This is opportunity cost at its finest action.

PROBABILITY OF VALUE REALIZATION


What do you do if there are multiple bargains at the same time?

How do you distinguish which ones offer better value than the other ones?

One stock is trading at 40% below its intrinsic value and another at 70% below its intrinsic value.

• WHICH ONE DO YOU INVEST INTO?
• WHAT IF ONE OF THE INVESTMENTS HAS A GREATER PROBABILITY OF VALUE REALIZATION THAN THE OTHER?

Note: The best absolute value may not always be your best investment choice.



As a focused value investors, we want no more than a few investments in the portfolio at any one time.

As the number of investments in the portfolio build up, every decision make will be based on whether it is a better investment in comparison to any of the current holdings.

This is opportunity cost at its finest action.

Investment Decisions and Fundamentals of Value

Investment Decision Rules:

Accept all investments with Net Present Value greater than Zero.

Accept all investments with Rates of Return greater than their Opportunity Costs of Capital





@ time 39.00

An example:

You are considering an investment opportunity that costs $100,000 and promises to return 10%.

A comparable investment in the financial market returns 15%.

A bank offers to lend you $100,000 at 8% with no conditions.


Questions:

1.  Do you invest $100,000 in the investment opportunity?

Answer:  NO

2.  What is the investment's cost of capital?

Answer:  15%.


Reasons:

You should invest the $100,000 in the financial market that returns 15%.

The financial market provides the investing return standards against which other investments are evaluated.

Financing by the bank loan at 8% was irrelevant to the investment decision.

The investment decision and the financing decision are separate and independent decisions.

After you have made the investment decision, thus:

You are considering an investment opportunity that costs $100,000 and promises to return 10%.

A comparable investment in the financial market returns 15%.

Then you make the financing decision, thus:

A bank offers to lend you $100,000 at 8% with no conditions.

Capital Management in Personal Finance

A simple equation in finance describes your approach to capital management:

Assets = Debt + Equity

Everything you own was funded either by incurring debt or by expending your own resources.

Subtracting all your debt from the total value of your assets shows you how much equity (net wealth) you have accumulated.

The BALANCE of debt and equity you have used to fund the value of your assets is a critical portion of your financial management strategy, known as CAPITAL MANAGEMENT.



Cost of capital

Whether you use debt or equity to fund your asset ownership, there are COSTS OF DEBT and EQUITY involved, known collectively as COST OF CAPITAL.

The cost of debt refers to the amount of interest you will pay over the life of your debt.

Most people don't realise that there is also a cost associated with using your own resources to purchase assets, known as the "cost of equity".

"OPPORTUNITY COST" is the value of the next best option; so if you have the choice between purchasing furniture and keeping your money in a bank account, the opportunity cost of buying the furniture is equal to the amount of interest you would have earned by keeping your money in the account.

This makes most purchases far more expensive than people realise, since each purchase you make not only includes spending money, but also losing any earnings on that money if you hadn't spent it.




Effective capital management

Effective capital management requires you to assess the cheapest sources of both debt and equity being used to fund your assets, and also to find the proper balance of equity and debt so that you choose the cheaper of the two at any given point.

As you come to rely on one more than the other, its costs will start to increase; the more debt you have, the more lenders will start to charge you in interest rates as a result of the shift in your credit report.

If you rely more on equity, you will begin to pull assets which are more valuable, making debt cheaper compared to the money you would be losing by selling your investments.

The goal is to maintain the lowest cost of capital possible, using variations on the core equation:


Cost of capital 
= Cost of Equity + Cost of Debt
= [(E/A)*CE] + [(D/A)*CD]

E= The amount of equity you have
D= The amount of debt you have
A= The total value of your assets (D+E)
CE= The average cost of your equity (the money you would earn o the next best option)
CD= The average cost of your debt (the interest payments you will make)

E/A= weight of source of capital from equity
D/A= weight of source of capital from debt

You can assess whether your debt or equity is costing you more money from the above equation, to help you to determine the proper balance.

If these are not about equal, it is likely you could fund your assets more cheaply.




Are your assets generating returns more than the cost of capital?

