duminică, 31 octombrie 2010

Imprecise Accounting

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What happened at Enron?


Everyone knows at least a little about the Enron story and the devastation it created in the lives of is employees. It's a story that belongs in any discussion of ethical accounting processes and what happens when accounting standards and ethics are discarded for personal greed.



Enron began in 1985 selling natural gas to gas companies and businesses. In 1996, energy markets were changed so that the price of energy could now be decided by competition among energy companies instead of being fixed by government regulations. With this change, Enron began to function more as a middleman than a traditional energy supplier, trading in energy contracts instead of buying and selling natural gas. Enron's rapid growth created excitement among investors and drove the stock price up. As Enron grew, it expanded into other industries such as Internet services, and its financial contracts became more complicated.



In order to keep growing at this rate, Enron began to borrow money to invest in new projects. However, because this debt would make their earnings look less impressive, Enron began to create partnerships that would allow it to keep debt off of its books. One partnership created by Enron, Chewco Investments (named after the Star Wars character Chewbacca) allowed Enron to keep $600 million in debt off of the books it showed to the government and to people who own Enron stock. When this debt did not show up in Enron's reports, it made Enron seem much more successful than it actually was. In December 2000, Enron claimed to have tripled its profits in two years.



In August 2001, Enron vice president Sherron Watkins sent an anonymous letter to the CEO of Enron, Kenneth Lay, describing accounting methods that she felt could lead Enron to "implode in a wave of accounting scandals." Also in August, CEO Kenneth Lay sent e-mails to his employees saying that he expected Enron stock prices to go up. Meanwhile, he sold off his own stock in Enron.



On October 22nd, the Securities and Exchange Commission (SEC) announced that Enron was under investigation. On November 8th, Enron said that it has overstated earnings for the past four years by $586 million and that it owed over $6 billion in debt by next year.



With these announcements, Enron's stock price took a dive. This drop triggered certain agreements with investors that made it necessary for Enron to repay their money immediately. When Enron could not come up with the cash to repay its creditors, it declared for Chapter 11 bankruptcy.


sâmbătă, 30 octombrie 2010

Personal Accounting




If you have a checking account, of course you balance it periodically to account for any differences between what's in your statement and what you wrote down for checks and deposits. Many people do it once a month when their statement is mailed to them, but with the advent of online banking, you can do it daily if you're the sort whose banking tends to get away from them.





You balance your checkbook to note any charges in your checking account that you haven't recorded in your checkbook. Some of these can include ATM fees, overdraft fees, special transaction fees or low balance fees, if you're required to keep a minimum balance in your account. You also balance your checkbook to record any credits that you haven't noted previously. They might include automatic deposits, or refunds or other electronic deposits. Your checking account might be an interest-bearing account and you want to record any interest that it's earned.





You also need to discover if you've made any errors in your recordkeeping or if the bank has made any errors.





Another form of accounting that we all dread is the filing of annual federal income tax returns. Many people use a CPA to do their returns; others do it themselves. Most forms include the following items:





Income - any money you've earned from working or owning assets, unless there are specific exemptions from income tax.





Personal exemptions - this is a certain amount of income that is excused from tax.





Standard deduction - some personal expenditures or business expenses can be deducted from your income to reduce the taxable amount of income. These expenses include items such as interest paid on your home mortgage, charitable contributions and property taxes.





Taxable income - This is the balance of income that's subject to taxes after personal exemptions and deductions are factored in.


joi, 28 octombrie 2010

Financial Accounting: A Mercifully Brief Introduction


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This book provides an easy to read concise introduction to accounting. The book is designed to help small business owners, accounting students, bookkeepers and non profit managers grasp the fundamentals they need to interpret and analyze financial statements. No prior accounting or business background is needed to understand the material in this book.

