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Introduction
1. Investment vehicle characteristics
2. Recommendations & strategies
3. Economic factors & business information
3.1 Basic economic concepts
3.2 Financial reporting
3.3 Analytical methods
3.4 Descriptive statistics
3.5 Systematic risks
3.6 Non-systematic risks
4. Laws & regulations
Wrapping up
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3.3 Analytical methods
Achievable Series 65
3. Economic factors & business information

Analytical methods

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Securities can be analyzed in several different ways. This chapter covers the following analytical methods:

  • Price to earnings (PE) ratio
  • Price to book ratio
  • Dividend payout ratio
  • Time value of money concepts, including:
    • Present value
    • Net present value
    • Internal rate of return
  • Descriptive statistics, including:
    • Mean
    • Median
    • Mode
    • Range
  • Alpha
  • Beta
  • Sharpe ratio

Price to earnings (PE) ratio

Price to earnings (PE) ratios help investors judge whether a company’s stock may be overvalued or undervalued. The price is the company’s market price per share. The earnings are the company’s profits on a per-share basis (earnings per share). Earnings are reported on a corporate income statement.

PE ratio=Earnings per shareCommon stock market price​

A higher PE ratio often suggests the stock is priced high relative to its current earnings. For example, a PE ratio of 100 means the market price is 100 times the company’s annual earnings per share. Unless profits are expected to grow substantially, the stock may be overpriced. On average, PE ratios often fall in the 15-25 range, depending on the company and industry.

Growth companies typically have higher PE ratios. These businesses are expanding and are expected to generate higher profits in the future. As a result, the stock may look “expensive” today, but investors may still consider it attractive if they expect strong long-term growth.

For example, Roku stock (symbol: ROKU) reflected a PE ratio of 180 as of October 2021. That means the stock price was 180 times the company’s annual earnings per share. If you bought the entire company and earnings stayed the same, it would take 180 years to earn back the purchase price through profits. Investors accept a PE ratio this high only if they believe profits will rise significantly.

Value companies typically have lower PE ratios. These businesses are often large, established firms with a long history of profits. Because investors usually don’t expect dramatic growth from mature companies, they’re generally less willing to pay a high multiple of current earnings.

For example, Allstate stock (symbol: ALL) reflected a PE ratio of 6 as of October 2021. That means the stock price was 6 times the company’s annual earnings per share. If you bought the entire company and profits stayed the same, it would take about 6 years to recoup the purchase price through profits. Compared with Roku, Allstate appears much cheaper.

Because value companies usually don’t grow as quickly, value stocks often don’t produce large capital gains. So where does the return come from? Many value companies pay cash dividends. Allstate is an example; it has consistently paid quarterly dividends to shareholders.

Price-to-book ratio

There are several ways to estimate a company’s value. Book value uses accounting measures - especially assets and liabilities - to estimate what the company is worth. There are multiple ways to calculate book value, but the details aren’t important for the exam. In general, you can think of book value as the company’s value from an accountant’s perspective.

The price to book ratio compares a company’s stock price to its book value. You’re unlikely to be asked to calculate it, but here’s the formula:

PB ratio=Book value per shareCommon stock market price​

The higher the stock price is relative to book value, the higher the price-to-book ratio. High price-to-book ratios may indicate a company is overvalued. For example, if an accountant estimates a company is worth $2 million (book value), but the market values it at $100 million (market price), the price-to-book ratio would be 50. For reference, most stocks don’t exceed a ratio of 5:1, and the average ratio in the S&P 500 is roughly 3.

The lower the stock price is relative to book value, the lower the price-to-book ratio. Low price-to-book ratios may indicate a company is undervalued. For example, if book value is $2 million but the market price is $1 million, the price-to-book ratio would be 0.5, well below the S&P 500 average of about 3.

Dividend payout ratio

After a corporation pays its cost of goods sold, operating expenses, interest and principal on outstanding debts, and taxes, it has net earnings (profits). To see how this works, here’s the sample income statement from the fundamental analysis chapter:

Line item Amount
Sales revenue +$200,000
Cost of goods sold (COGS) -$80,000
Gross profit $120,000
Operating expenses -$30,000
Income from operations (EBIT)* $90,000
Interest (bonds & loans) -$25,000
Income before taxes (EBT)* $65,000
Taxes -$10,000
Net income $55,000

*EBIT = earnings before interest & taxes
*EBT = earnings before taxes

In this example, the corporation has $55,000 of net income (net earnings). When profits exist, a corporation can use them in one of three ways:

  • Retain the profits for future business expenses
  • Distribute the profits to shareholders (cash dividend)
  • Retain part, distribute part

Growth companies often retain profits so they have capital to expand. Value companies, which tend to be larger and consistently profitable, often distribute part of their profits as cash dividends and retain the rest for future business needs. It’s rare for a company to distribute 100% of its earnings.