Adding the cost of equity to the cost of debt gives you the total cost of capital.

The question remaining is whether your assets, on average, are generating MORE value than they are costing.

If yes, good for you.

If not, keep trying, because  right now you are losing money on your assets.

This equation only gives you a rough idea of your cost of capital, though.

The more precise you can be, even to the point of breaking down each source of debt and equity individually, the more accurate your calculation will be.

Investment Decisions and Fundamentals of Value

@ 6.47 min
Managers should invest in real assets and should not be involved in investing in financial assets which the shareholders can do on their own.


What is a Valuable Investment Opportunity?

1. An investment worth more than it costs.
2. An investment with a return greater than its opportunity cost of capital.

Why does an asset have value?

1. An asset provides a return on investment in the form of future cash payments.
2. When we make an investment, we are buying a cash flow stream.
3. When we assess the value of an asset, we assess the value of its cash flow stream.

Asset valuation is the answer to the following question:

What is the PRESENT VALUE of a Future Cash Flow Stream?

@ 13 min

What determines the present value of a cash flow stream?

1. Magnitude
2. Timing
3. Risk

@ 15 min

Risk of the cash flow stream

Consider 2 cash flows streams A and B

A pays $100 for certain.

B may pay as much as $100 but may pay as little as $60.

Choice:  Choose A

We are risk adverse.  A SAFE dollar is worth more than a RISKY dollar.

@ 17 min

Time Value of Money

Time value of money is the rate of exchange between present dollars and future dollars established in the financial market.

Time value of money is reflected in the rates of return available to all investors in the financial markets.

@ 18.30

Risk and Return Relationship

Safe dollars are more valuable than risky dollars

Risk averse investors prefer safe investments.

How do you induce risk averse investors to take a risky investment?

Risky investments must promise higher returns to induce investors to undertake them.

In the financial markets, investments are priced so that the higher the risk, the higher the expected return.

Risky investment's rate of return reflects a risk premium that rewards investors for taking on the investment's risk.

Investment's opportunity cost of capital is the return forgone on an investment in the financial market of comparable risk.

Riskier investments have higher opportunity costs of capital.

Rate of Return = Time Value of Money + Risk Premium

Rate of Return = Risk Free Rate + Risk Premium

@ 21.30

Value of an asset:

1.  Forecast the magnitude and timing of the cash flow stream over its economic life.

2.  Assess the risk of the cash flow stream.

3.  Value the cash flow stream given its magnitude, timing, and risk at its opportunity cost of capital.

Market Value and Rate of Return

@ 23 min

The cash flow stream's value is determined by the amount of money needed today to recreate its magnitude, timing, and risk in the financial market at its opportunity cost of capital.

@ 24.50

What is the investment's opportunity cost of capital?

PV = FV / (1+r)

The value of an investment asset is the money needed today to recreate its future cash flow stream in the financial market at its opportunity cost of capital (r).

The value of an investment asset is the present value of its future cash flow stream.

How much is the asset worth, and how much does it cost?

• What is the value of the asset's future cash flow stream today, and how much does it cost?
• What is its PRESENT VALUE, and how much does it cost?
• What is the prevent value net of cost?
• What is its NET PRESENT VALUE?

NPV = PV of Investment - Cost

A valuable investment opportunity is worth more than it costs.

@ 31 min

If 

NPV > 0, investment is worth more than it costs

NPV < 0, investment costs more than it is worth.

NPV =0, investment costs as much as it is worth.

NPV is the absolute dollar change in wealth from the acceptance of an investment opportunity.

Look for investment opportunities in those with positive NPV projects.

What is a valuable investment opportunity?

1. An investment with a net present value greater than zero.
2. An investment with a return greater than its opportunity cost of capital.

Investment Decision Rules

1. Accept all investments with Net Present Values greater than Zero.
2. Accept all investments with rates of return greater than their opportunity costs of capital.

@ 34 min

Example using the Net Present Value Rule

NPV = PV - Cost 

> 0, therefore we accept the project.

@ 35 min

Example using the Rates of Return greater than their Opportunity Cost of Capital

Rate of Return = 20%.

Opportunity cost of capital = 12%.