The Fundamental Accounting Equation
Recording Transactions
Cash versus Accrual Accounting
Receivables and Payables
Deferred Revenue and Prepaid Expenses
Fixed Assets and Depreciation
Inventory and Cost of Goods Sold
Adjusting and Closing the Books
Compiling the Financial Statements
Gauging the Reliability of Financial Statements
For the person who has no knowledge of accounting and wants to understand the very basics this book is indeed a good brief introduction. The author makes a good point of the fact that most introductory accounting texts spend a great deal of time covering the basics of transaction entry. In today's marketplace the software packages take care of these details of ensuring double entry occurs and the entries balance. When that information is removed you end up with the very basics of accounting including the basic accounting equation, cash and accrual accounting, receivables and payables, fixed assets, inventory, and financial statements. Explained at a level that a reader with no previous knowledge of accounting can follow the author does provide a mercifully brief introduction that is only the basics needed for everyday work.

Harold McFarland

This is a great book for small businesses. I've started recommending it to my clients who are doing their own bookkeeping (and all you professionals know what a nightmare that is!) and to bookkeepers who find themselves doing balance sheet accounting without a good background in the real story of debits and credits. This book covers the basics in an accessible, jargon-less prose yet still covers the essential points. I'm suggesting that this be a reference book my clients keep in their offices. That way they have a quick reference guide for themselves or their employees. Hopefully, when they go through 3 bookkeepers in a year the learning curve will be less steep than usual for the new employees, and I'll get fewer "just a quick question" phone calls during tax season.

M. Equinox EA

It is refreshing to read an accounting text with a liberal arts background. This author challenges you to think about what is useful to accounting but also its abuses. Good introduction for the curious reader.

Daniel J. Guilfoil

This book is an essential primer for small business owners who started their enterprise based upon their technical or creative skills - but now need to understand the basic terminology and 'physiology' of financial accounting in greater detail.

It is written in a very free flowing style and is as unthreatening an accounting text as I have encountered. The real life examples and Marxist humor (Groucho - not Karl) help make it that much more accessible. My favorite quote from the book, "Accounting can be accrual mistress." (These are the jokes folks.)

Robert Walter AEI

Financial Accounting: A Mercifully Brief Introduction is an informative and well-written primer on a range of important concepts necessary to ?get a handle on? the financial basics that small business owners and allied professionals frequently confront. The author successfully employs humor in developing scenarios, examples, and explanations which remain in the reader?s mind and make these oftentimes abstruse subjects understandable. The Summaries, Exercises and Problems sections of the book are particularly effective teaching tools. I found the most interesting and useful Chapters to be Chapter One (Introduction: Difficult Measurement Problems), Chapter 7 (Fixed Assets and Depreciation Methods), and particularly Chapter 10 (Financial Statement Reliability), for its treatment of embezzlement prevention and related issues.

I have practiced law for almost 33 years, and have represented many small businesses during that time. I am pleased to have encountered this book, which I will highly recommend as a very helpful tool for business owners and others in understanding, approaching and evaluating accounting issues.

Sara Clarenbach,Attorney

Financial Accounting is generally thought of as a very precise science. This 126 page book seeks to dispel the myth. In his own words, author Michael Sack Elmaleh has managed to erase the ill effects of nearly 30 years of formal accounting education and teaching. Michael has written an engaging and thoroughly readable overview of the accounting process so that you can actually understand it! The book is written primarily for small business owners and advisors to small business. He demonstrates how accounting information is organized and collected, and how the information contained in financial statements both informs and misinforms statement users. Since important management and investment decisions are often based on these statements it?s vital that small business owners gain a better understanding of what this information means and its inherent limitations.

John Nessell, President Restaurant Resource Group, Inc.

An easy to read, enjoyable guide to the basic principles that underpin accounting systems in businesses. Particularly useful in an educational setting as a supplementary reading to a technical textbook. However, also has a market for small business owners wanting to get to grips with the basics of how to get the most from their accounting function.

