Personal Finance - Money and the Time Value of Money

Overview
In the Accounting lessons we looked at the “language” of business, in Marketing we looked at Products, Services, Promotion, and Distribution, and Business Finance is concerned with ways to fund a business. 

Really, though everything in business is focused on one thing – money. 

In this lesson  we will look at what money is and what functions it performs in society.  We will also look at some basic banking functions, primarily how “interest” is calculated so next time you finance a car or home you will have an understanding of the process.

MONEY

History
Societies began to develop when people turned from nomadic groups of hunters and gatherers into village dwelling farmers and crafts people.  For the many thousands of years that followed, people exchanged goods or services with each other as a way of allocating all resources evenly.  This system is called “barter” and is still used to a small degree today.  When people began traveling great distances to trade, carrying all of the goods needed for bartering became too difficult, and an alternative medium of exchange was needed. This new medium of exchange would have to have value, and be trusted by all participants.  “Money” was the result.

What IS money?
The following story is from a book written by Milton Friedman, who some call the “father of monetarism”.  Monetarism is the policy through which the government, through the Federal Reserve Banking System, controls the supply of money in the economy through the manipulation of key interest and reserve rates.  We looked at this in greater detail earlier in the course.  Dr. Friedman has always been interested in the concept of “money” and wrote a book in 1992 entitled Money Mischief, in which he chronicled some of the history of money, and the ways economists have attempted to explain it and the ways governments have tried to control it.  He begins the book by quoting from a book written in 1910 called The Island of Stone Money.  I have paraphrased a few sections to help in it’s understanding, as it was written in 1910 in what now seems an old-fashioned style of writing.

The Island of Stone Money

 -- From Money Mischief by Milton Friedman.

The island of Yap in Micronesia is a German colony, with a local population of about five or six thousand natives and a handful of German administrators. The island yields no metal, so the local population has taken recourse to stone as a medium of exchange. They call this currency “fei”, and it consists of large, solid, thick, stone wheels, ranging in diameter from a foot to twelve feet, having in the center a hole varying in size with the diameter of the stone, wherein a pole may be inserted sufficiently large and strong to bear the weight and facilitate transportation.  These stone “coins” were made from limestone found on an island some four hundred miles distant.  They were originally quarried and shaped on that island and the product brought to Yap by some venturesome native navigators, in canoes and on rafts.

A noteworthy feature of this stone currency is that it is not necessary for its owner to reduce it to possession.  After concluding a bargain which involves the price of a fei too large to be conveniently moved, its new owner is quite content to accept the bare acknowledgement of ownership and without so much as a mark to indicate the exchange, the coin remains undisturbed on the former owners premises.

My faithful old friend, Fatumak, assured me that there was in the village near by a family whose wealth was unquestioned, and yet no one, not even the family itself, had ever laid eye or hand on this wealth.  It consisted of an enormous fei, whereof the size is known only by tradition; for the past two or three generations it had been, and at that very time it was lying at the bottom of the sea!  Many years ago an ancestor of this family, on an expedition after fei, secured this remarkably large and exceedingly valuable stone, which was placed on a raft to be towed homeward.  A violent storm arose, and the party, to save their lives, were obliged to cut the raft adrift, and the stone sank out of sight.  When they reached home, they all testified that the fei was of magnificent proportions and of extraordinary quality, and that it was lost through no fault of the owner.  Thereupon it was universally conceded in their simple faith that the mere accident of its loss overboard was too trifling to mention, and that a few hundred feet of water off shore ought not to affect its marketable value, since it was all chipped out in proper form.  The purchasing power of that stone remains, therefore, as valid as if it were leaning visibly against the side of the owner’s house.

So what are the characteristics of money, and how do they apply to fei?

Characteristics of Money
In order to be fully useful, money must have the following characteristics:

1. Divisibility – users must be able to pay using a variety of sizes or amounts.  We have coins and bills of a multitude of sizes, and can go as low as one cent.  Most other modern currencies have similar properties, though some of the amounts may differ.  Until after World War II, England had a cumbersome (to me, anyway) division of the main currency, the pound. Each pound had six shillings, or 100 pence. Each shilling was broken evenly into pence.  So each shilling was about 16 and 2/3 pence – yuck!  [Are fei divisible? Yes - they come in different sizes. ]
    

2. Portability – most of us carry money with us.  It’s relatively light, and the larger bills allow us to carry even a large quantity of money in our pocket or purse.  The case on page 511 of the text talks about the lack of acceptance of the new gold dollar coin – people in the U.S. have rejected the coin, partly because of its weight.  [Fei don’t do too well in the category, though a method of transport (the hole and a pole) has been worked out.]
    