Therefore, accept the project.

@ 36.50

You are considering an investment opportunity that costs $100,000 and promises to return 10%.

A comparable investment in the financial market returns 15%.

A bank offers to lend you $100,000 at 8% with no conditions.

Do you invest $100,000 in the investment opportunity?  NO.

Financing cost = 8%.

What is the investment's cost of capital? 15%.

The cost of capital is the return on comparable investments in the financial market, that is 15%.

The cost of capital is not the cost of raising the money to finance the investment.  That is a financing decision and not an investment decision.  

That return in the financial market is the standard against which other investment opportunities are evaluated.

The financing by the bank loan is irrelevant to the investment decision.

Investment decision and financing decision are separate and independent decisions.

First make the investment decision, after that, then make the financing decision.

Thanks for pointing this video out to me.
<  I found these very helpful : https://www.youtube.com/watch?v=ZtQKrPBz3XA https://www.youtube.com/watch?v=4q2Xcbrazhw on Financial Ratio Tutorial Anonymous on 4/7/13 >

Ways to Limit Opportunity Cost - Most Important is holding Part of your Portfolio in Cash

The most important determinant of whether investors will incur opportunity cost is whether or not part of their portfolios is held in cash.  

• Maintaining moderate cash balances or owning securities that periodically throw off appreciable cash is likely to reduce the number of foregone opportunities. 

Investors can manage portfolio cash flow (defined as the cash flowing into a portfolio minus outflows) by giving preference to some kinds of investments over others.  Portfolio cash flow is greater for securities of shorter duration (weighted average life) than those of longer duration.  Portfolio cash flow is also enhanced by investments with catalysts for the partial or complete realization of underlying value.

• Equity investments in ongoing businesses typically throw off only minimal cash through payment of dividends.  
• The securities of companies in bankruptcy and liquidation, by contrast, can return considerable liquidity to a portfolio within a few years of purchase.  
• Risk-arbitrage investments typically have very short lives, usually turning back into cash, liquid securities, or both in a matter of weeks or months.

An added attraction of investing in risk-arbitrage situations, bankruptcies, and liquidations is that not only is one's initial investment returned to cash, one's profits are as well.

Another way to limit opportunity cost is through hedging. 

• A hedge is an investment that is expected to move in a direction opposite that of another holding so as to cushion any price decline. 
• If the hedge becomes valuable, it can be sold, providing funds to take advantage of newly created opportunities .

If you are buying sound value at a discount, do short-term price fluctuations matter?

In the long run, they do not matter much; value will ultimately be reflected in the price of a security.  

• Indeed, ironically, the long-term investment implication of price fluctuations is in the opposite direction from the near-term market impact.  
• For example, short-term price declines actually enhance the returns of long-term investors.  

There are, however several eventualities in which near-term price fluctuations do matter to investors. 

1.  Security holders who need to sell in a hurry are at the mercy of market prices.  The trick of successful investors is to sell when they want to, not when they have to.  Investors who may need to sell should not own marketable securities other than U.S. Treasury bills.

2.  Near-term security prices also matter to investors in a troubled company.  If a business must raise additional capital in the near term to survive, investors in its securities may have their fate determined, at least in part, by the prevailing market price of the company's stock and bonds.

3.  The third reason long-term-oriented investors are interested in short-term price fluctuations is that Mr. Market can create very attractive opportunities to buy and sell.

• If you hold cash, you are able to take advantage of such opportunities.  If you are fully invested when the market declines, your portfolio will likely drop in value, depriving you of the benefits arising from the opportunity to buy in at lower levels.  This creates an opportunity cost, the necessity to forego future opportunities that arise.  
• If what you hold is illiquid or unmarketable, the opportunity cost increases further; the illiquidity precludes your switching to better bargains.

The Time Value of Money

"A bird in hand (today) is worth two in the bush (tomorrow)."

Everyone would rather have a dollar in his or her pocket today than to receive a dollar far into the future.  Today's dollar is worth more - that it has more value - than a dollar received tomorrow.

The three main reasons for this difference in value are:

1.  Inflation.
Inflation does reduce purchasing power (value) over time.  With a 5% per year inflation, a dollar received a year from today will only buy 95c worth of goods.

