DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS

Size: px
Start display at page:

Download "DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS"

Transcription

1 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 year from now, $1000 two years from now, and $1,500 three years from now. If you can earn 10% on your money, how much will you have to invest today to exactly cover these amounts in the future? FV with multiple CF Suppose you invest $750 today in an account that earns 7%. In 1 year, you will invest another $750. How much will you have at the end of 2 years? VALUING LEVEL CASH FLOWS: ANNUITIES Many situations involve multiple cash flows of the same amount. (consumer loans, home mortgages, etc.) Annuity: A level stream of cash flows for a fixed period of time. Ordinary annuity: Multiple, identical cash flows occurring at the end of each period, for a fixed number of periods. F301 Page 1 of 12

2 Annuity DUE: Multiple, identical cash flows occurring at the beginning of each period, for a fixed number of periods. Which type of annuity (an annuity due, or an ordinary annuity) would be worth more in present value terms? PRESENT VALUE OF ANNUITY CASH FLOWS Methods: 1) Discount each cash flow to present value and sum them up. 2) Use the Annuity Present Value Formula => let r = rate per period, t = # of periods C = annuity cash flow APV = Annuity Present Value 1 1 t 1 PVIF ( r, t) ( 1 r) APV = $C * [ ] => APV = $C * [ ] r r 3) (Recommended) Use TVM keys on your financial calculator. Suppose you can make 36 monthly payments of $100, at 1.5% interest per month. What size loan can you obtain? Loan amount = present value of 36-period annuity of $100, at 1.5% per period. Solve for PV on your financial calculator: N I/Y PV PMT FV ? $2, F301 Page 2 of 12

3 FINDING THE PAYMENT, C, GIVEN APV, rate and t: Suppose you borrow $400 with the agreement to repay in 4 monthly installments at 1% per month. What is the amount of each payment? You could solve for the payment amount C in the annuity present value formula: ( ( ) ) ( ) ( ) Or use the TVM keys on your calculator: N I/Y PV PMT FV ? Another example: You wish to take a Caribbean vacation in three years, and it will cost $5,000 at that time. You have $1200 now. If you can earn 6% annually on your investments, what amount will you have to put into savings at the end of each year to have the five grand available at the end of the third year? Answer: You must deposit $1, at the end of each year. What if you make the deposits at the beginning of each year, starting today? That is, today is the beginning of Year 1. What will be the amount of each deposit when it s an annuity due? Answer: Set your calculator to BEGIN mode and solve. The amount is $1, Set your calculator back to END mode right away! F301 Page 3 of 12

4 FINDING THE NUMBER OF PAYMENTS, GIVEN APV, r, AND C Use your financial calculator here! (Note: this can also be solved with logarithms) How many $100 payments are required to pay off a $5000 loan at 1% per period.? FINDING THE RATE, R A finance company offers to loan you $1000 today in return for 48 "low" monthly payments of $ What is the implicit interest rate on the loan? This is a rate per what time period? (Per month? Per year? Per day?) F301 Page 4 of 12

5 FUTURE VALUE FOR ANNUITIES Question: How much will an annuity of $X grow to over a specified number of periods? Method 1: Solve using the Annuity Future Value (AFV) formula let r = rate per period, t = # of periods C = annuity cash flow AFV = Annuity Future Value FVIF ( r, t) 1 AFV = $C * [ ] r (1 r) t 1 = $C *[ ] r Method 2 (Recommended): Use the TVM keys on your financial calculator. Suppose you make 20 deposits of $1000 at 10% per period. How much will be in your account at the end of the 20th period? Suppose you make no further deposits, but you leave the funds in the account, at 10% per period, for 4 more periods. Now how much is in the account? F301 Page 5 of 12

6 COMPARING RATES WITH DIFFERENT COMPOUNDING PERIODS To compare rates that differ in their number of compounding periods, we must convert them to a comparable basis (an Effective Annual Rate). Stated or quoted rate: The rate before considering any compounding effects. e.g. 10% compounded quarterly (the stated or quoted rate is 10%). The stated rate required on consumer loans is called the Annual Percentage Rate (A.P.R.). APR is the periodic compounding rate times the number of periods in a year. Quoted rates usually cannot be used in TVM calculations. Must use a rate that accounts for compounding: the periodic compounding rate. So change the APR to R: Divide by the number of periods in one year (m). Important equation Key terminology: APR = Quoted rate = Stated rate Effective annual interest rate (E.A.R.): The rate, on an annual basis, that reflects compounding effects. EAR is the rate per year which gives the same Future Value as a rate compounded on some other period (monthly, quarterly, etc.). ( ) F301 Page 6 of 12