Because of this, investors often want to know a company’s dividend payout ratio. Here’s the formula:

Dividend payout ratio=Net income (earnings)Total dividends paid​

Using the same income statement, we can add two lines to show dividends and retained earnings:

Line item Amount
Sales revenue +$200,000
Cost of goods sold (COGS) -$80,000
Gross profit $120,000
Operating expenses -$30,000
Income from operations (EBIT)* $90,000
Interest (bonds & loans) -$25,000
Income before taxes (EBT)* $65,000
Taxes -$10,000
Net income $55,000
Dividends paid -$20,000
Retained earnings $35,000

*EBIT = earnings before interest & taxes
*EBT = earnings before taxes

Can you calculate the dividend payout ratio?

(spoiler)

Answer = 36.4%

To calculate the dividend payout ratio, you need two items: net income and dividends paid. The corporation reported $55,000 in net income and paid $20,000 in dividends.

Dividend payout ratio=$55,000$20,000​

Dividend payout ratio=36.4%

You may also see this calculation using per-share figures. Here’s an example:

An investor is researching a stock and performing several calculations to determine its quality. They find the following pieces of data:

  • Quarterly dividend = $1.00
  • EPS = $10.00

When the inputs are per share, the dividend payout ratio is typically written as:

Dividend payout ratio=EPSAnnual dividends​

Earnings per share (EPS) measures profitability on a per-share basis. For example, a company with $10,000,000 of net earnings and 1,000,000 shares outstanding would have EPS of $10.

EPS=Shares outstandingNet earnings​

EPS=1,000,000$10,000,000​

EPS=$10

Now return to the dividend payout ratio question:

An investor is researching a stock and performing several calculations to determine its quality. They find the following pieces of data:

  • Quarterly dividend = $1.00
  • EPS = $10.00

What is the stock’s dividend payout ratio?

Can you figure it out?

(spoiler)

Answer = 40%

Watch the timing. Dividends are given quarterly, but the dividend payout ratio uses annual dividends. A $1.00 quarterly dividend equals $4.00 per year. EPS is already annual, so it stays $10.00.

Dividend payout ratio=EPSAnnual dividends​

Dividend payout ratio=$10.00$4.00​

Dividend payout ratio=40%

In summary, the dividend payout ratio shows how much of a company’s profits are paid out to shareholders. Growth companies tend to have low payout ratios (or no payout ratio if they don’t pay dividends), while value companies often have higher payout ratios.

Time value of money concepts

In the dividend models and discounted cash flow chapters, we introduced the time value of money. A dollar received today is worth more than a dollar received in the future because of opportunity cost. If you receive money later, you lose the chance to invest it and earn returns in the meantime.

For the rest of this chapter, the focus is on:

  • Present value (review)
  • Net present value (NPV)
  • Internal rate of return (IRR)

Present value

This section (Present value) is a repeat from the previous discounted cash flow chapter, but the NPV and IRR sections in this chapter are new. Regardless, you should re-read this section as the following sections build upon the example discussed below.

Present value tells you what a future amount of money is worth in today’s dollars.

PV=(1+DR)nFV​where:PVFVDRn​=present value=future value=discount rate=# of years​

Here’s what each part means:

  • Future value (FV): the cash you’ll receive in the future
  • Discount rate (DR): the market’s average rate of return (the return you give up by waiting)
  • n: how many years you must wait to receive the cash

Now work through an example:

An investor is considering the purchase of a $1,000 par, 2-year, 5% corporate debenture currently trading at 97. The rate of return in the market is 6%. What is the present value of the debenture?

Because this is a 2-year bond, there are two sets of cash flows to discount:

  • The interest payment at the end of year 1
  • The interest payment plus principal repayment at the end of year 2

Present value - year 1
The bond pays a 5% coupon, based on its par value of $1,000. That means it pays $50 of annual interest. In year 1, the investor receives only this $50.

PV=(1+DR)nFV​

PV=(1+0.06)1$50​

PV=1.06$50​

PV=$47.17

Interpreting the result: if the market return is 6%, then receiving $50 one year from now is equivalent to having $47.17 today and earning 6% for one year. The difference reflects the opportunity cost of waiting.

Present value - year 2
In year 2, the investor receives another $50 of interest and the $1,000 par value at maturity, for a total of $1,050.

PV=(1+DR)nFV​

PV=(1+0.06)2$1,050​

PV=1.062$1,050​

PV=1.1236$1,050​

PV=$934.50

Interpreting the result: receiving $1,050 two years from now is equivalent to having $934.50 today and earning 6% compounded for two years.

Putting it all together
Add the present values of the year 1 and year 2 cash flows:

Total PV=Year 1 PV + Year 2 PV

Total PV=$47.17 + $934.50

Total PV=$981.67

From a time value of money perspective, the bond’s present value is $981.67. This gives you a benchmark to compare against the bond’s current market price.

Net present value (NPV)

Once you’ve calculated present value, compare it to the investment’s market value (its cost). That comparison is the net present value (NPV):

NPV=Present value - investment cost

From the present value example above:

  • Bond’s market price = $970.00
  • Bond’s present value = $981.67

Now calculate NPV:

NPV=Present value - investment cost

NPV=$981.67 - $970.00

NPV=$11.67

Because present value ($981.67) is higher than the market price ($970.00), the bond appears underpriced by $11.67 based on this discounted cash flow approach. A positive NPV suggests the investment is a “good deal” relative to the discount rate used. If you’re comparing multiple investments using discounted cash flow, the one with the highest positive NPV would be preferred.

