Stock Investing 101 – Time Value of Money

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Time Value of Money

Time is money. Any sum of money payable in the future is worth less than if it is paid today. This is because that sum of money, if paid today, can be put into an interest bearing bank account to earn interest.

Present value

The present value of that future sum can be determined using the following formula.

PV = FV/(1 + r) n

where PV = Present Value, FV = Future Value, r = interest rate and n = number of years

Example

At 5% interest rate, the present value of a $1000 payment in 3 years’ time is only $863.84.

Future value

Correspondingly, there exist a future value of any sum of money can be computed using the following formula.

FV = PV(1 + r) n

where PV = Present Value, FV = Future Value, r = interest rate and n = number of years

Example

At 5% interest rate, the future value of $1000 in 3 years’ time is $1157.63.

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Writing Puts to Purchase Stocks

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Value Investing 101: Intrinsic Value (Part 1)

What is Intrinsic Value?

If you’ve read any of the articles on this website – or if you’re familiar with value investing concepts – then you may know that an Intelligent Investor will only buy a stock when its market value (that is, its stock price) is less than its intrinsic value.

In other words, a smart investment is one where you are buying a stock for less than its intrinsic value.

But what exactly is intrinsic value and how do you calculate it?

In the Berkshire Hathaway Owner’s Manual, Warren Buffett writes this about intrinsic value:

Viewing a Business as a Bond

What does Buffett mean by this? Imagine a bond, for instance, which pays the bondholder interest every year and principal back at maturity. From Value Investing 101: The Time Value of Money, we know that a dollar today is worth more than a dollar tomorrow, and vice versa that a dollar tomorrow is worth less than a dollar today. Therefore, the interest and principal payments we receive in the future must be discounted to a lower value in order to determine their value today.

So, the present value of a bond = the discounted value of the bond’s future interest and principal payments. (If this doesn’t make sense, then please read my Time Value of Money article before reading on).

Now picture a company.

What is the purpose of a company? Answer: To generate dividends for the company’s shareholders.

This is a lot like a bond isn’t it? Except instead of being paid interest every quarter, a shareholder is paid dividends every quarter. This means you can discount the value of future dividends just the same way that you can calculate a bond’s future interest and principal payments.

Remember that the present value of a future payment = the future value of the payments, discounted at a certain rate?

In math form, this equation is the following (where i = the discount rate):

If the future payments will growth at a constant rate, then the equation can be simplified as:

The above equation is called the Dividend Discount Model (or the Gordon Growth Model) and its output is the intrinsic value of a stock.

Limitations of the Dividend Discount Model

“But,” you might argue, “not all stocks pay dividends, and even the ones that do pay dividends don’t have a consistent dividend growth rate.”

You’re right, of course. Unlike with a bond, a company doesn’t have any contractual obligations to pay a dividend to its shareholders.

Furthermore, dividends alone don’t capture all of a company’s earnings. Besides paying a dividend, a business can also use the cash it generates to acquire new equipment or machines, to improve its factories or buildings, for research & development, to acquire another company, or to make other investments.

Any of these can be a better allocation of capital than if the company had paid a dividend. So while the dividend growth model (DDM) provides a good framework to understand intrinsic value, it doesn’t actually generate a realistic result.

Next Up: DCF and Owner Earnings

In Part 2, we’ll take the DDM one step further and will use a Discounted Cash Flow analysis to calculate a more accurate intrinsic value of a stock.

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Stock Investing 101 – Time Value of Money

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