2.  Risk
There is always the chance that the promise of a dollar in the future will not be met and you will be out of luck.  The risk could be low with a CD at an FDIC insured bank; or the risk could be high if it is your brother-in-law who is promising to repay a personal loan.

3.  Opportunity Cost.
If you loan your dollar to someone else, you have lost the opportunity to use it yourself.  That opportunity has a value to you today that makes today's dollar worth more than tomorrow's.

These three concepts - inflation, risk, and opportunity cost - are the drivers of present value (PV) and future value (FV) calculations used in capital budgeting and investing.

Present value (PV) calculations are used in business to compare cash flows (cash spent and received) at different times in the future.  Converting cash flows into present values puts these different investments and returns onto a common basis and makes capital budgeting analysis more meaningful and useful in decision-making.

Nominal dollars are just the actual amount spent in dollars taken out of your wallet.  Real dollars are adjusted for inflation.  When you take out inflation (i.e. convert from 'nominal dollars' into 'real dollars') the price difference becomes much more comparable and easy to explain.

Capital Budgeting

In capital budgeting, different projects require different investment and will have different returns over time.  In order to compare projects "apples to apples" and "oranges to oranges" on a financial basis, we will need to convert their cash flows into a common and comparable form.  That common form is present value.

Simply put, a little bit of cash that is invested today followed by lots of cash returned in the near future would be a REALLY GOOD financial investment.  

However, lots of cash invested today followed by a little bit of cash returned in a long time would be a REALLY  BAD investment.

Capital budgeting analysis is as simple as that.

What Was Your Worst Investment Mistake in 2009?

What Was Your Worst Investment Mistake in 2009?
By Dan Caplinger
December 15, 2009

In 2008, nearly everybody made bad investments. By comparison, 2009 was a complete delight.

Still, investors made mistakes. Even with the huge rally, some stocks, including Valero Energy (NYSE: VLO), MetroPCS (NYSE: PCS), and Apollo (Nasdaq: APOL), managed to drop this year. In addition, Treasury bonds, which rode high during 2008, also knocked investors for a big loss this year.

What might have been
Personally, though, my biggest mistake this year was in cutting my winners short. The decision to take some profits on part of my positions in Starbucks (Nasdaq: SBUX) and Freeport-McMoRan (NYSE: FCX) well into the rally seemed like a no-brainer at the time, but those stocks just kept going up. Similarly, I trimmed my holdings in junk bond mutual funds and some international bonds, figuring that gains might well prove short-lived. Although that didn't cause any losses, the opportunity cost of getting out too early was extremely high.

There's a lesson in that. Plenty of investors are smart enough to buy top performers like Apple (Nasdaq: AAPL) and Green Mountain Coffee Roasters (Nasdaq: GMCR), and a good number of them earn decent profits from them. But only the most disciplined, patient investors stick with those winners for the long haul, squeezing every penny of potential gain out of their shares and turning a modest winner into a gold mine for their portfolio.

How about you?


http://www.fool.com/investing/dividends-income/2009/12/15/what-was-your-worst-investment-mistake-in-2009.aspx

Opportunity costs of our investments

"There is this company in an emerging market that was presented to Warren. His response was, 'I don't feel more comfortable buying that than I do of adding to Wells Fargo.' He was using that as his opportunity cost. No one can tell me why I shouldn't buy more Wells Fargo. Warren is scanning the world trying to get his opportunity cost as high as he can so that his individual decisions are better."

When you are evaluating any investment, you must compare it to every other available investment, including ones you may already own. Instead, many investors collect stocks like baseball cards and the resulting portfolio bloat will likely not increase returns or reduce risk. So when you hear about the new hot stock in the next can't-miss sector, ask yourself two questions:

(1) Do I understand the investment as well or better than one I already own?

(2) Is the risk and reward profile of the investment superior to all other alternatives?

If the answer is "no" to either questions, it is probably best to stay away.

