YOUR PIPE RENEWAL CIP, PART 2: THE SANDS OF TIME

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "YOUR PIPE RENEWAL CIP, PART 2: THE SANDS OF TIME"

Transcription

1 YOUR PIPE RENEWAL CIP, PART 2: THE SANDS OF TIME Ken Harlow, Director of Management Services, Brown and Caldwell In Part 1 we considered a problem pipe with observed defects. We decided that it would be in the community s interest to renew this pipe through spot repairs, but if more costly measures were required the case might be otherwise. But we also identified some deficiencies in the methodology we used. The most serious (at least the one I went on the longest about) was that we didn t consider the time value of money. In this part we ll explore the time value of money and then take another look at our problem pipe to see if our plans should be changed. We're going to get a bit technical here, so be patient. If you take the time to plow through the next section, you'll find that applying time value of money principles to our pipe example is quick and easy. In this part we ll explore the time value of money and then take another look at our problem pipe to see if our plans should be changed. The Time Value of Money Investment is what utility managers do every day, as surely as if they were fund managers, oil drillers, or aircraft makers. They spend community money to gain future benefits for the community. The observation seems basic and obvious, but it is surprising how few utility managers ever see their work in this light. Every time we spend money, whether building a new treatment plant or greasing a machine, we expect (and if we re smart we require) that the benefits gained will outweigh the costs just as in any other business. Otherwise, we re hardly bringing value to our community. We need to remember, of course, that both costs and benefits are very broadly construed to include not just direct financial impacts but other community impacts as well. This means we need a benefit/cost analysis to ensure value. But we typically invest now for future benefits. But how do we compare today's outlay with tomorrow's benefits when we know very well that future events are less important than things happening right now? The question is appropriate and, fortunately, has an answer. Conceptually, we (or our community) has a required rate of return. An investment yielding less has no attraction. An investment yielding more will be very interesting. Most public utilities consider their required rate of return to be their cost of long-term borrowing (say, 20-year bonds). The idea, of course, is that if they can use somebody else s money at 5% and earn 6% by investing it in their assets, the community comes out ahead essentially for free Investment is what utility managers do every day, as surely as if they were fund managers, oil drillers, or aircraft makers.

2 Example 1: The grasshopper and the ant. We have deposited $1,000 in a savings account earning 4 percent annually. How much will we have in the account after ten years? Let s do the numbers. The formula for the future value (FV) of an amount earning compound interest is: Future value = Present value x (1 + Interest rate) Number of years Substituting the actual numbers for the elements of the equation: Future value = $1,000 x (1 +.04) 10 After ten years we will have $1, in our savings account. Example 2: A bad investment. If we invest $1,000 dollars today, we will receive $1,480 ten years from now. Is this a good investment at our required rate of return of 5.5 percent? Let s do the numbers. The formula for the present value (PV) of a single future cash flow is: Present value = Future value (1+k) Number of years where k is the required rate of return. Substituting the actual numbers for the elements of the equation: Present value = $1, ( ) 10 From this formula, the PV of the future cash flow is $867. In other words, we are being asked to invest $1,000 in return for an amount that, today, is worth less to us than $1,000. The investment is not a good one for us. Single payments So let s get started. Example 1 at the left shows something we all know the effect of compound interest. We put money in the bank and it earns interest, and the interest earns interest. Rather slowly these days to be sure, but it does happen. If our required rate of return is 4% as shown, and somebody says, You can have $1,000 today or $1,480 ten years from now, we will be indifferent. One will be as good as the other to us (assuming that we have no immediate need for the money, total faith in the other party, and so forth). We will immediately pay $1,000 for a higher future payment and just as readily reject a lower payment. But what if somebody makes us exactly the same offer, but our required rate of return is 5.5%? In the first case we asked, What is the future value of $1, years from now at 4%? In this case, we simply turn the question around and ask, What is the present value of $1, years from now at 5.5%? The term present value, or PV, is simply the value today of some cost or benefit in the future. Similarly, we turn the equation around and instead of compounding the interest we decompound it as shown in Example 2. And we find that the most we are willing pay today for the $1,408 that we will receive 10 years out, at our required rate of return of 5.5%, is $867. So paying $1,000 is not for us. And that s really all there is present value, at least in principle. In finance-speak, to bring a future value back to the present as in Example 2 is to discount it. Thus the terms discounted cash flow (or DCF) analysis and "discount rate" for the rate at which the discounting is done. Not very complex or mysterious. Annuities There is one more thing that s useful to know a kind of shortcut, actually. We are often faced with investments that yield similar costs or benefits over a number of years. Examples might be reduced maintenance costs, lower energy consumption, a long-term continuing reduction in spills, and so forth. If we ignore inflation, those benefits can often be seen as level cash flows or, again in finance-speak, an "annuity." We can see that calculating the present value of each of (for instance) 20 years of savings would be more than a nuisance if we proceeded as above. But if we consider the savings as an annuity, things get a lot simpler