3. Durability – coins can last 30 years or more (then collectors probably get them!).  Paper money is less durable, but still can last for three to five years in circulation. [Fei is stone, which is very durable.]
    

4. Difficult to counterfeit – with the rise of highly efficient copiers, money has become more intricate in design and materials.  Some countries are experimenting with currencies embedded with electronic “smart chips” designed to prevent copying. [It seems that fei could be easily copied, but everyone on the island seems to have a personal relationship with each fei, thus making it hard to copy someone else’s fei without others noticing.]
    

5. Stability – possibly the most important characteristic necessary for money is stability.  Would we accept money as payment for a car if we didn’t think we could use that money to buy something of equal value to the car?  In order for money to be an effective medium of exchange, we have to have confidence that its value will remain stable.  This is one reason inflation is bad for the economy – inflation is a decrease in the value of the money, not the goods or services.  Inflation can get so bad that people begin to demand other things as payment instead of money – historically, gold has been a common alternative, though in post-WWII Germany it was a loaf of bread.  [The buying power of fei seems to remain very stable, even when under hundreds of feet of water!]

The Money Supply
So we have come back to our concept that inflation is bad, primarily because it decreases the value of our money, which in turn undermines its stability as a medium of exchange.  So how is the Money Supply measured, and who does the measuring?

First, it is the responsibility of the US Department of the Treasury to report on the Money Supply, and they measure the supply by looking at:

• The total amount of currency in circulation. 
• The total amount of coins in circulation.
• Demand Deposits - these are checking accounts, and accounts that act like checking accounts (Money Market accounts, some brokerage accounts, etc.)

The total is reported as the current value of “M1”.

Banks Create Money
The real key in this is that while the Treasury prints money, it is banks who create money by making loans.  The bank makes a loan and issues a cashiers check to the borrower, who takes it to their bank and exchanges it for money. That bank takes the cashiers check to the Treasury (via the Federal Reserve Banking System) and gets – CASH.  New lovely green dollars.

So, when “The Fed” raises rates, the banks raise their rates to consumers, who ask for fewer loans.  Fewer cashiers checks are issued, and viola!, less money in circulation.

INTEREST AND THE TIME VALUE OF MONEY

Interest
Interest is a charge for borrowing money.  The interest rate is a percentage of the amount borrowed over a specific period of time.   The prevailing market rate is composed of:

• The Real Rate of Interest that compensates lenders for postponing their own spending during the term of the loan.  [This is the real “price” of the money borrowed.]
• An Inflation Premium to offset the possibility that inflation may erode the value of the money during the term of the loan.  During a period of inflation, a given amount of money will purchase progressively fewer goods and services.  [Currently, this premium is very low.]
• Various Risk Premiums to compensate the lender for risky loans such as those made to borrowers with questionable credit ratings or for illiquid loans that the lender may not be able to readily resell.  [Remember “risk vs. return’?  The more risk the lender takes on, the more profit he expects to make.]

The first two components of the interest rate listed above, the real rate of interest and an inflation premium, collectively are referred to as the nominal risk-free rate.  In the US, the nominal risk-free rate can be approximated by the rate of 13 week US Treasury bills since they are generally considered to have a very small risk.

Simple Interest
Simple interest is calculated on the original principal only.  Accumulated interest from prior periods is not used in calculations for the following periods.

Simple Interest = p *  i  * n

- where:
    p = principal (original amount borrowed or loaned)
    i = interest rate for one period
    n = number of periods

Example: You borrow $10,000 for 3 years at 5% simple annual interest.

- interest = p *  i * n = 10,000 * .05 * 3 = 1,500  [$10,000 * .05 = $500 for each of three years.]

Compound Interest
Compound interest is calculated each period on the original principal and all  interest accumulated during past periods.  Although the interest may be stated as a yearly rate, the compounding periods can be yearly, semiannually, quarterly, or even continuously.

You can think of compound interest as a series of back-to-back simple interest contracts. The interest earned in each period is added to the principal of the previous period to become the principal for the next period.  For example, you borrow $10,000 for three years at 5% annual interest compounded annually:

- interest year 1 = p *  i  *  n = 10,000 x .05 * 1 = 500
- interest year 2 =  (p2 = p1 + i1) *  i  * n = (10,000 + 500) * .05 x 1 = 525
- interest year 3 = (p3 = p2 + i2) *  i *  n = (10,500 + 525)  * .05 x  1 = 551.25

Total interest earned over the three years = 500 + 525 + 551.25 = 1,576.25.   Compare this to 1,500 earned over the same number of years using simple interest.

