SWC Investment Club

Introduction to Valuation Models

The Discounted Cash Flow Model

“Value matters. You ignore value at your peril.”

‒ Greg Ireland, mutual fund manager with over 35 years experience

“It is a capital mistake to theorize before one has data.”

‒ Famed Detective Sherlock Holmes (Sir Arthur Conan Doyle)

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Common Stock Valuation

• Stock Valuation
• The process by which the underlying value of a stock is established on the basis of its forecasted risk and return performance
• At any given time, the price of a share of common stock depends on investors’ expectations about the future behavior of the security
• A fundamental assertion of finance holds that the value of a stock is based on the present value of its future cash flows (aka earnings or dividends or both)

The worth of a company is primarily based on the earnings the company will produce in the future. But if we knew what was going to happen in the future, it would not be called the future, would it?

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Common Stock Valuation

• Stock Valuation
• “The most fundamental influence on stock prices is the level and duration of the future growth of earnings and dividends. [However,] future earnings growth is not easily estimated, even by market professionals.” – Burton Malkiel, A Random Walk Down Wall Street

So, if someone were to ask you, “What is the most important factor in determining the future value of a company?” In a few words, you could say, “FUTURE EARNINGS!” (or FUTURE DIVIDENDS)

But do any of us know what is going to happen in the future? “NO!”

So is valuing stock going to be easy? “NO!”

(continued)

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Dividend Discount Models

• One popular group of models of fundamental analysis are the dividend discount models
• Shares of stock are valued on the basis of the present value of the future dividend streams the stock is projected to produce
• Recall: The value of a stock is based on the present value of its future cash flows
• Therefore, dividend discount models should be extremely popular, right?

During the late 1990’s, investors who adhered to these types of models were considered old fashioned and outdated. But those investors weathered the 2000-2002 downturn very well. Dividends have become important again. “Dividends don’t lie.”

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The Discount Rate

• The discount rate is the required rate of return that we choose to calculate the value of shares of a stock using the dividend discount models
• The predicted valuations are very sensitive to our required rate of return
• Our results will vary widely depending upon our choice of the required rate of return

The fact that everyone has a different required rate of return means that different investors will expect and demand different stock prices. Someone might be happy with 6%. Another might expect 10%. A third wants 15%.

“It is the difference of opinion that makes horse races.”

‒ Mark Twain

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Discounted Cash Flow Model

• A powerful version of the DDMs is the Discounted Cash Flow Model
• Value of stock = present value of all expected future annual cash flows

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• Example: Three annual dividends of $10 per share
• And then zero dividends from then on
• Required rate of return = 7%
• ($10/1.07)+($10/1.07²)+($10/1.07³) = $26.24

But how often do companies pay three annual dividends and then promptly go out of business?! Plus, we keep using this term “present value.” What does present value mean anyway?

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What is “Present Value?”

• Present Value
• The value today of a lump sum or series of payments to be received at some future date
• It is the opposite of future value (aka the inverse)
• That you might have learned about in BUS-121 or BUS-183

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• Future value of $10,000 in 10 years at 10%
• $10,000 * 2.594 = $25,940 (1 + 10%) ^{10 years}

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• Present value of $25,940 in 10 years at 10%
• $25,940 * 0.386 = $10,000 1 1

$10,000 * 2.1589 = $2 1,589 (1 + 10%) ^{10 years}

Present value and future value are just two sides of the same coin.

In finance, present value tells us what the future value is worth today. Computing the present value is called “discounting.” (I know. It sounds kinda’ dumb but get used to it because that is the term we use.)

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Present Value & Discounting

• Did the formula for the model scare you?

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• This formula has the present value calc built into it
• We mortals simply use the Present Value tables to discount the future annual cash flows
• We use the Future Value tables for future value
• The formula becomes:

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PVM₁ is the present value multiplier for year #1, PVM₂ is the multiplier for year #2, etc. We use the present value multipliers to “discount” the future cash flow values back to the present.

Value = CashFlow₁*PVM₁ + CashFlow₂*PVM₂ + CashFlow₃*PVM₃ + etc

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Present Value & Discounting

• Let’s do the same example over again
• Using the Present Value Multipliers from the Present Value Table on the class website
• http://wonderprofessor.com/123/Chap04/Chap04_PresentValueTable.pdf
• Three annual dividends of $10 per share
• Required rate of return = 7%

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Value = ($10*0.935) + ($10*0.873) + ($10*0.816)

= $9.35 + $8.73 + $8.16

= $26.24 (same as result using the formula on slide 21)

What is the present value of the future stream of dividends?

At 7%, $10 in 1 year is worth $9.35, in 2 years $8.73, 3 years $8.16.