3 So our shortcut is to calculate the present value of a level series of future costs or benefits in short the present value of an annuity all at once. This can be done by a rather complicated formula or, much more easily and quickly, with Excel's annuity functions. Example 3: Investing to avoid costs. A new pump is expected to save $1,000 a year in energy and maintenance costs over its 20-year life. What is the value of those savings today if our required rate of return is 5.5 percent? Let s do the numbers. We know that the payment (Pmt) is $1,000, the number of periods (Nper) is 20, and the required rate of return (Rate) is 5.5%. We need to solve for the present value (PV), which uses, by more than mere chance, Excel s PV function. Using Excel s help screens, we find that the proper format is PV(rate,nper,pmt,fv,type). The last two entries are not in bold so they aren t required (and we can just ignore them here). So we click on a blank cell and type in =PV(.055,20,1000). We hit the return key and see: The amount looks reasonable, but it s negative. What s up? Excel is simply analyzing the annuity as an investment. It s saying, A 20-year annuity consisting of inflows of $1,000 a year at a required rate of return of 5.5% is worth the investment (i.e., an outflow) of $11, today. To Excel, inflows are positive (they add to our checkbook balance) and outflows are negative. They always balance one another in annuity analysis. When we think about it, this makes sense. In the case at hand, we now know that we are justified in spending up to $11,950 more for the new pump to achieve the savings anticipated. In the example at the left, we look at the PV (present value) of 20 years of anticipated cost savings over the life of a pump. The pump certainly seems attractive, but we need to know if its benefits are worth its higher price. The simplest way to approach this is to calculate the PV of the savings to us, given our required rate of return, and then to compare the result with the added cost of the pump. We obviously want the PV of the savings to exceed the added cost. In this example, it is exactly as if somebody has offered us an iron-clad promise of $1,000 a year for 20 years. If our required rate of return is 5.5% and the price demanded is $11,950, we will be "indifferent" and say, "I really don't care either way." If the price is lower, we will accept the offer. If higher, we will reject it. Note that there are always four values associated with an annuity: the present value or value today (PV), the discount rate (rate), the number of periods (nper), and the periodic payment (pmt). Excel will solve for any of the four if the other three are known. For example, if we were offered a choice $10,000 today or $1,000 a year for 10 years, we d readily take the $10,000 now because we could then invest it in something that might earn a return. But if our required rate of return were 5% and we were offered $1,400 a year, we could use Excel s PMT function and quickly calculate that we are indifferent between getting $10,000 now and $1,295 a year for 10 years, so $1,400 a year sounds pretty good. In fact, we could use Excel s RATE function and find that our actual return would be 6.6%, enough to put a smile on our face. This last example will be of some importance later. We will use the PMT function to convert a one-time capital investment yielding benefits over a certain number of years to an equivalent annual capital cost of ownership that can be compared with annual benefits to help in our analysis. Two other things and then we can move on. 1. In annuity calculations, we usually need to exclude any component for expected inflation. An inflationary component is always part of our actual borrowing rate because lenders need to be sure that the payments they receive will give them some profit over and above the loss of buying power of money over time. In annuities, though, we often intentionally - 3 -