Note that in comparing growth graphs of simple and compound interest, investments with simple interest grow in a linear fashion and compound interest results in geometric growth. So with compound interest, the further in time an investment is held the more dramatic the growth becomes.

Charts - Copyright© 1999-2001 studyfinance.com

THE TIME VALUE OF MONEY

The “Real Rate of Interest” described above is based on the idea that a dollar received today is more valuable than a dollar to be received in the future.

A dollar in hand today is worth more than a dollar to be received in the future because a dollar today can be invested so you will have more than a dollar in the future. 

                         – Rock Mathis, New Jersey Institute of Technology

Suppose you were given two choices:  $10,000 received today, or $12,000 received in five years time.

Which would you choose? 

Well, to answer this you would have to know how much more money you would need in five years to have the same buying power, at that time, as the $10,000 has today.

Keeping up with inflation might be your first concern.  How much would the original amount have to be in order to have grown with inflation.  Let’s say inflation is 3%.  If we add 3% per year we will have a chart that looks like this:   (Gee, this looks just like compound interest!)

Year One:       $10,000 * 3% (.03) = $300 + original $10,000 =      $10,300
Year Two:       $10,300 * 3% (.03) = $309 + last years $10,300 =   $10,609
Year Three:    $10,609 * 3% (.03) = $318 + last years $10,609 =   $10,927
Year Four:      $10,927 * 3% (.03) = $328 + last years $10,927 =   $11,255
Year Five:       $11,255 * 3% (.03) = $338 + last years $11,255 =   $11,593

At 3%, then, if you took the original $10,000 and it grew in value at just the inflation rate, you would have $11,593 in five years.  So at an assumed rate of 3%, the $12,000 in five years offer is better than $10,000 today. This is true, however, only if you believe that 3% is the maximum growth you could expect. 

If you expect a 5% growth rate, the chart looks like this:

Year One:       $10,000 * 5% (.05) = $500 + original $10,000 =      $10,500
Year Two:       $10,500 * 5% (.05) = $525 + last years $10,500 =   $11,025
Year Three:    $11,025 * 5% (.05) = $551 + last years $11,025 =   $11,576
Year Four:      $11,576 * 5% (.05) = $579 + last years $11,576 =   $12,155
Year Five:       $12,155 * 5% (.05) = $608 + last years $12,155 =   $12,763

$10,000 would grow to $12,763, so now you would choose the $10,000 today instead of the $12,000 in five years.

Now the opposite - what if we are given the choice of a payment in the future, or a lesser amount today; how do you choose?  (In the lottery, winners are given a choice, $1,000,000 over 20 years, or a lump sum today – what analysis should they use to figure which one to pick?)

Present Value
With Present Value, we can calculate the amount needed TODAY in order to have the same buying power as an amount to be received at a future date.    Let’s say we are going to receive $12,000 in five years; what is it worth today? (What is its present value?)

The calculation for this will tell us the Present Value of $12,000 in five years at 3%.

                                                                                                x
                                                                PV = FV/ (1+ i)   

                                                      -        where PV = present Value
                                                                       -         FV = Future Value
                                                                       -         i = interest rate per year or period
                                                                        -         x = number of years or periods          

                                                                                                                  5
                                                                PV = $12,000 / (1+.03)

                                                     = $12,000/ (1.03 * 1.03 * 1.03 * 1.03 * 1.03)

                                                     = $12,000/ 1.16

                                                     = $10,345

So given the choice of $10,000 today or $12,000 in five years, at 3% the Present Value of $12,000 is $10,345.  Since we would only be getting $10,000 today, we would choose the $12,000 in five years.

Now assume the same amount and length of time, except at an expected growth rate of  5%.

                                                                                                                  5
                                                                PV = $12,000 / (1+.05)

                                                     = $12,000/ (1.05 * 1.05 * 1.05 * 1.05 * 1.05)

                                                     = $12,000/ 1.28                                

                                                     = $9,375

At 5% the $12,000 in five years has a Present Value of only $9,375.   If we take the $10,000 today, we would potentially be able to have more than $12,000 in five years.  (As we learned about with compound interest, we would actually have $12,763 in five years!)  At 5%, take the $10,000 today.

The following link goes over these concepts again from a different angle.  http://www.studyfinance.com/lessons/timevalue/

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