How to Value Stocks

The Stock Market

The stock market can be a great place to make money. However, the stock market can also be an incredibly frustrating place, where losing money becomes an everyday occurrence. Knowing what to buy and what to sell in the stock market can be very complicated. However, there is a method for estimating the true value of a stock that is both logical and often overlooked. Learning and implementing this method isn't easy, but once fully understood it is fairly easy to use and the results can be very rewarding.

Time Value of Money

This method centers around the concept of the time value of money. It is easiest to begin this lesson with an example. For instance, if a person was given a choice between receiving $1,000,000 today or receiving $1,000,000 two years from now, which option would he/she most likely choose? Of course he/she would choose to receive the $1,000,000 today. The reason is simple. If that person invests the $1,000,000 he/she receives today at say a 10% interest rate, that $1,000,000 would be worth $1,100,000 one year later, $1,210,000 two years later, and so on. Therefore, the $1,000,000 today is worth more than the $1,000,000 two years from now.

In Summary

Value one year later: $1,000,000 x 10% + $1,000,000 = $1,100,000

Value two years later: $1,100,000 x 10% + $1,100,000 = $1,210,000

The above equations can be written in a general form: PW x (1 + i)ⁿ = FW, where PW is the present worth, i is the interest rate, n is the number of years, and FW is the future worth. For simplicity, this equation will be referred to as the PW equation. Although it may not be evident, the time value of money is a very powerful concept. The following examples will further illustrate its usefulness.

If an investor knows a business is going to earn $2,000,000 three years from now, he/she can use the PW equation to calculate an equivalent income that occurs today.

Worth today: PW = FW / [(1+i)ⁿ] = $2,000,000 / [(1+0.10)³] = $1,502,630

Therefore, that $2,000,000 earnings that will occur three years from now is equivalent to earning $1,502,630 today. Just for clarification, the 0.10 means that a 10% interest rate was used in the equation.

Now suppose an investor knows that a business would be continuously earning $2,000,000 every year starting one year from now and he/she wants to calculate an equivalent income that occurs today. The formula for such a case is PW = A / i, where A is the annual earnings. This equation will be referred to as the annuity equation. The derivation of this equation is relatively complicated and lengthy, so it will not be covered. At a 10% interest rate, the $2,000,000 earnings occurring every year and starting one year from now is equivalent to earning $20,000,000 today.

PW = $2,000,000 / 0.10 = $20,000,000

If the $2,000,000 annual earnings is growing by a fixed percentage such as 5%, the equation is similar to the annuity equation. PW = A /(i - g), where g is the growth rate. This equation will be referred to as the perpetuity equation. At a 10% interest rate, this type of earnings is equivalent to earning $40,000,000 today.

PW = $2,000,000 / (0.10 - 0.05) = $40,000,000

Lastly, consider the case of a business that is going to be growing at a rate of 15% for the next five years. Given that the business will earn $2,000,000 on the first year and then earn zero after the fifth year, an equivalent present day income can be calculated. Again, the derivation for the equations are relatively lengthy and complex so it will not be covered.

For this scenario, there are two equations. For the case where the growth rate is the same as the interest rate the equation is PW = A x [n / (1 + i)], where A is the starting earnings (so in this case it is $2,000,000). This is equation 1.

For the case where the growth rate is not the same as the interest rate the equation is PW = A x [(1 - [(1 + g)/(1 + i)]ⁿ) / (i - g)], where g is the growth rate and A is the starting earnings (so in this case it is $2,000,000). This is equation 2.

The last equation seems very complex to use, but this writer can assure that it is not. To use the last equation, one simply inputs the correct numbers and the equation gives the answer. The process can be further simplified if one saves the equation in a spreadsheet. To give a thorough example, an interest rate of 10% will be used. Therefore, equation 2 will have to be used because the 10% interest rate does not equal the 15% growth rate. Using equation 2,

PW = $2,000,000 x [(1 - [(1 + 0.15)/(1 + 0.10)]⁵) / (0.10 - 0.15)] = $9,956,000.

Hence, this series of incomes is equivalent to an income of $9,956,000 today. If you have read this far, you are past the most difficult section and are ready to move onto applying what you have learned into valuing stocks. Congratulations.

Valuing Stocks

Owning a stock means owning a part of the business. Since businesses are organizations that earn money, the concept of the time value of money can be applied to estimate the value of the stock. Consider a hypothetical company called company A as an example.

The above table shows the data needed for the stock price calculation. This information is widely available and can be found on the income statement, balance sheet, and cash flow statement of any company. Here is a quick overview:

Net Income is the profit of the company (or loss if negative). It is the revenue minus expenses. This value is found on the income statement.