The sum of the present values of the future annual dividend cash flows equals our perceived value of the stock.

(continued)

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Present Value & Discounting

• The present value multipliers come from the present value table on the class website
• http://wonderprofessor.com/123/Chap04/Chap04_PresentValueTable.pdf

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We multiplied the cash flow from the dividends in year #1 by the present value multiplier at 7% for year #1. We then did the same for the dividend payments for years #2 and #3. Adding them all together gives us the present value of the future stream of dividend payments.

(continued)

Present Value = ($10*0.935) + ($10*0.873) + ($10*0.816) = $9.35 + $8.73 + $8.16 = $26.24

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Discounted Cash Flow Model

• Our example did not take into account that the stock will still have worth at the end of the three years
• To make the model more useful, we simply add our predicted market price of the stock at the end of the three years
• We treat the price of the stock at the end of the three years as a future cash flow
• Value of stock = present value of future dividends +

present value of the price of stock when we plan to sell

• Again, we use the present value multipliers

This model is very sensitive to our estimates and our choice of required rate of return and, hence, the results vary wildly.

(continued)

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Discounted Cash Flow Model

• Let’s say the current price of the stock is $125 and we predict the market price of the stock will be $135 at the end of the three years

Our model says that the present value of the future stream of cash flows from this stock is $136.40. The current market price is $125. The model is telling us that this is a potentially good investment for us at 7%.

(continued)

Notice that the present value multiplier for the dividend in year #3 and the expected stock price at the end of year #3 are the same. We are receiving the future cash flows in the same year so we use the same present value multiplier.

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Discounted Cash Flow Model

• Example 2:
• Pretzels Unlimited is currently selling for $22 per share and will pay $2.00 per share in dividends in 2024. PU expects to increase their dividends to $2.20 in 2025, $2.30 in 2026, and $2.30 in 2027. We will be selling the stock at the end of 2027 and we expect the price to be $27 per share at that time. Our required rate of return is 12%.
• Value of stock = present value of future dividends

+ present value of price of stock when you plan to sell

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Value = ($2.00*0.893)+(2.20*0.797)+(2.30*0.712)+(2.30*0.636)

+ ($27.00*0.636) =

= [ $1.786 + $1.7534 + $1.6376 + $1.4628 ] + $17.172 =

= $6.6398 + $17.172 = $23.8118 ≅ $23.81

We believe it is worth $23.81 if our required rate of return is 12%. With a market price of only $22, this is a potentially good investment.

(continued)

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Discounted Cash Flow Model

• Example 2:
• Pretzels Unlimited in Table Format

(continued)

Here is the problem in spreadsheet format. I think it is much easier to comprehend and calculate in this format, yes?

But let’s simplify it a bit …

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Discounted Cash Flow Model

• Example 2 (Simplified):
• Pretzels Unlimited in a More Simplified Table Format

(continued)

Adding the dividend and the stock price in the last year saves us a couple of manual calculations but more importantly, it also allows us to use a special spreadsheet function to calculate …

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Discounted Cash Flow Model

• Internal Rate of Return (aka IRR)
• The Internal Rate of Return is a measure of what rate of return we expect to get from a series of cash flows, including positive and negative flows
• Someday, when you take an upper-level or graduate finance or investment class, you will learn how to manually compute Internal Rate of Return
• Hopefully, you will not have a sadistic professor who will require you to calculate it manually more than once!
• We are simply going to enter the numbers into a spreadsheet formula and press , okay?

(continued)

In other words, we required a 12% rate of return from Pretzels Unlimited, but what do our numbers tell us will be our expected rate of return?

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Discounted Cash Flow Model

• Internal Rate of Return (aka IRR), continued
• The spreadsheet formula is:
• =IRR(values,approximate-rate-of-return) where
• values is the block of cells containing the cash flows, both positive and negative, and
• approximate-rate-of-return is our guess as to what the Internal Rate of Return will be

(continued)

Let’s take a look at the example spreadsheet on the class web page …

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Discounted Cash Flow Model

• Example 3:
• Genes ’R’ Us, symbol GRUS, is currently selling for $21 per share. It pays no dividends. We believe that GRUS will sell for around $50 per share in five years. Our required rate of return is 13%. How can we determine if this is a potentially good investment?
• With no dividends, which model can we use?
• The Discounted Cash Flow Model can still be used!
• Value of stock = present value of future dividends

+ present value of price of stock when you plan to sell

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Value = $0.00 (from dividends) + ($50.00*0.543) = $27.15

(continued)

Unlike the other DDM’s, the Discounted Cash Flow Model can still be used if there are no dividends. We simply treat the expected future price of the stock as a single future cash flow. Very cool!