4 exclude inflation to keep things simple and the cash flows level. If so, we need to exclude it from our required rate of return as well and base our discount rate instead on the socalled "real cost of money" without inflation, which has historically been between 3% and 3.5%. 2. We often overestimate benefits for a number of reasons that all of us know or can imagine. This is true in all businesses, so most establish an investment "hurdle rate" well above their cost of money. This discounts future benefits more severely. Hunter Water in Australia, for example, normally uses a discount rate of 7%. Since the uncertainties are quite pronounced when we deal with pipes, we'd better keep this in mind. We often overestimate benefits for a number of reasons that all of us know or can imagine. Let's Revisit our Pipe Now let's take another look at our problem pipe from Part 1. This time we'll take the time value of money into account and see if it changes anything. Here's a repeat of what we know about this pipe: Cost of failure This is an 8-inch residential area pipe without too much consequence. We estimate the cost of failure at $20,000 including community costs. Probability of failure Our pipe people's consensus is that the pipe has a 10 percent chance of failure over the next 10 years and is almost certain to fail within 40 years. Cost of renewal We can renew this pipe in either of two ways: First, spot repairs at $5,000 with a useful life of 20 years; second, relining the pipe at $25,000 with a useful life of 40 years. Both these costs include, of course, community costs. A simple approach We know we want to perform a benefit/cost analysis of renewing this pipe. So let's start with the benefit, which is the avoidance of the community's costs arising from the potential failure of the pipe. Since we re about to calculate a present value, we first need a discount rate. We know that our pipe experts are a conservative lot and may well be painting a grimmer picture than actually exists. That means that the risk costs, and thus our renewal benefits, may be overstated. Even without this, we know that there is a lot of uncertainty in their estimates. So we'll go a bit high and use a 5% hurdle rate as our discount rate rather than our real cost of money of about 3%. Now we can proceed. Since the pipe is essentially certain to fail within 40 years, we might well set the most likely failure of this pipe at 20 years out. The cost of failure is $20,000. The present value of a $20,000 benefit to be received 20 years from now at our 5% hurdle rate is $7,538 per Example 2 above. Thus the benefit of renewal is $7,538. The cost of renewal via spot repairs is $5,000, so that seems quite worth doing. Relining will cost $25,000, so that s not a good idea at all. Verdict: Do the spot repairs immediately

5 An annuity approach The simple approach above doesn t take into account that relining will yield benefits for longer than spot repairs. Maybe using an annuity approach will help with that. Based on our pipe people's consensus is that the pipe is almost certain to fail within 40 years, there is on average a 2.5% chance of failure each year. So the community's risk exposure is 2.5% of $20,000 each year, or $500 per year. Yes, this still seems a clumsy way to look at risk and ignores some of the detail in our pipe people s consensus, but we'll address that in Part 3. If we renew the pipe, the benefit is the avoidance of this $500 per year cost for however many years the renewal is effective. In other words, the benefit is an annuity. Now we have two analyses to do, one for spot repairs and one for relining. Excel gives us our answers very quickly, just as in Example 3 above: The benefit of spot repairs is a 20-year annuity of $500 per year (20 years because that s how long spot repairs will have a benefit). That's worth, today, $6,231 at our hurdle rate of 5%. Since that's more than the $5,000 cost, the spot repairs still look like a good investment. The benefit of relining is a 40-year annuity, again of $500 a year. That's worth, today, $8,580, so relining brings quite a bit more benefit than spot repairs. However, we have to pay $25,000 for that benefit. Not a good idea. So once again spot repairs look like a good investment. We re gradually gaining a bit more faith in our analysis (although some rough edges still remain). Stay Tuned... We're way beyond the matrix now and maybe even closing in on the "truth," even if some more work still lies ahead of us. In Part 3 we'll deal with that pesky issue of how to deal with pipe failure probabilities and expected failure costs. Are they really level from year to year? Somehow that doesn't seem quite right. Exploring this issue will show us something else we may be able to start to puzzle out not just whether and how to renew the pipe but when to do it. A hint: It may not be when we think! We're way beyond the matrix now and maybe even closing in on the "truth," even if some more work still lies ahead of us. Until next time. Interested? Bookmark Ken Harlow s Asset Management Page:

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

rate nper pmt pv Interest Number of Payment Present Future Rate Periods Amount Value Value 12.00% 1 0 $100.00 $112.00

rate nper pmt pv Interest Number of Payment Present Future Rate Periods Amount Value Value 12.00% 1 0 $100.00 $112.00 In Excel language, if the initial cash flow is an inflow (positive), then the future value must be an outflow (negative). Therefore you must add a negative sign before the FV (and PV) function. The inputs

