amortized Loans You borrow \$5,000 from your parents to purchase a used car. You agree to make payments at the end of each year for the next 5 years. If the interest rate on this loan is 6%, how much is your annual payment? \$5,000 \$? \$? \$? \$? \$? ENTER: N = 5 I/YR = 6 PV = 5,000 CPT PMT =? 1, N I/YR PV PMT FV 5 6 5,000? 30

31 Amortized Loans You borrow \$20,000 from the bank to purchase a used car. You agree to make payments at the end of each month for the next 4 years. If the annual interest rate on this loan is 9%, how much is your monthly payment? 1 - (1+k) PVA = PMTx( n ) k (1.0075) 48 \$20,000 = PMT ( ).0075 \$20,000 = PMT( ) PMT =

32 Amortized Loans You borrow \$20,000 from the bank to purchase a used car. You agree to make payments at the end of each month for the next 4 years. If the annual interest rate on this loan is 9%, how much is your monthly payment? ENTER: N = 48 I/YR =.75 PV = 20,000 CPT PMT =? Note: N = 4 * 12 = 48 I/YR = 9/12 = N I/YR PV PMT FV ,000? 32

33 Perpetuities A perpetuity is a series of equal payments at equal time intervals (an annuity) that will be received into infinity. PVP = PMT k 33

34 Perpetuities A perpetuity is a series of equal payments at equal time intervals (an annuity) that will be received into infinity. Example: A share of preferred stock pays a constant dividend of \$5 per year. What is the present value if k =8%? PVP = PMT k 34

35 Perpetuities A perpetuity is a series of equal payments at equal time intervals (an annuity) that will be received into infinity. Example: A share of preferred stock pays a constant dividend of \$5 per year. What is the present value if k =8%? PVP = PMT k If k = 8%: PVP = \$5/.08 = \$

36 Solving for k Example: A \$200 investment has grown to \$230 over two years. What is the ANNUAL return on this investment? \$200 \$230 FV = PV(1+ k) n 230 = 200(1+ k) = (1+ k) = (1+ k) = 1+ k k =.0724 = 7.24% 36

37 Solving for k - Calculator Solution Example: A \$200 investment has grown to \$230 over two years. What is the ANNUAL return on this investment? Enter known values: N = 2 I/YR =? PV = -200 FV = 230 Solve for: PMT. =? N I/YR PV PMT FV ?

38 Compounding more than Once per Year \$500 invested at 9% annual interest for 2 years. Compute FV. \$500(1.09) 2 = \$ Annual \$500(1.045) 4 = \$ Semi-annual \$500(1.0225) 8 = \$ Quarterly \$500(1.0075) 24 = \$ Monthly \$500( ) 730 = \$ Daily Compounding Frequency 38

39 Continuous Compounding Compounding frequency is infinitely large. Compounding period is infinitely small. Example: \$500 invested at 9% annual interest for 2 years with continuous compounding. FV = PV x e kn FV = \$500 x e.09 x 2 = \$

### Chapter 4. Time Value of Money

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

### 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 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

### 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 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

### 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 4 Time Value of Money

Chapter 4 Time Value of Money Solutions to Problems P4-1. LG 1: Using a Time Line Basic (a), (b), and (c) Compounding Future Value \$25,000 \$3,000 \$6,000 \$6,000 \$10,000 \$8,000 \$7,000 > 0 1 2 3 4 5 6 End

### 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

### 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

### THE TIME VALUE OF MONEY

QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost

### 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:

### 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

### 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

### 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

### 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

### 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

### 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

### Chapter 5 Time Value of Money

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 of Cash Flows 7. Other Compounding

### 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

### 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

### TIME VALUE OF MONEY PROBLEM #7: MORTGAGE AMORTIZATION

TIME VALUE OF MONEY PROBLEM #7: MORTGAGE AMORTIZATION Professor Peter Harris Mathematics by Sharon Petrushka Introduction This problem will focus on calculating mortgage payments. Knowledge of Time Value

### 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.

### 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

### International Financial Strategies Time Value of Money

International Financial Strategies 1 Future Value and Compounding Future value = cash value of the investment at some point in the future Investing for single period: FV. Future Value PV. Present Value

### 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

### 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

### 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

### Lesson TVM-10-040-xx Present Value Ordinary Annuity Clip 01

- - - - - - Cover Page - - - - - - Lesson TVM-10-040-xx Present Value Ordinary Annuity Clip 01 This workbook contains notes and worksheets to accompany the corresponding video lesson available online at:

### LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.

LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely

### 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

### 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

### 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 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

### Time Value of Money Practice Questions Irfanullah.co

1. You are trying to estimate the required rate of return for a particular investment. Which of the following premiums are you least likely to consider? A. Inflation premium B. Maturity premium C. Nominal

### 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

### 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

### Future Value of an Annuity Sinking Fund. MATH 1003 Calculus and Linear Algebra (Lecture 3)

MATH 1003 Calculus and Linear Algebra (Lecture 3) Future Value of an Annuity Definition An annuity is a sequence of equal periodic payments. We call it an ordinary annuity if the payments are made at the

### Chapter The Time Value of Money

Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest

### 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 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest \$1,000 at 6% simple interest for 3 years.

6-1 Chapter 6 Time Value of Money Concepts 6-2 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in

### Finance 331 Corporate Financial Management Week 1 Week 3 Note: For formulas, a Texas Instruments BAII Plus calculator was used.

