Complete Guide To Corporate Finance


Discounted Cash Flow Valuation - The Effect Of Compounding

Compounding is the ability of an asset to generate earnings, which are then reinvested in order to generate their own earnings. In other words, compounding refers to generating earnings from previous earnings.

Suppose you invest $10,000 into Cory's Tequila Company (ticker: CTC). The first year, the shares rises 20%. Your investment is now worth $12,000. Based on good performance, you hold the stock. In Year 2, the shares appreciate another 20%. Therefore, your $12,000 grows to $14,400. Rather than your shares appreciating an additional $2,000 (20%) like they did in the first year, they appreciate an additional $2,400, because the $2,000 you gained in the first year grew by 20% too.

If you extrapolate the process out, the numbers can start to get very big as your previous earnings start to provide returns. In fact, $10,000 invested at 20% annually for25 years would grow to nearly $1,000,000 - and that's without adding any money to the investment!

Interest is often compounded monthly, quarterly, semiannually or annually. With continuous compounding, any interest earned immediately begins earning interest on itself. Albert Einstein allegedly called compound interest "the greatest mathematical discovery of all time." We think this is true partly because, unlike the trigonometry or calculus you studied back in high school, compounding can be applied to everyday life.

The wonder of compounding (sometimes called "compound interest") transforms your working money into a highly powerful income-generating tool. Compounding is the process of generating earnings on an asset's reinvested earnings. To work, it requires two things: the reinvestment of earnings and time. The more time you give your investments, the more you are able to accelerate the income potential of your original investment.

To demonstrate, let's look at another example:

If you invest $10,000 today at 6%, you will have $10,600 in one year ($10,000 x 1.06). Now let's say that rather than withdraw the $600 gained from interest, you keep it in there for another year. If you continue to earn the same rate of 6%, your investment will grow to $11,236.00 ($10,600 x 1.06) by the end of the second year.

Because you reinvested that $600, it works together with the original investment, earning you $636, which is $36 more than the previous year. This little bit extra may seem like peanuts now, but let's not forget that you didn't have to lift a finger to earn that $36. More importantly, this $36 also has the capacity to earn interest. After the next year, your investment will be worth $11,910.16 ($11,236 x 1.06). This time you earned $674.16, which is $74.16 more interest than the first year. This increase in the amount made each year is compounding in action: interest earning interest on interest and so on. This will continue as long as you keep reinvesting and earning interest.

Starting Early
Consider two individuals; we'll name them Pam and Sam. Pam and Sam are the same age. When Pam was 25 she invested $15,000 at an interest rate of 5.5%. For simplicity, let's assume the interest was compounded annually. By the time Pam reaches 50, she will have $57,200.89 ($15,000 x [1.055^25]) in her bank account.

Pam's friend, Sam, did not start investing until he reached age 35. At that time, he invested $15,000 at the same interest rate of 5.5% compounded annually. By the time Sam reaches age 50, he will have $33,487.15 ($15,000 x [1.055^15]) in his bank account.

What happened? Both Pam and Sam are 50 years old, but Pam has $23,713.74 ($57,200.89 - $33,487.15) more in her savings account than Sam, even though he invested the same amount of money. By giving her investment more time to grow, Pam earned a total of $42,200.89 in interest and Sam earned only $18,487.15.

The following chart shows Pam and Sam's earnings:

You can see that both investments start to grow slowly and then accelerate, as reflected in the increase in the curves' steepness. Pam's line becomes steeper as she nears her 50s not simply because she has accumulated more interest, but because this accumulated interest is itself accruing more interest.

Pam's line gets even steeper (her rate of return increases) in another 10 years. At age 60 she would have nearly $100,000 in her bank account, while Sam would only have around $60,000 - a $40,000 difference!

The effect of compound interest depends on frequency. Assume an annual interest rate of 12%. If we start the year with $100 and compound only once, at the end of the year, the principal grows to $112 ($100 x 1.12 = $112). If we instead compound each month at 1%, we end up with more than $112 at the end of the year. Specifically, we end up with $100 x 1.01^12 at $112.68. The final amount is higher because the interest compounded more frequently.

