# Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1

 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 "Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1"

## Transcription

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 Be able to understand: the difference between the APR and the EAR the difference between ordinary annuity and annuity due 6- Multiple Cash Flows Future Value Example Answer 6. You think that you will be able to deposits 4 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have 7 in the account? How much will you have in three years? In four years? 6- Find the value at year of each cash flow and add them together. Today (year ): FV = 7(.8) = 8,87.98 Year : FV = 4,(.8) = 4,665.6 Year : FV = 4,(.8) = 4, Year : value = 4, Total value in years = =, Value at year 4 =,8.58(.8) =, Multiple Cash Flows FV Example 6. Timeline 6. 7, 4, 4, 4, Suppose you invest \$5 in a mutual (shared, joint) fund today and \$6 in one year. If the fund pays 9% annually, how much will you have in two years? 4, ,

2 Multiple Cash Flows FV Example 6. Answer 6. How much will you have in 5 years if you make no further deposits? First way: FV = 5(.9)5 + 6(.9)4 = 66.6 Second way use value at year : FV = 48.5(.9) = 66.6 A) Suppose you plan to deposit \$ into an account in one year and \$ into the account in the third year. How much will be in the account in five years if the interest rate is 8%? 6-6 B) Suppose you plan to deposit \$ into an account in one year and \$ into the account in the fifth year. How much will be in the account in five years if the interest rate is 8%? 6-7 C) Suppose you plan to deposit \$ into an account in one year and \$ in the next four year. How much will be in the account in five years if the interest rate is 8%? 6-8 Multiple Cash Flows Present Value Example 6.4 You are offered an investment that will pay you \$ in one year, \$4 the next year, \$ 6 the next year, and \$8 at the end of fourth year. You can earn % on very similar investments Timeline

3 Answer 6.4 Timeline 6.4 Find the PV of each cash flows and add them Year CF: / (.) = Year CF: 4 / (.) = 8.88 Year CF: 6 / (.) = 47.7 Year 4 CF: 8 / (.)4 = 58.4 Total PV = = Multiple Cash Flows PV Another Example 6.5 Timeline 6.5 You are considering an investment that will pay you \$ in one year, \$ in two years and \$ in three years. If you want to earn % on your money, how much would you be willing to pay?,,, Answer 6.5 Annuities Annuity: a sequence of equal cash flows, occurring at the end of each period

4 Annuities Basic Formula Examples of Annuities: Annuity equal payments that occur at regular intervals If you buy a bond, you will receive equal coupon interest payments over the life of the bond. If you borrow money to buy a house or a car, you will pay a stream of equal payments. PV A FV A ( r ) t r t ( r ) r 6-9 Annuities and Perpetuities Basic Formula Notice that the calculator solution is slightly different because of rounding errors in the tables. 6- Example 6.6 : Future Value - annuity :If you invest \$, at the end of the next years, at 8%, how much would you have after years? Perpetuity infinite series of equal payments Special case of an annuity arises when the level of stream of CF (month, year etc.) continues forever. PV = A r 6- Example 6.7: Present Value - annuity What is the PV of \$, at the end of each of the next years, if the opportunity cost is 8%? Solution:

5 Annuity Example 6.9 Example 6.8: What should you be willing to pay in order to receive \$, annually forever, if you require 8% per year on the investment? You have determined that you can afford to pay \$6 per month toward a new Italian sports car. You call up your bank and find out that the going rate is % per month for 5 months. How much can you borrow? 6-5 Example 6.: Future Values for Annuities Suppose you begin saving for your retirement by depositing \$ per year in an IRA. If the interest rate is 7.5%, how much will you have in 4 years? Answer Earlier, we examined this ordinary ordinary annuity: Answer 6. Using an interest rate of 8%, we find that: The Future Value (at ) is \$,46.4. The Present Value (at ) is \$,577..