Dr. Diane L. Boone, University of Maine, Augusta

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duminică, 24 octombrie 2010

Building Cash Reserves




Building a financial cushion for your business is never easy. Experts say that businesses should have anywhere from six to nine months worth of income safely stored away in the bank. If you're a business grossing $250,000 per month, the mere thought of saving over $1.5 million dollars in a savings account will either have you collapsing from fits of laughter or from the paralyzing panic that has just set in. What may be a nice well-advised idea in theory can easily be tossed right out the window when you're just barely making payroll each month. So how is a small business owner to even begin a prudent savings program for long-term success?





Realizing that your business needs a savings plan is the first step toward better management. The reasons for growing a financial nest egg are strong. Building savings allows you to plan for future growth in your business and have ready the investment capital necessary to launch those plans. Having a source of back-up income can often carry a business through a rough time.



When market fluctuations, such as the dramatic increase in gasoline and oil prices, start to affect your business, you may need to dip into your savings to keep operations running smoothly until the difficulties pass. Savings can also support seasonal businesses with the ability to purchase inventory and cover payroll until the flush of new cash arrives. Try to remember that you didn't build your business overnight and you cannot build a savings account instantly either.





Review your books monthly and see where you can trim expenses and reroute the savings to a separate account. This will also help to keep you on track with cash flow and other financial issues. While it can be quite alarming to see your cash flowing outward with seemingly no end in sight, it's better to see it happening and put corrective measures into place, rather than discovering your losses five or six months too late.


sâmbătă, 23 octombrie 2010

Investing and financing




Another portion of the statement of cash flows reports the investment that the company took during the reporting year. New investments are signs of growing or upgrading the production and distribution facilities and capacity of the business. Disposing of long-term assets or divesting itself of a major part of its business can be good or bad news, depending on what's driving those activities. A business generally disposes of some of its fixed assets every year because they reached the end of their useful lives and will not be used any longer. These fixed assets are disposed of or sold or traded in on new fixed assets. The value of a fixed asset at the end of its useful life is called its salvage value. The proceeds from selling fixed assets are reported as a source of cash in the investing activities section of the statement of cash flows. Usually these are very small amounts.





Like individuals, companies at times have to finance its acquisitions when its internal cash flow isn't enough to finance business growth. financing refers to a business raising capital from debt and quity sources, by borrowing money from banks and other sources willing to loan money to the business and by its owners putting additional money in the business. The term also includes the other side, making payments on debt and returning capital to owners. it includes cash distributions by the business from profit to its owners.





Most business borrow money for both short terms and long terms. Most cash flow statements report only the net increase or decrease in short-term debt, not the total amounts borrowed and total payments on the debt. When reporting long-term debt, however, both the total amounts and the repayments on long-term debt during a year are generally reported in the statement of cash flows. These are reported as gross figures, rather than net.


miercuri, 20 octombrie 2010

Time Values of Money Concepts

Michael Sack Elmaleh, C.P.A., C.V.A.

The idea that a dollar available today is not equivalent to a dollar available at some point in the future is drilled into all accounting, economic and finance students heads very early in their professional training. The basic principle, we are taught, is that a dollar in the future is not worth as much as a dollar today. When we examine these ideas closely we find that they contain much subtlety and complexity.

The rudimentary concepts of present values usually are explained in terms of a series of simple investment versus consumption choices. Here is an example that will demonstrate that converting future dollars into present dollars is not just a matter of making some compound interest computations on a calculator.

The Inheritance

Lola inherits $10,000. She can spend the money now on a cruise, or she can invest it in any of a wide variety of investments, or she can loan the money to her nephew for five years to help pay his college tuition. The nephew is hard working and honest, so she is reasonably sure that the loan would be repaid. But she wonders if she makes the loan if she should charge interest on the loan, and if so how much? How should she think about her options?

In our finance and accounting classes we gloss over a host of difficult questions and look at the problem this way: If she lends the nephew the money for five years, she will be foregoing the ability to go on the cruise or invest the money. So lending or investing the money now involves deferring the satisfaction of taking the cruise. So how much should she charge for delaying her cruise?

Suppose Lola lends her nephew the money. Well at the very least the nephew should pay enough interest so that Lola will accumulate enough cash five years from now to afford a comparable cruise. The assumption here is that inflation will cause the cost of the cruise will go up. So the interest charged the nephew should cover the expected loss of purchasing power to inflation.