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Discounted Cash Flow Model

• Let’s apply the two spreadsheets to GRUS
• Current market price = $21 and we expect the stock price to be $50 in five years. GRUS pays no dividends
• Present value multiplier for 5 years at 13% is 0.543

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(continued)

We tell the BUS-123 students that they can’t leave Introduction to Investments without knowing how to compute the Discounted Cash Flow Model! If they don’t learn how to compute these problems, it is very bad for my self-esteem!

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Sources of Information

• Okay, Paiano, this is all great, but just where are we supposed to get all this historical information, anyway? And just who decides what next year’s earnings or dividends per share, the dividend growth rate, etc. are going to be, let alone the expected price of a stock in 3 to 5 years?!
• Before the Internet (BI?), this information was not readily available
• Normally, you would ask your broker for it
• Or you would use one of the securities industry’s trusted information sources
• Traditionally, the most respected source was …

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The Value Line

• Still one of the most respected and trusted sources of data and analysis
• Traditionally, it was often the only source many investors used for data and analysis
• Along with the company’s materials
• Expensive ($598 per year, www.valueline.com), but can be obtained for free at various libraries (See class website)

I am a big fan of The Value Line, especially their Timeliness and Safety indicators and 3- to 5-year price appreciation prediction.

One study (which ignored transaction costs and tax consequences) only used their Timeliness indicator. It showed how you would have beaten the market handsomely over a twenty year period by just buying and selling stocks as they received and lost their #1 Timeliness designation.

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The Value Line

• Can you find the following?
• The Value Line indicators
• The future price projections
• The historical data
• The cash assets, receivables, inventory, and other assets
• The description and analysis of the business
• The historical annual rates
• The insider and institutional buying & selling
• The amount of debt and number of shares outstanding
• The company’s financial strength, stability, price growth, and earnings predictability ratings

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The Value Line Example: Johnson & Johnson, 9 February 2024

(continued)

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The Value Line

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The Value Line

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The Value Line

• A Sip from the Financial Firehose!
• Interspersed among the mountain of data, did you notice the highlighted historical dividends, the future stock price predictions, and the predicted dividend growth?
• There are other models that use the sales, earnings, cash flow, profit margins, etc.
• Did you read the company analysis?
• Personally, Your Humble Instructor does not make any decisions about individual stocks without consulting The Value Line

Now let’s take a look at a spreadsheet that uses data from The Value Line to quickly calculate the predicted values of the Discounted Cash Flow Model and another model, the Gordon Growth Model.

(continued)

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The Value Line

(continued)

In the shaded areas, we enter the historical dividends per share, the current price, the predicted price in 3, 4, or 5 years, and The Value Line’s predicted dividend growth. The spreadsheet does the rest! This part calculates the Gordon Growth Model predictions (which we didn’t covered today but we will cover in the BUS-123, Introduction to Investments, class starting next week).

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The Value Line

(continued)

Here we calculated the predictions from the Discounted Cash Flow Model using both our computed average dividend growth rate of 5.71% over the past several years and The Value Line’s predicted dividend growth rate of 6.0% for the next five years.

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The Value Line

(continued)

The Internal Rate of Return calculations using both our average dividend growth rate and The Value Line’s predicted dividend growth rate give us similar results. Would you consider owning Johnson ‘n’ Johnson? You may have gotten their Covid-19 vaccine.

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The Bottom Line

• Okay, once we have finished all our valuation calculations, what should we do? Should we really place much value in our predictions? The answer is, “NO!” Rather, we should…
• Hurl them into the vast ocean along with the ashes of our dead pets and relatives, or
• Shred them into millions of little pieces and use them as confetti at our next party, or
• Burn them in a huge bonfire as we dance naked under the full moon, or all three!

We do these calculations to simply tilt the odds in our favor. Instead of placing any significance in our predictions, after we have finished, we should ignore them and ask ourselves some very simple questions:

Do I want to own this company? Do I believe this business will succeed?

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A Final Word on Valuation

“The problem is that it is easy to confuse the capability to make precise forecasts with the ability to make accurate ones. Any attempt to value businesses with precision will yield values that are precisely inaccurate.”

– Margin of Safety, Seth A. Klaman

We know beforehand that as we make these calculations that there is a 99.99% chance that they will be inaccurate. So why do we perform them? These calculations help us identify companies that are prudent, long-term oriented investments. They won’t make us wealthy quickly, but they will make us wealthy. To quote a very wise client of mine, “I don’t have to win big. I just have to win.”

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SWC Investment Club

Next week in the BUS-123, Introduction to Investments, class, we will begin chapter 4 on Fundamental Analysis: Valuation Models where we teach these models. You are all welcome to join us at https://www.wonderprofessor.com/123.

Introduction to Valuation Models

The Discounted Cash Flow Model

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