6 Future Value - annuity due What about this annuity? If you invest \$, at the beginning of each of the next years at 8%, how much would you have at the end of year? Same -year time line, Same \$ cash flows, but The cash flows occur at the beginning of each year, rather than at the end of each year. This is an annuity due. ( + - r FV =, -,, PV = A (PVIFA r, n ) ( + r) PV =, (PVIFA.8, ) (.8) Uneven Cash Flows Simply compound the ordinary annuity one more period: PV Mathematical Solution: Simply compound the FV of the ordinary annuity one more period: Mathematical Solution: PV Present Value - annuity due What is the PV of \$, at the beginning of each of the next years, if your opportunity cost is 8%? ( + r) (.8) - (.8) =,56..8 ( r ) t A r Simply compound the FV of the ordinary annuity one more period: FV = A (FVIFA i, n ) ( + i) FV =, (FVIFA.8, ) (.8) FV = A Mathematical Solution: Mathematical Solution: Simply compound the FV of the ordinary annuity one more period: r)n ( r ) (. 8 ) (. 8 ), , 6, 7, 4 Is this an annuity? How do we find the PV of a cash flow stream when all of the cash flows are different? (Use a % discount rate).

7 -,, 4, 6, 7, 4 period CF PV (CF) -, -,.,,88.8 4,,5.79 6, 4, , 4,78.9 PV of Cash Flow Stream: \$ 4,4.95 Example 6. Cash flows from an investment are expected to be \$4, per year at the end of years 4, 5, 6, 7, and 8. If you require a % rate of return, what is the PV of these cash flows? Answer 6. Timeline Answer 6. Things to Remember Compounding Intervals You ALWAYS need to make sure that the interest rate and the time period match. If you are looking at annual periods, you need an annual rate. If you are looking at monthly periods, you need a monthly rate. Suppose that rate is quoted as % Compounded Annually, t=5 years; Then FV=? FV=PV (+.)5 Compounded Semi-Annually r=./ =.5, t=5*= FV=PV (+.5) Then this means that investment actually pays 5% every 6 months

8 Compounding Intervals Compound Quarterly r=./4=.5, t=5*4= FV=PV (+.5) Compound Monthly r=./=.8, t=5*=6 FV=PV (+.8)6 Compound Daily r=./65=.7, t=5*65=85 Answer 6. Example 6. : After graduation, you plan to invest \$4 per month in the stock market. If you earn % per year on your stocks, how much will you have accumulated when you retire in years? 6-4 House Payment Example 6. If you borrow \$, at 7% fixed interest for years in order to buy a house, what will be your monthly house payment? Answer 6. Finding the Payment Example 6.4 Suppose you want to borrow \$, for a new car. You can borrow at 8% per year compounded monthly. If you take a 4 year loan, what is your monthly payment? 6-47

9 Answer 6.4 APRs and EARs Interest rates are quoted in different way, is the way that mislead borrowers and investors. Annual Percentage Rate (APR) Effective Annual Rate (EAR) Annual Percentage Rate APR APR is the nominal interest rate that is not adjusted for the full effect of compounding. (Also known as nominal annual rate) Nominal interest rate ignores the time value of money. APR = Period Rate * the number of periods per year This is the annual rate that is quoted by law If the i.r is quoted in terms of an APR, then this indicates the amount of simple interest earned in year, i.e. the amount of interest earned without the effect of compounding. As the APR does not include the effect of compounding, the APR quote is typically less than the actual amount of interest that you will earn. To compute the acual amount that you will earn in year, the APR must first be converted to an Effective Annual Rate (EAR). 6-5 Effective Annual Rate (EAR) 6-5 EAR - Formula This is the actual rate paid or received after accounting for compounding that occurs during the year When time value of money is taken into consideration, the interest rate is called effective interest rate. If you want to compare different investments (or interest rates) with different compounding periods you need to compute the EAR and use that for comparison. 6-5 m APR EAR m Remember that the APR is the quoted rate m is the number of compounding periods per year 6-5

10 Computing APRs from EARs EAR Example 6.5 a If you have an effective rate, how can you compute the APR? Rearrange the EAR equation and you get: a) You are looking at two savings accounts. One pays 5.5%, with daily compounding. The other pays 5.% with semiannual compounding. Which account should you use? APR m ( EAR) m Answer 6.5 a Example 6.5 b b) Which of this is the best if you are thinking of openning a savings account? Which of these is best if they represent loan rates? Bank A: 5 % compounded daily Bank B: 5.5 % compounded quarterly Bank C: 6 % compounded annually 6-57 Answer 6.5 b Example 6.6 Suppose that a credit card agreement quotes an interest rates of 8% APR. Monthly payments are required. What is the actual interest rate you pay on such a credit card? 6-59