The Power of Avoiding Losses

Losses occur for three primary reasons:

1. You took bigger risks and exposed yourself to a higher probability of loss.

2. You invested in an instrument that failed to keep pace with inflation and interest rates (e.g. CDs).

3. You didn't hold the instrument long enough to let its true intrinsic value be realized.

There aren't many ways an investor can avoid periodic losses. The best way is to invest all of your assets in bonds and hold them to maturity. You would, of course, experience an erosion in the value of the bond due to inflation. If interest rates rise during your holding period, the intrinsic value of the bond would fall and the yearly coupon wouldn't compensate you for inflationary pressures.

To reduce the chance of losses, you must minimise mistakes. The fewer errors made over your investing career, the better your long-term returns.

We've seen the advantage of adding extra points of gain to your yearly returns. Earnings an extra 2% points a year on your portfolio compounds into tremendous amounts. Beating the market's presumed 11% yearly return by 2% points would translate into hundreds of thousands of dollars of extra profits over time.

The same holds true if you can avoid a loss. When you lose money, even if for just a year, you greatly erode the terminal value of your portfolio.

• You consume precious resources that must be replaced.
• In addition, you waste precious time trying to make up lost ground.
• Losses also reduce the positive effects of compounding.

The effects of avoiding losses can be studied by considering 3 portfolios, A, B, and C, each of which normally gains 10% a year for 30 years. Portfolio B, obtains zero gains (0%) in years 10, 20, and 30. Portfolio C suffers a 10% loss in years 10, 20 and 30.

• A $10,000 investment in portfolio A would return $174,490 by the 30th year.
• Portfolio B would return considerably less - $131,100 - because of three break-even years. The portfolio never actually lost money, but will forever lag far behind porfolio A by virtue of having three mediocre years. Historically speaking, portfolio B's returns aren't all that bad, for the investor managed to avoid losses every year.
• Portfolio C, by contrast, loses 10% in years 10, 20, and 30. It's return of $95,572 was considerably lower. The effects of those three not-so-unreasonable years is to lop nearly $79,000 off the final value of the portfolio. That's what compounding can do. The actual loss in the 10th year was only $2,357. The loss in the 20th year was just $5,004; the final year loss was $10,619. But the power of compounding turned $17,980 in total yearly losses into $79,000 of lost opportunities.

Buffett once summarized the essence of successful investing in a simple quip:

Rule number 1: Don't lose money

Rule number 2: Don't forget rule number 1

Understanding Buffett's frugal convictions

Warren Buffett once joked that he spent 6% of his net worth buying his wife Susie an engagement ring, thus depriving himself of immeasurable millions in future gains.

Indeed, Buffett once was seen picking up a penny on an elevator on his way to the office and remarked to the stunned witnesses, "the beginning of the next billion."

To Warren, a $100 bill lying on a sidewalk should not be valued on its present-day worth or on the present-day efforts needed to accumulate it, but on the future value of the greenback. Suppose, for example, that Buffett could compound $100 at 25% annual rates. In 10 years, his $100 discovery would be worth $931. After 30 years, it would be worth $80,779, unadjusted for inflation.

To understand Buffett's frugal convictions, one must view them from the point of view of mathematics and by using the types of calculation just shown. To Buffett, every dollar not accumulated now or spent needlessly could have productively been turned into numerous dollars later.

Thus, everything you buy or do not buy has the potential to greatly increase or decrease your net worth, depending on the rate of return you can obtain on investments. This principle applies whether you spend money on a poorly chosen investment or on an unnecessary personal expense or luxury item.

Buffett has to make such choices because of his high opportunity costs. In contrast, a household that has no opportunity costs, that is, it doesn't invest or derives no returns from investments, may be just as well off making the various types of purchases.

A household with zero oppoortunity costs can be a net consumer with no detrimental impact to its long-term fortune, but, to Buffett, money saved is money compounded. He has been known buy 50 12-packs of Coca-Cola at once from the grocery store to get a volume discount. Each year, the money he saves buying cases of pop will ultimately increase his net worth by thousands of dollars.

Opportunity costs of our investments

Every dollar spent on a single item is a dollar unavailable for other items. That dollar must provide a suitable return - measured against what you could have earned on tha dollar somewhere else.

Investors should look at their investments similarly.