More information

How To Use Excel To Compute Compound Interest

How To Use Excel To Compute Compound Interest Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout

More information

Time Value of Money 1

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

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

Module 5: Interest concepts of future and present value

Module 5: Interest concepts of future and present value Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities

More information

CAPITAL BUDGETING: How a business firm decides whether or not to acquire durable real assets

CAPITAL BUDGETING: How a business firm decides whether or not to acquire durable real assets EC100 REINHARDT CAPITAL BUDGETING: How a business firm decides whether or not to acquire durable real assets In this write-up, I shall explain as simply as is possible (1) how modern business firms decide

More information

THE MYTH OF DEEP PIPES: CRITICALITY AND PIPE REHABILITATION STRATEGIES

THE MYTH OF DEEP PIPES: CRITICALITY AND PIPE REHABILITATION STRATEGIES THE MYTH OF DEEP PIPES: CRITICALITY AND PIPE REHABILITATION STRATEGIES Ken Harlow, Director of Management Services, Brown and Caldwell kharlow@brwncald.com Introduction A fundamental principal of asset

More information

Lesson 1. Key Financial Concepts INTRODUCTION

Lesson 1. Key Financial Concepts INTRODUCTION Key Financial Concepts INTRODUCTION Welcome to Financial Management! One of the most important components of every business operation is financial decision making. Business decisions at all levels have

More information

TVM Problem Set 1: Self-Correcting, Hyperlinked File

TVM Problem Set 1: Self-Correcting, Hyperlinked File JR DeLisle, Ph.D. TVM Problem Set 1: Self-Correcting, Hyperlinked File Purpose of Problem Set The purpose of this problem set is to present you with a series of Time Value of Money (TVM) problems that

More information

Numbers 101: Cost and Value Over Time

Numbers 101: Cost and Value Over Time The Anderson School at UCLA POL 2000-09 Numbers 101: Cost and Value Over Time Copyright 2000 by Richard P. Rumelt. We use the tool called discounting to compare money amounts received or paid at different

More information

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;

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.

More information

Accounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money

Accounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money Accounting Building Business Skills Paul D. Kimmel Appendix B: Time Value of Money PowerPoint presentation by Kate Wynn-Williams University of Otago, Dunedin 2003 John Wiley & Sons Australia, Ltd 1 Interest

More information

CHAPTER 4. The Time Value of Money. Chapter Synopsis

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

More information

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets Ch. 3: Decision Rules Harry Campbell & Richard Brown School of Economics The University of Queensland Applied Investment Appraisal

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

If I offered to give you $100, you would probably

If I offered to give you $100, you would probably File C5-96 June 2013 www.extension.iastate.edu/agdm Understanding the Time Value of Money If I offered to give you $100, you would probably say yes. Then, if I asked you if you wanted the $100 today or

More information

Compounding Quarterly, Monthly, and Daily

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

More information

Module 5: Interest concepts of future and present value

Module 5: Interest concepts of future and present value file:///f /Courses/2010-11/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present

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

This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1).

This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/

More information

PV Tutorial Using Excel

PV Tutorial Using Excel EYK 15-3 PV Tutorial Using Excel TABLE OF CONTENTS Introduction Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise 8: Exercise 9: Exercise 10: Exercise 11: Exercise

More information

Investment, Time, and Present Value

Investment, Time, and Present Value Investment, Time, and Present Value Contents: Introduction Future Value (FV) Present Value (PV) Net Present Value (NPV) Optional: The Capital Asset Pricing Model (CAPM) Introduction Decisions made by a

More information

Problems on Time value of money January 22, 2015

Problems on Time value of money January 22, 2015 Investment Planning Problems on Time value of money January 22, 2015 Vandana Srivastava SENSEX closing value on Tuesday: closing value on Wednesday: opening value on Thursday: Top news of any financial

