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Calculating Perpetuity Values (download this book in pdf)
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We're almost there—we have cash flow estimates, and we have a discount rate. We need only one more element, called a perpetuity value, and we're ready to put the whole thing together. We need a perpetuity because it's not feasible to project a company's future cash flows out to infinity, year-by-year, and because companies have theoretically infinite lives.

The most common way to calculate a perpetuity is to take the last cash flow (CF) that you estimate, increase it by the rate at which you expect cash flows to grow over the very long term (g), and divide the result by the discount rate (R) minus the expected long-term growth rate. In formula terms, this equals:

The result of this calculation then must be discounted back to the present, using the method I discussed previously. Let's run through an example to show you what I mean.

For example, suppose we're using a 10-year DCF model for a company with an 11 percent discount rate. We estimate that the company's cash flow in year 10 will be Si billion and its cash flows will grow at a steady 3 percent annual rate after that. (Three percent is generally a good number to use as your long-run growth rate because it's roughly the average rate of U.S. gross domestic product [GDP] growth. If you're valuing a firm in a declining industry, you might use 2 percent.)

First, multiply Si billion by 1.03 to get an estimated Si.03 billion cash flow in year 11.

Si billion X 1.03 = $1.03 billion

Divide $1.03 billion by 0.08 (our 11 percent discount rate minus 3 percent long-run growth rate) to get SI2-88 billion in estimated cash flows from year 11 onward.

S1.03 billion = SI2.88 billion

0.11-0.03

To get the present value of these cash flows, we need to discount them using the formula we saw earlier: CF /(i + R) n , where n is the number of years in the future, CF is the cash flow in year n, and R is the discount rate. Plugging in the numbers:

CF n = $12.88 billion

R = o.u $12.88 S1288

= $4,536 billion

(i.n) 10 2.839

Now, all we need to do is add this discounted perpetuity value to the discounted value of our estimated cash flows in years I through 10, and divide by the number of shares outstanding (see Figure 10.2).

I'll go through a couple of detailed examples in the next chapter, but here's a brief outline of the process. I'll use Clorox as an example again. Ifou can follow along by matching the following steps to Figure 10.3:

I. Estimate free cash flows for the next four quarters. This amount will de­pend on all of the factors we discussed earlier in the book—how fast the

Step 1 Forecast free cash flow (FCF) for the next 10 years.

Step 2 Discount these FCFs to reflect the present value:

? Discounted FCF - FCF for that year -^ (1 +RJ"

(where R = discount rate and N - year being discounted!

Step 3 Calculate the perpetuity value and discount it to the present:

•  Perpetuity Value = FCF,, X (1 + g) -h (R - g)

•  Discounted Perpetuity Value = Perpetuity Value -^ (1 + R) 1D

Step 4 Calculate total eguity value by adding the discounted perpetuity value

to the sum of the 10 discounted cash flows (calculated in step 2): *~ Total Equity Value = Discounted Perpetuity Value + 10 Discounted Cash Flows

Step 5 Calculate per share value by dividing total equity value by shares outstanding:

*~ Per Share Value = Total Equity Value -=- Shares Outstanding

Figure 10.2 A step-by-step discounted cash flow model for calculating the equity value of a company. Source: Morningstar, Inc.

company is growing, the strength of its competitors, its capital needs, and so on. (We get into more detail on estimating cash flows in the next chapter when we analyze and value two firms top to bottom.) For Clorox, our first step is to see how fast free cash flow has grown over the past decade, which turns out to be about 9 percent when you do the math. We could just increase the $600 million in free cash flow that Clorox generated in 2003 by 9 percent, but that would assume that the future will be as rosy as the past. During the 1990s, the rise of mega-retailers like Wal-Mart— which now accounts for almost a quarter of Clorox's sales—has hurt the bargaining power of consumer-products firms. So, let's be conservative and assume free cash flow increases by only 5 percent over last year, which "would "work out to $630 million.