11 Answer 6.6 Example 6.7 You have just received your first credit card and the problem is the rate. It look pretty high to you. The annual percentage rate (APR) is listed at.7 percent, and when you look closer, you notice that the interest rate is compounded daily. What is the annual percentage yield, or effective annual rate, on your credit card? 6-6 Answer APR Example 6.8 Suppose you want to earn an effective rate of % and you are looking at an account that compounds on a monthly basis. What APR must they pay? Computing Payments with APRs Example 6.9 Answer 6.8 Suppose you want to buy a new computer system and the store is willing to sell it to allow you to make monthly payments. The entire computer system costs \$5. The loan period is for years and the interest rate is 6.9% compounded monthly. What is your monthly payment?

12 Future Values with Monthly Compounding Example 6. Answer 6.9 Suppose you deposit \$5 a month into an account that has an APR of 9% compounded monthly. How much will you have in the account in 5 years? Present Value with Daily Compounding Example 6. Answer 6. You need \$5, in years for a new car. If you can deposit money into an account that pays an APR of 5.5%, compounded daily. How much would you need to deposit? Example 6. Answer 6. Upon retirement, your goal is to spend 5 years traveling around the world. To travel in style will require \$5, per year at the beginning of each year. If you plan to retire in years, what are the equal monthly payments necessary to achieve this goal? The funds in your retirement account will compound at % annually. 6-7

13 Answer 6. Answer 6. Example 6. Answer 6. a Suppose you are looking at the following possible cash flows: Year CF = \$; Years and CFs = \$; Years 4 and 5 CFs = \$. The required discount rate is 7% a) What is the value of the cash flows at year 5? b) What is the value of the cash flows today? 6-74 Answer 6. b Example 6.4 You want to receive 5 per month in retirement. If you can earn 7.5% per month and you expect to need the income for years, how much do you need to have in your account? 6-77

14 Answer 6.4 Example 6.5 You want to receive \$5 per month for the next 5 years. How much would you need to deposit today if you can earn.75% per month? 6-78 Answer Example 6.6 Find the present value of the CF provided below given a 6% discount rate. Year CF Year CF \$ Answer 6.6 Timeline 6-8 Answer

15 Example 6.7 Answer 6.7 Timeline What is the PV of an investment involving \$ received at the end of years through 5, a \$ cash outflow at the end of year 6, and \$5 received at the end of years 7 through, given a 5% discount rate? 6-84 Answer 6.7 Table 6-86 Suggested Problems -9,, 4-8,, -8, 4, 4-44, 46,

### 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

### 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

### 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.

### 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

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

### 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?

### 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

### 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

### 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

### 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 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. 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 2 Present Value

Chapter 2 Present Value Road Map Part A Introduction to finance. Financial decisions and financial markets. Present value. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted

### 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

### 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

### TIME VALUE OF MONEY. In following we will introduce one of the most important and powerful concepts you will learn in your study of finance;

In following we will introduce one of the most important and powerful concepts you will learn in your study of finance; the time value of money. It is generally acknowledged that money has a time value.

### 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

### 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

### 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

### 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

### 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. 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 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 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 (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

### Ch. Ch. 5 Discounted Cash Flows & Valuation In Chapter 5,

Ch. 5 Discounted Cash Flows & Valuation In Chapter 5, we found the PV & FV of single cash flows--either payments or receipts. In this chapter, we will do the same for multiple cash flows. 2 Multiple Cash

### 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

### 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

### 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 Inflation & Time Value The Time Value of Money

### Time Value Conepts & Applications. Prof. Raad Jassim

Time Value Conepts & Applications Prof. Raad Jassim Chapter Outline Introduction to Valuation: The Time Value of Money 1 2 3 4 5 6 7 8 Future Value and Compounding Present Value and Discounting More on

### 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.

### 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

### 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

### Business 2019. Fundamentals of Finance, Chapter 6 Solution to Selected Problems

Business 209 Fundamentals of Finance, Chapter 6 Solution to Selected Problems 8. Calculating Annuity Values You want to have \$50,000 in your savings account five years from now, and you re prepared to

### 3. Time value of money

1 Simple interest 2 3. 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

### 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

### 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

### 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 (TVM) A dollar today is more valuable than a dollar sometime in the future...