But figuring out the interest rate to accomplish this is a very tricky matter. First off the purchasing power of dollars can actually increase, rather than decrease. A dollar today may sometimes buy less goods and services than it will tomorrow. In the real world, the variance of purchasing power measured in dollars depends on what categories of potential goods and services are being considered. For some sectors the purchasing power of nominal dollars has gone up over time. There are many obvious examples such as computer technology and telecommunications. The cost of food relative to other necessities rises and falls but is much less than it was one hundred years ago.

In finance and accounting the interest rates used to convert future dollars to present dollars are usually called discount and capitalization rates. The rates that we use to convert future to present values cannot fully and accurately capture the potential loss of the purchasing power of nominal dollars. Although prevailing interest rates do partially reflect market expectations about the direction and extent of inflation or deflation, these expectations do not fully determine interest rates.

Now there are all kinds of other issues besides the purchasing power of the dollar at stake in the choice as to whether to spend, lend or invest. The timing of personal satisfaction from consumption might be the source of a fundamental time value principle: we might say that in principle immediate satisfaction is always preferred to delayed satisfaction. A time value computation should then attempt to measure and reflect this loss of satisfaction due to delay. Perhaps we might say that the longer the delay the greater the loss in satisfaction. But alas, we are defeated by the complexity of human preferences.

In our example Lola may think that with five more years of life experience she will enjoy the cruise more than she would today. So from the standpoint of personal utility, it definitely is not always true that present gratification (and the dollars needed to secure that satisfaction) are necessarily worth more than the delayed satisfaction to be acquired with future dollars.

There is another wrinkle to the story. It is even possible for Lola to believe quite accurately that the satisfaction of helping her nephew will be deeper and longer lasting than the satisfaction she will get from taking the cruise. Therefore, the choice of lending the money to her nephew versus going on the cruise immediately is not simply a choice between deferring satisfaction versus not deferring, but rather a choice between varying levels of current satisfaction.

These are indeed messy considerations and we finance and accounting types do not like messy considerations. There is simply no universally applicable straightforward way to measure these kinds of consumption preferences. So whatever we are trying to measure when we perform present value computations, it cannot simply be about personal consumption preferences.

There is of course the matter of risk. Not just the risk that the nephew will fail to pay the loan back. There is a risk that Lola may not be alive five years from now. Or she may become physically or mentally impaired. So deferring the cruise for five years may be tantamount to deferring it forever. From the traditional finance point of view Lola should expect some compensation for bearing the risk of deferring her cruise to lend the money to her nephew.

However, barring extreme health problems, advanced age or high genetic risk Lola is likely to believe, like most other people, that they will live forever. So she will greatly discount the probability of death or impairment. This is good news for the finance theorists because they do not want to have to include the probabilities of death and disability into present value computations. So from the standpoint of standard finance theory the probability of events like death and disability are treated as zero.

What of the risk of the nephew not paying the loan back? This is not a risk that Lola is likely to discount to zero. Nonetheless there is not an obvious answer to how she might adjust interest rates to reflect this risk. Standard finance theory says that she ought to get a higher interest rate for a riskier loan than a safer one. In a paradoxical way charging a higher rate of interest to her nephew might actually make it harder for him to pay back the loan and thus actually increase the probability of default.

In the realm of personal utility preferences and purchasing power there is no absolute rule for time values of money. However, in an important restricted economic sense there is an absolute time value principle. If we restrict our attention simply to investment opportunities, we can say as a nearly absolute principle that present dollars are worth more than future dollars. What we assume is that as long as there are investment opportunities that yield some positive return, nominal future dollars will not be equivalent to current dollars. The difference will be based on the opportunity cost of failing to invest in some investment that would yield a positive return.