More information

TVM Functions in EXCEL

TVM Functions in EXCEL TVM Functions in EXCEL Order of Variables = (Rate, Nper, Pmt, Pv, Fv,Type, Guess) Future Value = FV(Rate,Nper,Pmt,PV,Type) Present Value = PV(rate,nper,pmt,fv,type) No. of Periods = NPER(rate, pmt, pv,

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

SUMMARY AND CONCLUSIONS

SUMMARY AND CONCLUSIONS 150 PART THREE Valuation of Future Cash Flows TABLE 5.4 Summary of Time Value Calculations I. Symbols: PV Present value, what future cash flows are worth today FV t Future value, what cash flows are worth

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 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS

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

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

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

Time Value of Money Dallas Brozik, Marshall University

Time Value of Money Dallas Brozik, Marshall University Time Value of Money Dallas Brozik, Marshall University There are few times in any discipline when one topic is so important that it is absolutely fundamental in the understanding of the discipline. The

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

CHAPTER 7: NPV AND CAPITAL BUDGETING

CHAPTER 7: NPV AND CAPITAL BUDGETING CHAPTER 7: NPV AND CAPITAL BUDGETING I. Introduction Assigned problems are 3, 7, 34, 36, and 41. Read Appendix A. The key to analyzing a new project is to think incrementally. We calculate the incremental

More information

Lease Analysis Tools

Lease Analysis Tools Lease Analysis Tools 2009 ELFA Lease Accountants Conference Presenter: Bill Bosco, Pres. wbleasing101@aol.com Leasing 101 914-522-3233 Overview Math of Finance Theory Glossary of terms Common calculations

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

How to Calculate Present Values

How to Calculate Present Values How to Calculate Present Values Michael Frantz, 2010-09-22 Present Value What is the Present Value The Present Value is the value today of tomorrow s cash flows. It is based on the fact that a Euro tomorrow

More information

hp calculators HP 17bII+ Discounting & Discounted Cash Flow Analysis It's About Time The Financial Registers versus Discounted Cash Flow

hp calculators HP 17bII+ Discounting & Discounted Cash Flow Analysis It's About Time The Financial Registers versus Discounted Cash Flow HP 17bII+ Discounting & Discounted Cash Flow Analysis It's About Time The Financial Registers versus Discounted Cash Flow Discounting a Single Sum Discounting and Compounding Discounting a Series of Sums

More information

e C P M 1 0 5 : P o r t f o l i o M a n a g e m e n t f o r P r i m a v e r a P 6 W e b A c c e s s

e C P M 1 0 5 : P o r t f o l i o M a n a g e m e n t f o r P r i m a v e r a P 6 W e b A c c e s s e C P M 1 5 : P o r t f o l i o M a n a g e m e n t f o r P r i m a v e r a P 6 W e b A c c e s s Capital Budgeting C o l l a b o r a t i v e P r o j e c t M a n a g e m e n t e C P M 1 5 C a p i t a l

More information

Exam #1 (100 points)

Exam #1 (100 points) Exam #1 (100 points) Take the exam during an uninterrupted period of no more than 2 hours. (It should not take that long.) The space provided below each question should be sufficient for your answer, but

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

NOTE: All of the information contained in this file has been collected from the various HELP files found in Excel for each of these functions.

NOTE: All of the information contained in this file has been collected from the various HELP files found in Excel for each of these functions. NOTE: All of the information contained in this file has been collected from the various HELP files found in Excel for each of these functions. PV Returns the present value of an investment. The present

More information

Part 7. Capital Budgeting

Part 7. Capital Budgeting Part 7. Capital Budgeting What is Capital Budgeting? Nancy Garcia and Digital Solutions Digital Solutions, a software development house, is considering a number of new projects, including a joint venture

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

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

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

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

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

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

Excel Financial Functions

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

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

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

Ing. Tomáš Rábek, PhD Department of finance

Ing. Tomáš Rábek, PhD Department of finance Ing. Tomáš Rábek, PhD Department of finance For financial managers to have a clear understanding of the time value of money and its impact on stock prices. These concepts are discussed in this lesson,

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

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

Calculating Loan Payments

Calculating Loan Payments IN THIS CHAPTER Calculating Loan Payments...............1 Calculating Principal Payments...........4 Working with Future Value...............7 Using the Present Value Function..........9 Calculating Interest

More information

Sample problems from Chapter 10.1

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

More information

CHAPTER 1. Compound Interest

CHAPTER 1. Compound Interest CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.