Depreciation is the decline in the value of an asset. It is found on the cash flow statement. This is a non cash expense. Basically, just remember that this value adds to the net income when calculating free cash flow, which will be discussed later. This is found on the cash flow statement.

Changes in working capital is the change in working capital (current assets - current liabilities) from the previous period. This value can be either positive or negative. Just remember that this number is ONLY used if it's negative. This is found on the cash flow statement.

Capital expenditures is the amount of money spent on equipment and property (such as buildings or land). As the name suggests this is an expenditure, so it is always subtracted from the net income when calculating the free cash flow. This is found on the cash flow statement.

Number of Shares is the number of shares. This can be easily found on many investment websites.

Total debt is the amount of money the company owes and is paying interest on. This is found on the balance sheet.

The first step to calculating the stock price is to gather the above data. Next, calculate the free cash flow. Free cash flow is the true earnings of a company because it takes into account the amount of expenses necessary to replace old equipment, buildings, etc, that are needed to keep the company going.

Free cash flow = Net Income + Depreciation - Changes in Working Capital - Capital Expenditures

Using the data from company A, the free cash flow is

Free cash flow = $14,569 + $2,562 - $1,195 - $3,119 = $12,817 million. It is a very good idea to make a spread sheet to ease the calculations.

The calculations done by the spreadsheet will now be covered in detail. As shown in the spread sheet, a growth period of ten years, a rate of growth of 5%, and an interest rate of 10% were used. The free cash flow of $12,817 million occurs at the present day, which is at year zero. Since the rate of growth and the interest rate are not equal, equation 2 must be used in calculating the growth value (the equations are defined in the Time Value of Money section).

Equation 2: PW = A x [(1 - [(1 + g)/(1 + i)]ⁿ) / (i - g)], where PW stands for the present worth, g is the growth rate, i is the interest rate, n is the number of years of growth, and A is the free cash flow at year 1.

The free cash flow at year zero is known. To get the free cash flow at year 1, the PW equation has to be used. Since the earnings are projected to grow by 5% from year zero to year 1, the free cash flow at year 1 is

Free cash flow at year one: FW = $12,817 x (1 + 0.05)¹ = $13,458 million

Now all the numbers needed for equation 2 are available. Using equation 2, the growth value can be calculated.

Growth Value: PW = $13,458 x [(1 - [(1 + .05)/(1 + 0.10)]¹⁰) / (0.10 - 0.15)] = $10,0125 million.

The slight difference in value with the spread sheet is due to round off error. It is important to note that the $10,0125 million is the present worth of the income during the growth period only. The present worth of the income after the growth period also needs to be calculated. A terminal growth rate of 1% is projected (NOTE: the time period after the growth period is referred to as the terminal period). To calculate this value, the free cash flow at year ten needs to be calculated.

Year 10 free cash flow: FW = $12,817 x (1 + 0.05)¹⁰ = $20,878 million

Since the free cash flow from year ten to year eleven will grow by 1%, the Year eleven free cash flow is FW = $20,878 x (1 + 0.01)¹ = $21,087 million

Hence, the perpetuity value at year ten is $21,087 / (0.10 - 0.01) = $234,300 million

It is important to note that this is the value at year ten, not it's present value. Therefore, the PW equation has to be used to find its present value.

Terminal Value: PW = $234,300 / (1 + 0.10)¹⁰ = $90,333 million

As previously stated, the difference in value with the spread sheet is due to round off error. If the last part is confusing, just remember that when using the perpetuity equation, the value that is calculated is the value at the last year of the growth period not the value at year zero. Therefore, it is necessary to use the PW equation to get its present value.

Finally, to get the stock price use the following equation.

Stock price = (Growth Value + Terminal Value - Total Debt) / number of shares

Stock Price = ($10,0125 + $90,333 - $5,996) / (8,900) = $20.73

The total debt is subtracted because it is interest bearing money that needs to be paid back by the company. Again, the slight difference with the spread sheet is due to round off error. Once the stock price has been calculated, an investor has a better idea of whether the stock is a bargain or overpriced. That's it. Once a person masters the basics, he/she can start tweaking the numbers used (different interest rate, growth rate, terminal growth rate, etc).

Just some final advice, with respect to stock brokers. There is no need to find an expensive broker. Having an expensive broker doesn't significantly increase someone's chances of making money. I would recommend finding a cheap stock broker, but don't go with something shady. Personally, the broker I use is Scottrade, but one should do their own research and find the broker that's right for him/her. Good luck.

If you're interested in learning more about stocks, I cover some useful stock metrics here: http://hubpages.com/hub/Stocks-and-Useful-Financial-Metrics