Chapter 1 Finance 331 What is finance? - Finance has to do with decisions about money and/or cash flows. These decisions have to do with money being raised or used. General parts of finance include: -

### 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.

### 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

### 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

### first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest.

ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular

### 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

### 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

### 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

### 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

### Review Solutions FV = 4000*(1+.08/4) 5 = \$4416.32

Review Solutions 1. Planning to use the money to finish your last year in school, you deposit \$4,000 into a savings account with a quoted annual interest rate (APR) of 8% and quarterly compounding. Fifteen

### 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

### 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 3 Mathematics of Finance

Chapter 3 Mathematics of Finance Section 3 Future Value of an Annuity; Sinking Funds Learning Objectives for Section 3.3 Future Value of an Annuity; Sinking Funds The student will be able to compute the

### A = P (1 + r / n) n t

Finance Formulas for College Algebra (LCU - Fall 2013) ---------------------------------------------------------------------------------------------------------------------------------- Formula 1: Amount

### MHSA 8630 -- Healthcare Financial Management Time Value of Money Analysis

MHSA 8630 -- Healthcare Financial Management Time Value of Money Analysis ** One of the most fundamental tenets of financial management relates to the time value of money. The old adage that a dollar in

### With compound interest you earn an additional \$128.89 (\$1628.89 - \$1500).

Compound Interest Interest is the amount you receive for lending money (making an investment) or the fee you pay for borrowing money. Compound interest is interest that is calculated using both the principle

### 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

### 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

### ANNUITIES. Ordinary Simple Annuities

An annuity is a series of payments or withdrawals. ANNUITIES An Annuity can be either Simple or General Simple Annuities - Compounding periods and payment periods coincide. General Annuities - Compounding

### TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY

TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction In this assignment we will discuss how to calculate the Present Value

### Chapter 8. 48 Financial Planning Handbook PDP

Chapter 8 48 Financial Planning Handbook PDP The Financial Planner's Toolkit As a financial planner, you will be doing a lot of mathematical calculations for your clients. Doing these calculations for

### 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

### Solutions to Time value of money practice problems

Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if \$2,500 is deposited today and the account earns 4% interest,

### 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

### NPV calculation. Academic Resource Center

NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year

### The time value of money: Part II

The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods

### Topics Covered. Compounding and Discounting Single Sums. Ch. 4 - The Time Value of Money. The Time Value of Money

Ch. 4 - The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate For now, we will omit the section 4.5 on inflation

### 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

### 5.1 Simple and Compound Interest

5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?

### 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)

### APPENDIX. Interest Concepts of Future and Present Value. Concept of Interest TIME VALUE OF MONEY BASIC INTEREST CONCEPTS

CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists

### 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

### Important Financial Concepts

Part 2 Important Financial Concepts Chapter 4 Time Value of Money Chapter 5 Risk and Return Chapter 6 Interest Rates and Bond Valuation Chapter 7 Stock Valuation 130 LG1 LG2 LG3 LG4 LG5 LG6 Chapter 4 Time

### 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 1

Time Value of Money 1 This topic introduces you to the analysis of trade-offs over time. Financial decisions involve costs and benefits that are spread over time. Financial decision makers in households

### The Time Value of Money Part 2B Present Value of Annuities

Management 3 Quantitative Methods The Time Value of Money Part 2B Present Value of Annuities Revised 2/18/15 New Scenario We can trade a single sum of money today, a (PV) in return for a series of periodic

### 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

### 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

### Exercise 6 8. Exercise 6 12 PVA = \$5,000 x 4.35526* = \$21,776

CHAPTER 6: EXERCISES Exercise 6 2 1. FV = \$10,000 (2.65330 * ) = \$26,533 * Future value of \$1: n = 20, i = 5% (from Table 1) 2. FV = \$10,000 (1.80611 * ) = \$18,061 * Future value of \$1: n = 20, i = 3%

### 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

### Applying Time Value Concepts

Applying Time Value Concepts C H A P T E R 3 based on the value of two packs of cigarettes per day and a modest rate of return? Let s assume that Lou will save an amount equivalent to the cost of two packs

### 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

### ICASL - Business School Programme

ICASL - Business School Programme Quantitative Techniques for Business (Module 3) Financial Mathematics TUTORIAL 2A This chapter deals with problems related to investing money or capital in a business

### 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,

### 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

### APPENDIX 3 TIME VALUE OF MONEY. Time Lines and Notation. The Intuitive Basis for Present Value

1 2 TIME VALUE OF MONEY APPENDIX 3 The simplest tools in finance are often the most powerful. Present value is a concept that is intuitively appealing, simple to compute, and has a wide range of applications.

### 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

### 13-2. Annuities Due. Chapter 13. MH Ryerson

13-2 Annuities Due Chapter 13 13-3 Learning Objectives After completing this chapter, you will be able to: > Calculate the future value and present value of annuities due. > Calculate the payment size,

### Ordinary Annuities Chapter 10

Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate

### 1.3.2015 г. D. Dimov. Year Cash flow 1 \$3,000 2 \$5,000 3 \$4,000 4 \$3,000 5 \$2,000

D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of

### Solutions to Problems

Solutions to Problems P4-1. LG 1: Using a time line Basic a. b. and c. d. Financial managers rely more on present value than future value because they typically make decisions before the start of a project,

### 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

### 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

### 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

### 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

### 9. Time Value of Money 1: Present and Future Value

9. Time Value of Money 1: Present and Future Value Introduction The language of finance has unique terms and concepts that are based on mathematics. It is critical that you understand this language, because

University of Virginia - math1140: Financial Mathematics Fall 2011 Exam 1 7:00-9:00 pm, 26 Sep 2011 Honor Policy. For this exam, you must work alone. No resources may be used during the quiz. The only