2. Estimate how fast you think free cash flow will grow over the next 5 to 10 years. Remember, only firms "with very strong competitive advantages and low capital needs are able to sustain above-average growth rates for very long. If the firm is cyclical, don't forget to throw in some bad years. We won't do this for Clorox because selling bleach and Glad bags is a very stable business. We will, however, be conservative on our growth rate

Current stock price: $45.00

Shares outstanding (mil) 221.0

Next year's free cash flow (mil) $630.00

Perpetuity growth rate (g) 3.0%

Discount rate (R) 9.0%

10-Year Valuation Model for Clorox

Step 1: Forecast free cash flow (FCF) for the next 10 years. Assumes constant 5% growth rate, free cash flows in $ millions.

Yr1 Yr2 Yr3 Yr4 Yr5 Yr 6 Yr7 Yr 8 Yr9 Yr 10 Free cash flow -> 630.0 661.5 694.6 729.3 765.8 804.1 844.3 886.5 930.8 977.3

Step 2: Discount these free cash flows to reflect the present value. Discount Factor = (1 + R] N (where Rediscount rate and N = year being discounted]

Yr 1 Yr2 Yr3 Yr4 Yr5 Yr 6 Yr7 Yr 8 Yr9 Yr 10

Free cash flow 630.0 661.5 694.6 729.3 765.8 804.1 844.3 886.5 930.8 977.3

- Discount factor 1.09 s 1.09= 1 .OS 3 1.09' 1.09= 1.09 1 1.09' 1.09 5 1.09 s 1.09' °

= Discounted FCF 4 577.9 556.8 536.3 516.7 497.7 479.4 461.8 444.9 428.6 412.8

Step 3: Calculate the perpetuity value and discount it to the present.

Perpetuity Va lue = Yr 10 FCF X (1 + g)-J-(Fi — g) (where g = perpetuity growth rate and Rediscount rate)

Perpetuity value - ¥ (412.8 X 1.03) ^ (.09-. 03) = $16,777.61
Discounted -> $16,777.61 - 1.09 10 = $7,087.05

Step 4: Calculate total eguity value.

Add the discounted perpetuity value (see above) to the sum of the 10 discounted cash flows (see step 2).

Total equityvalue ¦* $7,087.05 +$4,913.01 = $12,000.06

Step 5: Calculate per share value. Divide total equity value by shares outstanding.

Per share value -* $12,000.06 * 221.00 = $54.30

Figure 10.3 Valuing Clorox using discounted cash flow. Source: Morningstar, Inc.

because of the "Wal-Mart factor," and we'll assume free cash flow increases at J percent annually over the next decade.

3. Estimate a discount rate. Financially, Clorox is rock-solid, with little debt, tons of free cash flow, and anoncyclical business. So, we'll use 9 percent for our discount rate, which is meaningfully lower than the 10.5 percent aver­age we discussed earlier. Clorox is a pretty predictable company, after all.

4- Estimate a long-run growth rate. Because I think people "will still need bleach and trash bags in the future, and it's a good bet that Clorox will continue to get a piece of that market, I use the long-run GDP average of 3 percent.

J. That's it! We discount the first 10 years of cash flows, add that value to the present value of the perpetuity, and divide by shares outstanding.

This is a very simple DCF model—the one we use at Morningstar has about a dozen Excel tabs, adjusts for complicated items such as pensions and operating leases, and explicitly models competitive advantage periods, among many other things. But a model doesn't need to be super complex to get you most of the way there and help you clarify your thinking. For example, our valuation of Clorox—"which pegs the value of the stock at about 15 percent higher than the stock price in late 2003—has the company generating free cash flow of about $800 million per year 10 years from now.

How realistic is this? As of late 2003, only 125 companies in Morningstar's database of more than 6,500 firms were able to accomplish such a feat, so it's certainly a high hurdle. However, given Clorox's portfolio of strong brands and solid track record of product innovation it's not unreasonable. Moreover, our 5 percent estimated annual growth rate in free cash flow is a good deal lower than the firm's past growth rate, which makes the model somewhat conservative. After all, Clorox has so many strong brands—including the eponymous bleach, Pine-Sol, and Formula 409—that it may be able to hold the line when it negotiates with big retailers like Wal-Mart.

The Important thing is that "we forced ourselves to think through these kinds of issues, which we wouldn't have if we'd just looked at Clorox's stock chart or if we'd just said, "Sixteen times earnings seems reasonable." By thinking about the business, we arrived at a better valuation in which we have more confidence.

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