In Lola?s case we should put aside all questions about the utility of consumption, risk of repayment, and purchasing power loss and simply compute the amount of interest she could receive if she invested the $5,000 rather than loan the money to her nephew. The issue of the loan to her nephew now becomes a choice not between a cruise and a loan, but between the loan and some other form of investment. As long as Lola has at least one investment alternative that yields some form of interest or dividend beyond the mere return of her original principal, then lending the money to her nephew imposes a definite cost to her: by lending the money to her nephew she foregoes the interest or dividends she could be realizing over the term of the loan. This is the opportunity cost of the loan.

Calculating this cost is much easier than figuring out the costs and benefits associated with lost or gained satisfaction from going on a cruise now rather than five years from now. The computation is simpler, but there is still an important conceptual questions that must be resolved. We must decide which of the vast multitude of investment options should be used to reflect this opportunity cost. The answer to this question is not obvious. Lola has a large range of investment opportunities with different potential levels of risk and return. Generally, the greater Lola?s risk tolerance, the greater the possible rates of return.

These are sticky issues. For the broadest use of time value computations we want to avoid considerations of individual differences in risk tolerances and other idiosyncratic constraints on investment. In the broadest application of time value computations we are content to identify the opportunity cost of investment with the safest possible investment alternative available to determine the amount of foregone interest or dividends. Usually the risk free treasury rate is utilized.

Here is a calculation involving Lola?s $5,000 inheritance on the assumption that the safest treasury rate is 5%. This calculation projects the Lola?s accumulation of principal and interest assuming she reinvests the interest income and interest is compounded annually.
So starting with $5,000 Lola would accumulate $6,381.41 by the end of year five.

Now here is a general formula for computing the future value of a lump sum:

The above formula and example assumes that all interest is reinvested or compounded. Importantly, the formula allows us to convert one lump sum payment in the future to an equivalent present value and vice versa. By rearranging terms we arrive at the formula for converting a future value into a present value:


Now these formulas can be expanded to cover cases of multiple future payments and a short cut can be applied if the future payments are equal. If we apply the above PV formula to each payment we can see how this works:

When you encounter present value computations it is important to remember that these conversions of future expected dollars do not necessarily reflect utility preferences or differences in purchasing power. These computations simply measure the opportunity cost associated with foregoing the use of dollars today in a very safe investment. If Lola lends her nephew $5,000 today over five years, in that five years she could have earned a certain amount of interest if she invested in treasury bonds. It would seem reasonable that she charge her nephew an interest rate comparable to the interest she could have earned had she simply invested the money.

By the author of the acclaimed book Financial Accounting: A Mercifully Brief Introduction. To get your copy for only $9.95 + $3 shipping click here.

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duminică, 17 octombrie 2010

What is financial window dressing?




Financial managers can do certain things to increase or decrease net income that's recorded in the year. This is called profit smoothing, income smoothing or just plain old window dressing. This isn't the same as fraud, or cooking the books.





Most profit smoothing involves pushing some amount of revenue and/or expenses into other years than they would normally be recorded. A common technique for profit smoothing is to delay normal maintenance and repairs. This is referred to as deferred maintenance. Many routine and recurring maintenance costs required for autos, trucks, machines, equipment and buildings can be delayed, or deferred until later.





A business that spends a significant amount of money for employee training and development may delay these programs until the next year so the expense in the current year is lower.





A company can cut back on its current year's outlays for market research and product development.





A business can ease up on its rules regarding when slow-paying customers are written off to expense as bad debts or uncollectible accounts receivable. The business can put off recording some of its bad debts expense until the next reporting year.





A fixed asset that is not being actively used may have very little current or future value to a business. Instead of writing off the un-depreciated cost of the impaired asset as a loss in the current year, the business might delay the write-off until the next year.





You can see how manipulating the timing of certain expenses can make an impact on net income. This isn't illegal although companies can go too far in massaging the numbers so that its financial statements are misleading. For the most part though, profit smoothing isn't much more than robbing Peter to pay Paul. Accountants refer to these as compensatory effects. The effects next year offset and cancel out the effects in the current year. Less expense this year is balanced by more expense the next year.


vineri, 15 octombrie 2010

Time Values of Money Concepts

Michael Sack Elmaleh, C.P.A., C.V.A.