Compounding amplifies the growth of your working money and maximizes the earning potential of your investments - but remember, because time and reinvesting make compounding work, you must keep your hands off the principal and earned interest. (For related reading, see Overcoming Compounding's Dark Side. For a more advanced discussion of compound interest, read Accelerating Returns With Continuous Compounding.

Introduction To Loans
Related Articles
  1. Investing

    Where the Price is Right for Dividends

    There are two broad schools of thought for equity income investing: The first pays the highest dividend yields and the second focuses on healthy yields.
  2. Professionals

    4 Must Watch Films and Documentaries for Accountants

    Learn how these must-watch movies for accountants teach about the importance of ethics in a world driven by greed and financial power.
  3. Personal Finance

    How Tech Can Help with 3 Behavioral Finance Biases

    Even if you’re a finance or statistics expert, you’re not immune to common decision-making mistakes that can negatively impact your finances.
  4. Investing Basics

    5 Tips For Diversifying Your Portfolio

    A diversified portfolio will protect you in a tough market. Get some solid tips here!
  5. Entrepreneurship

    Identifying And Managing Business Risks

    There are a lot of risks associated with running a business, but there are an equal number of ways to prepare for and manage them.
  6. Active Trading

    An Introduction To Depreciation

    Companies make choices and assumptions in calculating depreciation, and you need to know how these affect the bottom line.
  7. Forex Education

    Explaining Uncovered Interest Rate Parity

    Uncovered interest rate parity is when the difference in interest rates between two nations is equal to the expected change in exchange rates.
  8. Fundamental Analysis

    Using Decision Trees In Finance

    A decision tree provides a comprehensive framework to review the alternative scenarios and consequences a decision may lead to.
  9. Economics

    Understanding Tragedy of the Commons

    The tragedy of the commons describes an economic problem in which individuals try to reap the greatest benefits from a given resource.
  10. Investing

    What’s the Difference Between Duration & Maturity?

    We look at the meaning of two terms that often get confused, duration and maturity, to set the record straight.
  1. Accountant

    A professional who performs accounting functions such as audits ...
  2. Rule Of 72

    A shortcut to estimate the number of years required to double ...
  3. Laissez Faire

    An economic theory from the 18th century that is strongly opposed ...
  4. Personal Finance

    All financial decisions and activities of an individual or household, ...
  5. Audit

    An unbiased examination and evaluation of the financial statements ...
  6. Put-Call Parity

    A principle that defines the relationship between the price of ...
  1. What should I study in school to prepare for a career in corporate finance?

    Depending on which area you want to specialize in, corporate finance can be one of the most competitive fields in business. ... Read Full Answer >>
  2. Why would a company issue preference shares instead of common shares?

    Preference shares, or preferred stock, act as a hybrid between common shares and bond issues. As with any produced good or ... Read Full Answer >>
  3. What is the difference between cost of debt capital and cost of equity?

    In corporate finance, capital – the money a business uses to fund operations – comes from two sources: debt and equity. While ... Read Full Answer >>
  4. What is the difference between gross profit, operating profit and net income?

    The terms profit and income are often used interchangeably in day-to-day life. In corporate finance, however, these terms ... Read Full Answer >>
  5. What’s the difference between the two federal student loan programs (FFEL and Direct)?

    The short answer is that one loan program still exists (Federal Direct Loans) and one was ended by the Health Care and Education ... Read Full Answer >>
  6. Can working capital be depreciated?

    Working capital as current assets cannot be depreciated the way long-term, fixed assets are. In accounting, depreciation ... Read Full Answer >>

You May Also Like

Hot Definitions
  1. Turkey

    Slang for an investment that yields disappointing results or turns out worse than expected. Failed business deals, securities ...
  2. Barefoot Pilgrim

    A slang term for an unsophisticated investor who loses all of his or her wealth by trading equities in the stock market. ...
  3. Quick Ratio

    The quick ratio is an indicator of a company’s short-term liquidity. The quick ratio measures a company’s ability to meet ...
  4. Black Tuesday

    October 29, 1929, when the DJIA fell 12% - one of the largest one-day drops in stock market history. More than 16 million ...
  5. Black Monday

    October 19, 1987, when the Dow Jones Industrial Average (DJIA) lost almost 22% in a single day. That event marked the beginning ...
  6. Monetary Policy

    Monetary policy is the actions of a central bank, currency board or other regulatory committee that determine the size and ...
Trading Center