Because the market tempts us with thousands of potential investments each day, we tend to screen our stock choices until we find those that meet our risk and return characteristics. Likewise, we've learned to benchmark our investments by comparing their performance against the S&P 500 index or some other proxy.

If your portfolio rose just 8% in a year in which the S&P 500 index rose 20%, the opportunity cost on your money was great - you lost the chance at an extra 12 percent a year because the investments you chose did poorly.

Look at all spending decisions as opportunities - won or lost

Most individuals these days are astute enough to understand the power of time and understand the need to fund their own retirement rather than to rely on government programs whose long-term viability don't seem guaranteed anymore.

However, compounding works two ways.

An investment that compounds at, say, 20% annual rates, will swell into a tremendous amount after 30 years.

Conversely, a missed opportunity that could have compounded at 20% a year has the opposite effect on your portfolio. A poorly chosen stock tha rises just 5% a year ultimately costs you tens of thousands of dollars in lost opportunities.

Money that is misspent today and not invested can have the same injurious effect on your future net worth.

At any given moment, you have tens of thousands of investment opportunities worldwide from which to choose. You may decide to put your available cash into shares of Intel or into a home remodeliing project. You may decide to spend $50 at a restaurant, or on a new pair of slacks, or on a new golf putter. You may be faced with the choice of buying a new automobile or funding a college account for a chld. No matter how you choose, every possible use of your money must bring a return - tangible or intangible - or else you should not spend the money. When making the choice of buying, say, shares of Intel or new carpeting, you must think about the opportunity costs of the money spent.

As an investor, you must also look at all spending decisions as opportunities - won or lost. Every dollar spent on a single item is a dollar unavailable for other items. That dollar must provide a suitable return - measured against what you could have earned on that dollar somewhere else.

Columbus's four voyages to the Caribbean

The Joys of Compounding

In Buffett's annual report to partners for the year ending in 1962, he broke cadence from his routine review of the market to discuss "The Joys of Compounding." Anyone reading this passage, even four decades after Buffett penned it, could see the raw-boned logic behind the 32-year-old Buffett's stubborn frugality. As he saw it, every dollar put to productive use magnifies the benefit to society by virtue of compounding. Wasting that dollar had serious long-term ramifications - for him, his partners, even for society at large. What if, Buffett mused in his letter, Spain had decided not to finance Christopher Columbus? The results would be staggering.

In financial terms, Columbus's four voyages to the Caribbean yielded very little for the crown, except to pave the way for generations of future navigators. Think how that $30,000 (cost of the voyage Isabella originally underwrote for Columbus), if spent more judiciously by Spain in the late 15th century, could have greatly increased the wealth of the Spanish people. By 1999, 37 years after Buffett made the analogy, Isabella's $30,000 expenditure could have compounded into more than $8 trillion, nearly the total annual economic output of the United States. Spain would be a world economic powerhouse today.

On this topic, Buffett is behaving as any rational CEO would. If a company generates a high return on its assets, it should withhold dividends to investors and plow as much money as it can each year back into the business. Only when it can no longer generate a strong internal return should a company think about returning money to shareholders.

It's very doubtful that recipients of his wealth could have compounded their largesse at the rate Buffett did. Isn't it better, Buffett believes, to forego conspicuous consumption today if it means leaving even larger amounts for society tomorrow?

"My money represents an enormous number of claims checks on society. It's like I have these little pieces of paper that I can turn into consumption," Buffett told Esquire magazine in 1988. "If I wanted to, I could hire 10,000 people to do nothing but paint my picture every day for the rest of my life. And the (Gross Domestic Product) would go up. But the utility of the product would be zilch, and I would be keeping those 10,000 people from doing AIDS research, or teaching or nursing."

Letting money compound productively creates an enormous economic benefit.

Postulating the value of assets into the future holds meaning for investors who, if they're fortunate, can live many decades. Letting money compound productively creates an enormous economic benefit, not only to investors but also to their benefactors and to society at large.

Buffett is occasionally criticized for not donating more of his wealth to foundations and charities, as many other tycoons have. Buffett's reasoning, however, is perfectly consistent with his investing philosophy. As long as he can continue to compound money at great rates, society would be better off if he didn't give away money now.