A negative NPV suggests the opposite. Reset the numbers:

  • Bond’s market price = $990.00
  • Bond’s present value = $981.67

Now calculate NPV:

NPV=Present value - investment cost

NPV=$981.67 - $990.00

NPV=-$8.33

Here, the bond appears overpriced by $8.33 based on the same discounted cash flow approach.

One common point of confusion: NPV is not simply a measure of whether you’ll make money in absolute terms. Even with a negative NPV, the investor may still receive interest and principal and end with more dollars than they started with. NPV is best understood as a comparison to the market return used as the discount rate:

  • Positive NPV: returns are better than the market average (given the discount rate)
  • Negative NPV: returns are worse than the market average

What if NPV is zero? That means the investment is appropriately priced* - its present value equals its market price. In return terms, a zero NPV implies the investment’s return matches the average market return (the discount rate).

*When an investment is appropriately priced, the market it trades in is efficient. The more efficient a market, the more its prices reflect true value. On the other hand, an inefficient market has over and/or underpriced investments, which would reflect positive and/or negative NPVs.

Internal rate of return (IRR)

An investment’s internal rate of return (IRR) measures its overall rate of return. The word “internal” means the calculation focuses on the investment’s own cash flows rather than external forces (for example, inflation or other market risks). A common textbook definition is:

The IRR is the discount rate that results in the NPV of all future cash flows being equal to zero

This connects directly to what you just saw with NPV:

  • If NPV is zero, the investment’s return equals the market return used as the discount rate.

Return to the earlier example:

An investor is considering the purchase of a $1,000 par, 2-year, 5% corporate debenture currently trading at 97. The rate of return in the market is 6%.

We calculated the bond’s present value as $981.67. If the bond traded at exactly $981.67, NPV would be zero, and the bond’s IRR would be equal to the market return (6%).

Now compare that to different market prices:

  • If the market price is $970.00, NPV is positive ($11.67). A positive NPV implies the IRR is higher than the market return (6%).
  • If the market price is $990.00, NPV is negative (-$8.33). A negative NPV implies the IRR is lower than the market return (6%).

Here’s the relationship in table form:

NPV IRR
Positive Greater than average market return
Zero Equal to average market return
Negative Lower than average market return

A bond’s IRR is equal to its yield to maturity (YTM). YTM is the bond’s overall rate of return if held to maturity. Test questions may use IRR and YTM interchangeably.

Present value, NPV, and IRR work best when future cash flows are predictable. Bonds are a good fit because they pay fixed interest and return par value at maturity, so the future cash flows are known.

These tools are less useful when future cash flows are uncertain. That’s why present value, NPV, and IRR calculations are not typically associated with securities like common stock*. Many common stocks pay no cash dividends, and even dividend-paying companies may raise, suspend, or cancel dividends.

*While present value, NPV, and IRR calculations are not typically utilized for common stock due to its unpredictable future cash flow, it can be used for preferred stock. As a reminder, preferred stock pays a fixed, predictable dividend rate.

Bottom line: time value of money calculations are most appropriate when future cash flow is predictable. As cash flows become less predictable, present value, NPV, and IRR become less relevant and less accurate.

Key points

PE ratio

  • PE=earnings per sharemarket price​

High PE ratios

  • May indicate an overpriced investment
  • Typical of growth companies

Low PE ratios

  • May indicate an underpriced investment
  • Typical of value companies

Price to book ratio

  • PB=book value per sharecommon stock market price​

High price-to-book ratios

  • May indicate an overpriced investment

Low price-to-book ratios

  • May indicate an underpriced investment

Dividend payout ratio

  • Dividend payout ratio=Net income (earnings)Total dividends paid​

Dividend payout ratio (on a per share basis)

  • Dividend payout ratio=EPSAnnual dividends​

High dividend payout ratios

  • Company shares significant profits with shareholders
  • Typical for large, well-established value companies

Low dividend payout ratios

  • Company shares little-to-no profits with shareholders
  • Typical for growth companies

Earnings per share

  • EPS=Shares outstandingNet earnings​

Time value of money

  • Money received sooner is worth more due to opportunity cost

Opportunity cost

  • Lost returns from a missed investing opportunity

Discounted cash flow

  • Tool for determining the present value of future cash flows
  • Factors in opportunity cost

Present value

  • Value of future cash flows in today’s dollars

Present value formula

  • PV=(1+DR)nFV​

Net present value (NPV)

  • Compares present value to market value
  • Demonstrates a security’s investment worthiness
  • Positive NPV = undervalued
  • Zero NPV = priced appropriately
  • Negative NPV = overvalued

NPV calculation

  • NPV=Present value - investment cost

Internal rate of return (IRR)

  • The discount rate that results in the NPV of all future cash flows equal to zero
  • Represents a security’s overall rate of return
  • IRR is equal to a bond’s YTM
  • Best if analyzing predictable cash flows
  • Positive NPV = investment’s IRR > average market returns
  • Zero NPV = investment’s IRR = average market returns
  • Negative NPV = investment’s IRR < average market returns

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