Valuation Ratios, NPV & IRR
What this chapter covers
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
Note: the page’s own body content runs from the PE ratio through IRR. The descriptive-statistics items listed above are delivered in the following chapter (3.4 Descriptive statistics).
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.
🔑 Formula
PE ratio = common stock market price ÷ earnings per share
⚠️ Reconstructed fraction. The page’s text extraction flattens fractions and prints the denominator first — it renders as “PE ratio = Earnings per share / Common stock market price”. The correct orientation is market price over EPS, verified by the page’s own explanation: “a PE ratio of 100 means the market price is 100 times the company’s annual earnings per share.”
Interpretation
- 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.
| Company type | Typical PE | Why | Page’s example |
|---|---|---|---|
| Growth companies | Higher PE | These businesses are expanding and are expected to generate higher profits in the future. The stock may look “expensive” today, but investors may still consider it attractive if they expect strong long-term growth | Roku (ROKU) reflected a PE ratio of 180 as of October 2021 — the stock price was 180 times annual EPS. 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 | Lower PE | 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 | Allstate (ALL) reflected a PE ratio of 6 as of October 2021 — the stock price was 6 times annual EPS. 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.
🔑 Formula
PB ratio = common stock market price ÷ book value per share
⚠️ Reconstructed fraction. The page renders this as “PB ratio = Book value per share / Common stock market price” (denominator printed first). The correct orientation is market price over book value per share, verified by the page’s own worked example: book value $2 million vs. market price $100 million gives a ratio of 50 (100 ÷ 2), not 0.02.
Interpretation
| Ratio level | Meaning | Page’s example |
|---|---|---|
| High price-to-book | The higher the stock price is relative to book value, the higher the ratio. May indicate a company is overvalued | Accountant estimates a company is worth $2 million (book value), but the market values it at $100 million (market price) → price-to-book ratio of 50 |
| Low price-to-book | The lower the stock price is relative to book value, the lower the ratio. May indicate a company is undervalued | Book value $2 million but market price $1 million → price-to-book ratio of 0.5, well below the S&P 500 average of about 3 |
- For reference, most stocks don’t exceed a ratio of 5:1, and the average ratio in the S&P 500 is roughly 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).
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).
🔑 What a corporation can do with profits
When profits exist, a corporation can use them in one of three ways:
| # | Use of profits |
|---|---|
| 1 | Retain the profits for future business expenses |
| 2 | Distribute the profits to shareholders (cash dividend) |
| 3 | 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.
🔑 Formula
Dividend payout ratio = total dividends paid ÷ net income (earnings)
⚠️ Reconstructed fraction. The page renders this as “Dividend payout ratio = Net income (earnings) / Total dividends paid” (denominator printed first). The correct orientation is total dividends paid over net income, verified against the page’s own worked answer: $20,000 dividends ÷ $55,000 net income = 36.4%. (The page’s worked step also prints flattened as “$55,000 / $20,000”.)
Worked example 1 — whole-dollar figures
Income statement extended with 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 |
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 = total dividends paid ÷ net income Dividend payout ratio = $20,000 ÷ $55,000 Dividend payout ratio = 36.4%
🔑 Per-share version
You may also see this calculation using per-share figures.
Dividend payout ratio = annual dividends ÷ EPS
⚠️ Reconstructed fraction. The page renders it as “Dividend payout ratio = EPS / Annual dividends”. Correct orientation is annual dividends over EPS, verified by the page’s worked answer: $4.00 ÷ $10.00 = 40%.
🔑 Earnings per share (EPS)
EPS = net earnings ÷ shares outstanding
⚠️ Reconstructed fraction. The page renders it as “EPS = Shares outstanding / Net earnings”. Correct orientation is net earnings over shares outstanding, verified by the page’s worked example below.
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 = net earnings ÷ shares outstanding EPS = $10,000,000 ÷ 1,000,000 EPS = $10
Worked example 2 — per-share figures
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? 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 = annual dividends ÷ EPS Dividend payout ratio = $4.00 ÷ $10.00 Dividend payout ratio = 40%
Summary
The dividend payout ratio shows how much of a company’s profits are paid out to shareholders.
| Payout ratio | Typical of |
|---|---|
| Low (or none) | Growth companies |
| High | Value companies |
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.
🔑 Formula
PV = FV ÷ (1 + DR)^n
⚠️ Reconstructed fraction. The page renders this stacked/flattened as “PV = (1+DR) n FV”. The correct form is future value over (1 + discount rate) raised to n, verified by the page’s own worked calculations below.
Where:
| Symbol | Meaning | What it means in practice |
|---|---|---|
| PV | Present value | Value of the future cash in today’s dollars |
| FV | Future value | The cash you’ll receive in the future |
| DR | Discount rate | The market’s average rate of return (the return you give up by waiting) |
| n | # of years | How many years you must wait to receive the cash |
Worked 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 = FV ÷ (1 + DR)^n PV = $50 ÷ (1 + 0.06)^1 PV = $50 ÷ 1.06 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 = FV ÷ (1 + DR)^n PV = $1,050 ÷ (1 + 0.06)^2 PV = $1,050 ÷ 1.06^2 PV = $1,050 ÷ 1.1236 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).
🔑 Formula
NPV = Present value − investment cost
Worked example — positive NPV
From the present value example above:
- Bond’s market price = $970.00
- Bond’s present value = $981.67
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.
Worked example — negative NPV
- Bond’s market price = $990.00
- Bond’s present value = $981.67
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.
⚠️ 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:
| NPV | Meaning |
|---|---|
| Positive NPV | Returns are better than the market average (given the discount rate) — investment is undervalued |
| Zero NPV | Investment is appropriately priced — present value equals market price; the investment’s return matches the average market return (the discount rate) |
| Negative NPV | Returns are worse than the market average — investment is overvalued |
- *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).
🔑 Definition (word-for-word)
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.
Worked 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%).
🔑 NPV ↔ IRR relationship
| NPV | IRR |
|---|---|
| Positive | Greater than average market return |
| Zero | Equal to average market return |
| Negative | Lower than average market return |
🔑 IRR = YTM
- 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.
When these tools apply
- 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 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 = market price ÷ earnings per share ⚠️ (reconstructed from the page’s flattened “PE = earnings per share / market 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 = common stock market price ÷ book value per share ⚠️ (reconstructed from the page’s flattened “PB = book value per share / common 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 = total dividends paid ÷ net income (earnings) ⚠️ (reconstructed)
Dividend payout ratio (on a per share basis)
- 🔑 Dividend payout ratio = annual dividends ÷ EPS ⚠️ (reconstructed)
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 = net earnings ÷ shares outstanding ⚠️ (reconstructed)
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 = FV ÷ (1 + DR)^n ⚠️ (reconstructed from the page’s flattened “PV = (1+DR) n FV”)
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
Sources
Primary/official references for the material in this chapter. Every link was fetched and returned HTTP 200 on 2026-08-15.
| # | Source | Publisher |
|---|---|---|
| 1 | Beginners’ guide to financial statements — balance sheet, income statement | SEC |
| 2 | Compound interest / time value of money calculator | SEC / Investor.gov |
| 3 | e-Handbook of Statistical Methods — mean, median, dispersion | NIST/SEMATECH |
| 4 | Achievable Series 65 — chapter 3.3 | Achievable (course text) |