## Estimating Horizon Value

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There are several common formulas or rules of thumb for estimating horizon value. First, let us try the constant-growth DCF formula. This requires free cash flow for year 7, which we have from Table 4.7, a long-run growth rate, which appears to be 6 percent, and a discount rate, which some high-priced consultant has told us is 10 percent. Therefore,

The present value of the near-term free cash flows is

and, therefore, the present value of the business is

PV(business) = PV(free cash flow) + PV(horizon value) = -3.6 + 22.4

Now, are we done? Well, the mechanics of this calculation are perfect. But doesn't it make you just a little nervous to find that 119 percent of the value of the business rests on the horizon value? Moreover, a little checking shows that the horizon value can change dramatically in response to apparently minor changes in assumptions. For example, if the long-run growth rate is 8 percent rather than 6 percent, the value of the business increases from \$18.8 to \$26.3 million.9

In other words, it's easy for a discounted-cash-flow business valuation to be mechanically perfect and practically wrong. Smart financial managers try to check their results by calculating horizon value in several different ways.

Horizon Value Based on P/E Ratios Suppose you can observe stock prices for mature manufacturing companies whose scale, risk, and growth prospects today

9If long-run growth is 8 rather than 6 percent, an extra 2 percent of period-7 assets will have to be plowed back into the concatenator business. This reduces free cash flow by \$.53 to \$1.06 million. So,

FV(horizon value) = —(^ ) = \$29.9 PV(business) = —3.6 + 29.9 = \$26.3 million

78 PART I Value roughly match those projected for the concatenator business in year 6. Suppose further that these companies tend to sell at price-earnings ratios of about 11. Then you could reasonably guess that the price-earnings ratio of a mature concatenator operation will likewise be 11. That implies:

PV(horizon value) = ^^^ (11 X 3.18) = 19.7 PV(business) = -3.6 + 19.7 = \$16.1 million

Horizon Value Based on Market-Book Ratios Suppose also that the market-book ratios of the sample of mature manufacturing companies tend to cluster around 1.4. (The market-book ratio is just the ratio of stock price to book value per share.) If the concatenator business market-book ratio is 1.4 in year 6,

PV(horizon value) = (1.4 X 23.43) = 18.5 PV(business) = -3.6 + 18.5 = \$14.9 million

It's easy to poke holes in these last two calculations. Book value, for example, often is a poor measure of the true value of a company's assets. It can fall far behind actual asset values when there is rapid inflation, and it often entirely misses important intangible assets, such as your patents for concatenator design. Earnings may also be biased by inflation and a long list of arbitrary accounting choices. Finally, you never know when you have found a sample of truly similar companies.

But remember, the purpose of discounted cash flow is to estimate market value— to estimate what investors would pay for a stock or business. When you can observe what they actually pay for similar companies, that's valuable evidence. Try to figure out a way to use it. One way to use it is through valuation rules of thumb, based on price-earnings or market-book ratios. A rule of thumb, artfully employed, sometimes beats a complex discounted-cash-flow calculation hands down.

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### Responses

• Rudolph
What is horizon value in finance?
8 years ago
• Cheryl Glover
What is the formula for the finance horizon?
7 years ago