# 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.

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

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

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*.