He told Ted Koppel in a 1999 Nighline interview, for example, that if he had donated most of his money 20 years ago, society would have been $100 million richer. Because he chose not to donate, society will one day receive more than $30 billion.

Had he given away $100 million in the 1970s, it's very doubtful that recipients could ahve produced $30 billion in economic benefits for society becasue few people alive can compound money as Buffett can.

One day, the value of Buffett's foundation grants will certainly surpass $100 billion and then $200 billion, which would make Buffett's fortune the largest ever donated to charity.

Let time work to your advantage

Choosing good companies at fair prices seldom has produced losses for investors willing to wait patiently for the stock price to track the growth of the company.

"Time is the friend of the good business, the enemy of the poor," Buffett has said many times.

Strong enterprises see their intrinsic value rise consistently, lifting the stock every step of the way. Over a period of 5 years or more, there should be a very close correlation between the change in the value of the company and the change in the stock. Watching great companies increase their sales and earnings consistently is a dream come true for an investor.

The power of compounding begins working its magic as the years progress and allows your net worth to gather momentum and increase (in dollar value) by greater and greater amounts.

What happens to money that is allowed to sit and grow at different rates? Two principles should be readily apparent:

1. Time has a tremendous effect on terminal wealth. The longer that money can compound, the larger the sum will be.

2. The rate of return attained acts as a lever that magnifies or minimises your ultimate wealth. Adding just a few extra percentage points a year to your overall returns can have unfathomable consequences to your wealth. An investor who compounds $1 at 6 percent annual rates has $5.74 in his pocket at the end of 30 years. The same investor who can find ways to obtain higher returns (the purpose of posting all these materials here :-) ) walks away with much more. If you can obtain a 10 percent annual return, your $1 compounds into $17.45 in 30 years. Compounding $1 at 20 percent annual rates compounds into $237.

The mathematics of compounding excited Buffett in his earliest years, and stories abound of how he memorised compounding and annuity tables to help him calculate an investment's merit and to keep his personal portfolio on a straight upward track.

If the Indians wanted to buy back Manhattan

There's the story that, if the Indians wanted to buy back Manhattan, they would have had to pay more than $2.5 trillion by January 1, 2000. That's what the $24 sale price in 1626 would have compounded into at 7 percent annual rates. And the clock keeps ticking.

Next year, Manhattan's theoretical value jumps by $175 billion (7 percent of $2.5 trillion). The following year, another $187 billion is added. The year after that, $200 billion, and so on.

Letting wealth accumulate and compound unfettered and, if possible, untaxed is a potent formula individuals should use to increase their standard of living.

It goes without saying that to an investor, the power of compounding is paramount.

The Power of Compounding

No force exerts more influence on your portfolio than time. Time takes a bigger toll on your terminal wealth than do taxes, inflation and poor stock-picking combined. Time magnifies the effects of these critical issues.

A poorly chosen stock may cost you only $2,000 in losses today, but over time that one suspect decision could cost $50,000 in lost opportunities.

Trading frequently for short-term gains may net you strong gains periodically, but the overall result, validated by time, is to create an enormous tax burden that could have been avoided.

Likewise, persistent inflation exacts a weighty toll on your portfolio becasue it destroys value at increasing rates.

Means and end should not be confused. Buffett once wrote to his partners, "The end is to come away with the largest after-tax rate of compound."

Lost Opportunities

A poorly chosen stock may cost you only $2,000 in losses today, but over time that one suspect decision could cost $50,000 in lost opportunities.

Opportunity Cost and Opportunity Lost

A value investor's mind operates in a continuous buzz, deciding whether an investment is achieving its best possible returns or whether it should be replaced.

Value investors like cheap stocks, but if the stocks get cheap on an investor's watch, the investor should consider a serious reappraisal of a company's prospects.

Value investors continuously check for dead branches and aren't afraid to get out the pruning shears. Value investors know the cost of dead wood.

Likewise, the frugal citizens, value investors avoid squandering money that could be put to better use and always think of the best use for their capital. For Warren Buffett, a penny found on a sidewalk is "the start of the next billion."