7 Steps: 1) Divide the quoted rate (A.P.R.) by the # of compounding periods per year (m). 2) Add 1 (to step 1) and raise to the power of m (# of compounding periods) 3) Subtract 1 10% compounded quarterly = an effective annual rate of %. ( ( )) Note that these two rates DO give the same FV at the end of one year, so they are effectively the same rate. Start with $100, for example: Quarterly rate = 10% compounded quarterly 10% compounded quarterly means R = 10 4 = 2.5% per quarter. FV of $100 after one year (four quarters) = = Annual rate = 10.38% per year FV of $100 after one year = = Which option would you choose if you were getting a loan? A) 10% compounded monthly B) 10.2% compounded quarterly C) 10.3% compounded annually Compare by converting each to an annual rate (EAR), as follows: A) EAR of 10% compounded monthly = B) EAR of 10.2% compounded quarterly = C) EAR of 10.3% compounded annually = Which rate is lower? F301 Page 7 of 12

8 Which is lower, the E.A.R. of 15% compounded monthly, or the E.A.R. of 16% compounded yearly? IMPLICATIONS FOR SOLVING FOR PV AND FV When we solve for present or future value, we must either use the E.A.R. with years or the periodic rate (APR m) and the appropriate number of periods. FV = PV * ( 1 q mt ) m 1 ; PV = FV * [ ( 1 q ) m mt ] ; PV = FV q ( 1 ) m mt What is the present value of $100 to be received in 2 years at 10% compounded quarterly? Method 1: Use a quarterly rate and the total number of quarters Method 2: Use the E.A.R. and the number of years. F301 Page 8 of 12

9 RATE ADJUSTMENTS FOR MULTIPLE COMPOUNDING PERIODS Whenever the compounding periods differ from once per year (e.g. semiannually, quarterly, monthly, etc.) you must make the appropriate adjustments to all formulas! t (n) R = the # of years * # compounding periods per year = no. years m = stated rate / # compounding periods per year = APR m With annuities, you must be sure to match the appropriate rate to your cash flows! On the calculator: N and I/Y and PMT all must use the same time period. Suppose you borrow $10,000 to purchase a car and agree to repay the loan over 5 years of monthly payments. The A.P.R. (stated rate) is 12% per year (compounded annually). What is the amount of the payment monthly? Suppose you have just purchased a new washer and dryer for $700. You have financed the purchase and agreed to make annual payments starting in 1 year, for the next 5 years. The interest rate on the loan is 1% per month. What is the amount of the annual payment? F301 Page 9 of 12

10 Your car loan requires monthly payments of $ The amount borrowed was $20,000, for five years. What is the APR on this loan? What is the EAR? A corporation borrows $800,000. The loan will be repaid over 12 years of quarterly payments. The interest rate on the loan is 7.2% compounded monthly. What is the amount of each quarterly payment? Answer: $25, F301 Page 10 of 12

11 PERPETUITIES Perpetuity: An annuity in which the cash flows continue forever. Perpetuity Present value: C / r, where C is the amount of the perpetuity per period and r is the periodic interest rate (as a decimal). Suppose that starting at the end of one year from now, you will receive a perpetuity of $100 each year, forever. What is the present value of the series of cash flows at a 10% yearly interest rate? Suppose that starting 4 years from now, you will start receiving a perpetuity cash flow of $5,000 per year. What is the present value of these cash flows assuming a 12% yearly interest rate? F301 Page 11 of 12

12 AMORTIZATION SCHEDULES An amortization schedule is a repayment schedule for a typical consumer loan that shows: 1) the number of payments 2) the amount of each payment 3) the interest paid per period 4) the reduction in principal per period 5) the remaining loan balance Suppose you borrow $4,000 and agree to repay the loan in five equal installments over a 5-year period. Payments are made at the end of each year. The interest rate on the loan is 10% per year. Step 1: Solve for payment using the TVM keys. NOTE: The payment will be the same amount in every period. It s an annuity. Step 2: Complete the amortization table as follows: Period Beginning Balance Periodic Payment Interest Charge Reduction in Principal Ending Balance Calculations: Initial loan amount; then ending balance from prior period. PMT Beginning balance periodic interest rate PMT interest charge Beginning balance reduction in principal 1 $4, F301 Page 12 of 12

Discounted Cash Flow Valuation

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

More information

Discounted Cash Flow Valuation

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?