The idea that a dollar available today is not equivalent to a dollar available at some point in the future is drilled into all accounting, economic and finance students heads very early in their professional training. The basic principle, we are taught, is that a dollar in the future is not worth as much as a dollar today. When we examine these ideas closely we find that they contain much subtlety and complexity.

The rudimentary concepts of present values usually are explained in terms of a series of simple investment versus consumption choices. Here is an example that will demonstrate that converting future dollars into present dollars is not just a matter of making some compound interest computations on a calculator.

The Inheritance

Lola inherits $10,000. She can spend the money now on a cruise, or she can invest it in any of a wide variety of investments, or she can loan the money to her nephew for five years to help pay his college tuition. The nephew is hard working and honest, so she is reasonably sure that the loan would be repaid. But she wonders if she makes the loan if she should charge interest on the loan, and if so how much? How should she think about her options?

In our finance and accounting classes we gloss over a host of difficult questions and look at the problem this way: If she lends the nephew the money for five years, she will be foregoing the ability to go on the cruise or invest the money. So lending or investing the money now involves deferring the satisfaction of taking the cruise. So how much should she charge for delaying her cruise?

Suppose Lola lends her nephew the money. Well at the very least the nephew should pay enough interest so that Lola will accumulate enough cash five years from now to afford a comparable cruise. The assumption here is that inflation will cause the cost of the cruise will go up. So the interest charged the nephew should cover the expected loss of purchasing power to inflation.

But figuring out the interest rate to accomplish this is a very tricky matter. First off the purchasing power of dollars can actually increase, rather than decrease. A dollar today may sometimes buy less goods and services than it will tomorrow. In the real world, the variance of purchasing power measured in dollars depends on what categories of potential goods and services are being considered. For some sectors the purchasing power of nominal dollars has gone up over time. There are many obvious examples such as computer technology and telecommunications. The cost of food relative to other necessities rises and falls but is much less than it was one hundred years ago.

In finance and accounting the interest rates used to convert future dollars to present dollars are usually called discount and capitalization rates. The rates that we use to convert future to present values cannot fully and accurately capture the potential loss of the purchasing power of nominal dollars. Although prevailing interest rates do partially reflect market expectations about the direction and extent of inflation or deflation, these expectations do not fully determine interest rates.

Now there are all kinds of other issues besides the purchasing power of the dollar at stake in the choice as to whether to spend, lend or invest. The timing of personal satisfaction from consumption might be the source of a fundamental time value principle: we might say that in principle immediate satisfaction is always preferred to delayed satisfaction. A time value computation should then attempt to measure and reflect this loss of satisfaction due to delay. Perhaps we might say that the longer the delay the greater the loss in satisfaction. But alas, we are defeated by the complexity of human preferences.

In our example Lola may think that with five more years of life experience she will enjoy the cruise more than she would today. So from the standpoint of personal utility, it definitely is not always true that present gratification (and the dollars needed to secure that satisfaction) are necessarily worth more than the delayed satisfaction to be acquired with future dollars.

There is another wrinkle to the story. It is even possible for Lola to believe quite accurately that the satisfaction of helping her nephew will be deeper and longer lasting than the satisfaction she will get from taking the cruise. Therefore, the choice of lending the money to her nephew versus going on the cruise immediately is not simply a choice between deferring satisfaction versus not deferring, but rather a choice between varying levels of current satisfaction.

These are indeed messy considerations and we finance and accounting types do not like messy considerations. There is simply no universally applicable straightforward way to measure these kinds of consumption preferences. So whatever we are trying to measure when we perform present value computations, it cannot simply be about personal consumption preferences.

There is of course the matter of risk. Not just the risk that the nephew will fail to pay the loan back. There is a risk that Lola may not be alive five years from now. Or she may become physically or mentally impaired. So deferring the cruise for five years may be tantamount to deferring it forever. From the traditional finance point of view Lola should expect some compensation for bearing the risk of deferring her cruise to lend the money to her nephew.