Lecture: II 1 Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...! The intuitive basis for present value what determines the effect of timing on the value

### 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

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

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

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

### 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

### 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

### Chapter 1: Time Value of Money

1 Chapter 1: Time Value of Money Study Unit 1: Time Value of Money Concepts Basic Concepts Cash Flows A cash flow has 2 components: 1. The receipt or payment of money: This differs from the accounting

### 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 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.

### 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

### 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

### 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)

### 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

### 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

### 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

### 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

### 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

### CHAPTER 4. The Time Value of Money. Chapter Synopsis

CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money

### 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

### Real estate investment & Appraisal Dr. Ahmed Y. Dashti. Sample Exam Questions

Real estate investment & Appraisal Dr. Ahmed Y. Dashti Sample Exam Questions Problem 3-1 a) Future Value = \$12,000 (FVIF, 9%, 7 years) = \$12,000 (1.82804) = \$21,936 (annual compounding) b) Future Value

### 2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?

CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equal-sized

### 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 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

### 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 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. 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

### 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

### 15.401. Lecture Notes

15.401 15.401 Finance Theory I Haoxiang Zhu MIT Sloan School of Management Lecture 2: Present Value Lecture Notes Key concept of Lecture 1 Opportunity cost of capital True or False? A company s 10-year

### 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

### 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 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. 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.

### Principles of Managerial Finance INTEREST RATE FACTOR SUPPLEMENT

Principles of Managerial Finance INTEREST RATE FACTOR SUPPLEMENT 1 5 Time Value of Money FINANCIAL TABLES Financial tables include various future and present value interest factors that simplify time value

### F V P V = F V = P (1 + r) n. n 1. FV n = C (1 + r) i. i=0. = C 1 r. (1 + r) n 1 ]

1 Week 2 1.1 Recap Week 1 P V = F V (1 + r) n F V = P (1 + r) n 1.2 FV of Annuity: oncept 1.2.1 Multiple Payments: Annuities Multiple payments over time. A special case of multiple payments: annuities

### Chapter 6 Interest Rates and Bond Valuation

Chapter 6 Interest Rates and Bond Valuation Solutions to Problems P6-1. P6-2. LG 1: Interest Rate Fundamentals: The Real Rate of Return Basic Real rate of return = 5.5% 2.0% = 3.5% LG 1: Real Rate of Interest

### Time Value of Money (TVM)

BUSI Financial Management Time Value of Money 1 Time Value of Money (TVM) Present value and future value how much is \$1 now worth in the future? how much is \$1 in the future worth now? Business planning

### 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

### Financial Management Spring 2012

3-1 Financial Management Spring 2012 Week 4 How to Calculate Present Values III 4-1 3-2 Topics Covered More Shortcuts Growing Perpetuities and Annuities How Interest Is Paid and Quoted 4-2 Example 3-3

### 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

### 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

### The Time Value of Money

The Time Value of Money Future Value - Amount to which an investment will grow after earning interest. Compound Interest - Interest earned on interest. Simple Interest - Interest earned only on the original

### 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,

### 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

### Chapter 03 - Basic Annuities

3-1 Chapter 03 - Basic Annuities Section 7.0 - Sum of a Geometric Sequence The form for the sum of a geometric sequence is: Sum(n) a + ar + ar 2 + ar 3 + + ar n 1 Here a = (the first term) n = (the number

### 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

### 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

### 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

### 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

### Fin 3312 Sample Exam 1 Questions

Fin 3312 Sample Exam 1 Questions Here are some representative type questions. This review is intended to give you an idea of the types of questions that may appear on the exam, and how the questions might

### 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

### Check off these skills when you feel that you have mastered them.

Chapter Objectives Check off these skills when you feel that you have mastered them. Know the basic loan terms principal and interest. Be able to solve the simple interest formula to find the amount of

### Financial Markets and Valuation - Tutorial 1: SOLUTIONS. Present and Future Values, Annuities and Perpetuities

Financial Markets and Valuation - Tutorial 1: SOLUTIONS Present and Future Values, Annuities and Perpetuities (*) denotes those problems to be covered in detail during the tutorial session (*) Problem

### 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

### 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

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

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