More information

Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

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

More information

The Time Value of Money

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

More information

Discounted Cash Flow Valuation

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

More information

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.

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

More information

Chapter 4. The Time Value of Money

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

More information

Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows

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

More information

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 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

More information

CHAPTER 2. Time Value of Money 2-1

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

More information

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26

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.

More information

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.

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

More information

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%?

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

More information

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

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

More information

Problem Set: Annuities and Perpetuities (Solutions Below)

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

More information

International Financial Strategies Time Value of Money

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

More information

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

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

More information

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

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

More information

TIME VALUE OF MONEY (TVM)

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

More information

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?

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

More information

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

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

More information

Chapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.

Chapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved. 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

More information

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

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

More information

Chapter 4. The Time Value of Money

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

More information

HOW TO CALCULATE PRESENT VALUES

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

More information

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

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

More information

Chapter 4 Discounted Cash Flow Valuation

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

More information

Key Concepts and Skills

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

More information

Time Value Conepts & Applications. Prof. Raad Jassim

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

More information

FIN 3000. Chapter 6. Annuities. Liuren Wu

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

More information

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 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

More information

Ordinary Annuities Chapter 10

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

More information

Chapter 2 Present Value

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

More information

Chapter The Time Value of Money

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

More information

5. Time value of money

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

More information

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

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

More information

Week 4. Chonga Zangpo, DFB

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

More information

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

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.

More information

Solutions to Time value of money practice problems

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,

More information

Chapter 4: Time Value of Money

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)

More information

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY

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

More information

Main TVM functions of a BAII Plus Financial Calculator

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

More information

FinQuiz Notes 2 0 1 4

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.

More information

Oklahoma State University Spears School of Business. Time Value of Money

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

More information

Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...

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

More information

CHAPTER 9 Time Value Analysis

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

More information

Chapter 28 Time Value of Money

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:

More information

CHAPTER 6 DISCOUNTED CASH FLOW VALUATION

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

More information

How to calculate present values

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

More information

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

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

More information

Present Value and Annuities. Chapter 3 Cont d

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

More information

Chapter 2 Applying Time Value Concepts

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

More information

The Time Value of Money C H A P T E R N I N E

The Time Value of Money C H A P T E R N I N E The Time Value of Money C H A P T E R N I N E Figure 9-1 Relationship of present value and future value PPT 9-1 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure

More information

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. 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.

More information

3. Time value of money. We will review some tools for discounting cash flows.

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

More information

Chapter 5 & 6 Financial Calculator and Examples

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

More information

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 ]

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

More information

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

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

More information

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

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

More information

3. Time value of money

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

More information

Chapter 5 Time Value of Money

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

More information

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

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

More information

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

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

More information

PowerPoint. to accompany. Chapter 5. Interest Rates

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

More information

NPV calculation. Academic Resource Center

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

More information

MAT116 Project 2 Chapters 8 & 9

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

More information

CHAPTER 5. Interest Rates. Chapter Synopsis

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)

More information

Solutions to Problems: Chapter 5

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

More information

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 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,

More information

Financial Management Spring 2012

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

More information

Time Value of Money (TVM)

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

More information

Time Value of Money. Background

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

More information

The time value of money: Part II

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

More information

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION

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

More information

Chapter 5 Discounted Cash Flow Valuation

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

More information

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

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

More information

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

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

More information

Key Concepts and Skills

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

More information

EXAM 2 OVERVIEW. Binay Adhikari

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

More information

FinQuiz Notes 2 0 1 5

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.

More information

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY

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

More information

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

More information

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved. 2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical defined-contribution

More information

Chapter 4. Time Value of Money

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

More information

ANNUITIES. Ordinary Simple Annuities

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

More information

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

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: -

More information

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

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

More information

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

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

More information

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! 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

More information

Time-Value-of-Money and Amortization Worksheets

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

More information

Chapter 4: Time Value of Money

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

More information

1. Annuity a sequence of payments, each made at equally spaced time intervals.

1. Annuity a sequence of payments, each made at equally spaced time intervals. Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology

More information

10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans

10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans 10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans Introduction This chapter continues the discussion on the time value of money. In this chapter, you will learn how inflation

More information

Chapter 1: Time Value of Money

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

More information

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?

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

More information

Ehrhardt Chapter 8 Page 1

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,

More information

TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007

TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007 TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007 The purpose of this tutorial is to help students who use the HP 17BII+, and HP10bll+ calculators understand how

More information

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

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

More information

THE TIME VALUE OF MONEY

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

More information