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

Chapter 02 How to Calculate Present Values

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

More information

Unit VI. Complete the table based on the following information:

Unit VI. Complete the table based on the following information: Aqr Review Unit VI Name 1. You have just finished medical school and you have been offered two jobs at a local hospital. The first one is a physical therapist for the hospital with a salary of $45,500.

More information

Cash Flow: Know Its Value Today When Buying, Selling, or Expanding

Cash Flow: Know Its Value Today When Buying, Selling, or Expanding The Business Library Resource Report #26 Cash Flow: Know Its Value Today When Buying, Selling, or Expanding! Rate of Return Components! Risk and Present Value Analysis! You as Seller, You as Buyer! Today

More information

CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA

CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Answers to Concepts Review and Critical Thinking Questions 1. A payback period less than the project s life means that the NPV is positive for

More information

MODULE 2. Capital Budgeting

MODULE 2. Capital Budgeting MODULE 2 Capital Budgeting Capital Budgeting is a project selection exercise performed by the business enterprise. Capital budgeting uses the concept of present value to select the projects. Capital budgeting

More information

Scenic Video Transcript Direct Cash Flow Statements Topics. Introduction. Purpose of cash flow statements. Level 1 analysis: major categories

Scenic Video Transcript Direct Cash Flow Statements Topics. Introduction. Purpose of cash flow statements. Level 1 analysis: major categories Cash Flow Statements» What Do I See?» Direct Cash Flow Statements» Scenic Video http://www.navigatingaccounting.com/video/scenic-direct-cash-flow-statements Scenic Video Transcript Direct Cash Flow Statements

More information

Capital Budgeting OVERVIEW

Capital Budgeting OVERVIEW WSG12 7/7/03 4:25 PM Page 191 12 Capital Budgeting OVERVIEW This chapter concentrates on the long-term, strategic considerations and focuses primarily on the firm s investment opportunities. The discussions

More information

The Time Value of Money

The Time Value of Money CHAPTER 7 The Time Value of Money After studying this chapter, you should be able to: 1. Explain the concept of the time value of money. 2. Calculate the present value and future value of a stream of cash

More information

EXCEL PREREQUISITES SOLVING TIME VALUE OF MONEY PROBLEMS IN EXCEL

EXCEL PREREQUISITES SOLVING TIME VALUE OF MONEY PROBLEMS IN EXCEL CHAPTER 3 Smart Excel Appendix Use the Smart Excel spreadsheets and animated tutorials at the Smart Finance section of http://www.cengage.co.uk/megginson. Appendix Contents Excel prerequisites Creating

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

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.

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

More information

Outline. Not assigned problems Chapter 11. Q10 Go Chapter 11. Q14 Go Chapter 11. Q20 Go Chapter 11. Q22 Go Chapter 11. Q26 Go

Outline. Not assigned problems Chapter 11. Q10 Go Chapter 11. Q14 Go Chapter 11. Q20 Go Chapter 11. Q22 Go Chapter 11. Q26 Go Outline Not assigned problems Chapter 11. Q10 Go Chapter 11. Q14 Go Chapter 11. Q20 Go Chapter 11. Q22 Go Chapter 11. Q26 Go Assignment problems: Chapter 11. Q4 Go Chapter 11. Q8 Go Chapter 11. Q12 Go

More information

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed. Time Value Analysis

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed. Time Value Analysis This is a sample of the instructor resources for Understanding Healthcare Financial Management, Fifth Edition, by Louis Gapenski. This sample contains the chapter models, end-of-chapter problems, and end-of-chapter

More information

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

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

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

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

The Time Value of Money

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

More information

LOS 56.a: Explain steps in the bond valuation process.

LOS 56.a: Explain steps in the bond valuation process. The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Introduction

More information

Calculations for Time Value of Money

Calculations for Time Value of Money KEATMX01_p001-008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with

More information

Net present value is the difference between a project s value and its costs.