However, barring extreme health problems, advanced age or high genetic risk Lola is likely to believe, like most other people, that they will live forever. So she will greatly discount the probability of death or impairment. This is good news for the finance theorists because they do not want to have to include the probabilities of death and disability into present value computations. So from the standpoint of standard finance theory the probability of events like death and disability are treated as zero.

What of the risk of the nephew not paying the loan back? This is not a risk that Lola is likely to discount to zero. Nonetheless there is not an obvious answer to how she might adjust interest rates to reflect this risk. Standard finance theory says that she ought to get a higher interest rate for a riskier loan than a safer one. In a paradoxical way charging a higher rate of interest to her nephew might actually make it harder for him to pay back the loan and thus actually increase the probability of default.

In the realm of personal utility preferences and purchasing power there is no absolute rule for time values of money. However, in an important restricted economic sense there is an absolute time value principle. If we restrict our attention simply to investment opportunities, we can say as a nearly absolute principle that present dollars are worth more than future dollars. What we assume is that as long as there are investment opportunities that yield some positive return, nominal future dollars will not be equivalent to current dollars. The difference will be based on the opportunity cost of failing to invest in some investment that would yield a positive return.

In Lola?s case we should put aside all questions about the utility of consumption, risk of repayment, and purchasing power loss and simply compute the amount of interest she could receive if she invested the $5,000 rather than loan the money to her nephew. The issue of the loan to her nephew now becomes a choice not between a cruise and a loan, but between the loan and some other form of investment. As long as Lola has at least one investment alternative that yields some form of interest or dividend beyond the mere return of her original principal, then lending the money to her nephew imposes a definite cost to her: by lending the money to her nephew she foregoes the interest or dividends she could be realizing over the term of the loan. This is the opportunity cost of the loan.

Calculating this cost is much easier than figuring out the costs and benefits associated with lost or gained satisfaction from going on a cruise now rather than five years from now. The computation is simpler, but there is still an important conceptual questions that must be resolved. We must decide which of the vast multitude of investment options should be used to reflect this opportunity cost. The answer to this question is not obvious. Lola has a large range of investment opportunities with different potential levels of risk and return. Generally, the greater Lola?s risk tolerance, the greater the possible rates of return.

These are sticky issues. For the broadest use of time value computations we want to avoid considerations of individual differences in risk tolerances and other idiosyncratic constraints on investment. In the broadest application of time value computations we are content to identify the opportunity cost of investment with the safest possible investment alternative available to determine the amount of foregone interest or dividends. Usually the risk free treasury rate is utilized.

Here is a calculation involving Lola?s $5,000 inheritance on the assumption that the safest treasury rate is 5%. This calculation projects the Lola?s accumulation of principal and interest assuming she reinvests the interest income and interest is compounded annually.
So starting with $5,000 Lola would accumulate $6,381.41 by the end of year five.

Now here is a general formula for computing the future value of a lump sum:

The above formula and example assumes that all interest is reinvested or compounded. Importantly, the formula allows us to convert one lump sum payment in the future to an equivalent present value and vice versa. By rearranging terms we arrive at the formula for converting a future value into a present value:


Now these formulas can be expanded to cover cases of multiple future payments and a short cut can be applied if the future payments are equal. If we apply the above PV formula to each payment we can see how this works:

When you encounter present value computations it is important to remember that these conversions of future expected dollars do not necessarily reflect utility preferences or differences in purchasing power. These computations simply measure the opportunity cost associated with foregoing the use of dollars today in a very safe investment. If Lola lends her nephew $5,000 today over five years, in that five years she could have earned a certain amount of interest if she invested in treasury bonds. It would seem reasonable that she charge her nephew an interest rate comparable to the interest she could have earned had she simply invested the money.

By the author of the acclaimed book Financial Accounting: A Mercifully Brief Introduction. To get your copy for only $9.95 + $3 shipping click here.

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