Net present value is the difference between a project s value and its costs. 1 2 Net present value is the difference between a project s value and its costs. We need to calculate the Present Value of future cash flows (discounted by the opportunity cost of capital) and subtract

More information

Double-Entry Bookkeeping: Assets and Liabilities

Double-Entry Bookkeeping: Assets and Liabilities Double-Entry Bookkeeping: Assets and Liabilities The purpose of this chapter is to introduce the fundamentals of double-entry bookkeeping and its role in accounting for business. The objectives of accounting

More information

Chapter 1: The time value of money *

Chapter 1: The time value of money * Chapter 1: The time value of money * minor bug fix: September 9, 2003 Chapter contents Overview... 2 1.1. Future value... 3 1.2. Present value... 18 1.3. Net present value... 26 1.4. The internal rate

More information

Bank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later.

Bank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later. ü 4.4 lternative Discounted Cash Flow Decision Rules ü Three Decision Rules (1) Net Present Value (2) Future Value (3) Internal Rate of Return, IRR ü (3) Internal Rate of Return, IRR Internal Rate of Return

More information

Topic 3: Time Value of Money And Net Present Value

Topic 3: Time Value of Money And Net Present Value Topic 3: Time Value of Money And Net Present Value Laurent Calvet calvet@hec.fr John Lewis john.lewis04@imperial.ac.uk From Material by Pierre Mella-Barral MBA - Financial Markets - Topic 3 1 2. Present

More information

Will the future benefits of this project be large enough to justify the investment given the risk involved?

Will the future benefits of this project be large enough to justify the investment given the risk involved? Chapter 1 The Overall Process Capital Expenditures Whenever we make an expenditure that generates a cash flow benefit for more than one year, this is a capital expenditure. Examples include the purchase

More information

AN INTRODUCTION TO REAL ESTATE INVESTMENT ANALYSIS: A TOOL KIT REFERENCE FOR PRIVATE INVESTORS

AN INTRODUCTION TO REAL ESTATE INVESTMENT ANALYSIS: A TOOL KIT REFERENCE FOR PRIVATE INVESTORS AN INTRODUCTION TO REAL ESTATE INVESTMENT ANALYSIS: A TOOL KIT REFERENCE FOR PRIVATE INVESTORS Phil Thompson Business Lawyer, Corporate Counsel www.thompsonlaw.ca Rules of thumb and financial analysis

More information

Financial Math on Spreadsheet and Calculator Version 4.0

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

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

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. 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

More information

Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value

Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations

More information

DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS

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

More information

Introduction (I) Present Value Concepts. Introduction (II) Introduction (III)

Introduction (I) Present Value Concepts. Introduction (II) Introduction (III) Introduction (I) Present Value Concepts Philip A. Viton February 19, 2014 Many projects lead to impacts that occur at different times. We will refer to those impacts as constituting an (inter)temporal

More information

Introduction to Discounted Cash Flow and Project Appraisal. Charles Ward

Introduction to Discounted Cash Flow and Project Appraisal. Charles Ward Introduction to Discounted Cash Flow and Project Appraisal Charles Ward Company investment decisions How firms makes investment decisions about real projects (not necessarily property) How to decide which

More information

Practice Set #1 and Solutions.

Practice Set #1 and Solutions. Bo Sjö 14-05-03 Practice Set #1 and Solutions. What to do with this practice set? Practice sets are handed out to help students master the material of the course and prepare for the final exam. These sets

More information

Important Financial Concepts

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

More information

PMT. 0 or omitted At the end of the period 1 At the beginning of the period

PMT. 0 or omitted At the end of the period 1 At the beginning of the period PMT Calculates the payment for a loan based on constant payments and a constant interest rate. PMT(rate,nper,pv,fv,type) For a more complete description of the arguments in PMT, see the PV function. Rate

More information

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

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

More information

Mathematics. Rosella Castellano. Rome, University of Tor Vergata

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

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 Focus. Why Study Family finance? To Achieve Financial Success. Chapter Outline. Understanding Important Economic Trends. Your Goals in Life

Chapter Focus. Why Study Family finance? To Achieve Financial Success. Chapter Outline. Understanding Important Economic Trends. Your Goals in Life Chapter Focus Chapter 1: Financial Planning-- Why It s Important This chapter puts financial planning in perspective in relation to your goals in life. The key to financial success is to know your goals

More information