Today's value from tomorrow's numbers

A fornight ago, we discussed two possible ways to value a company.

The first way values a company using an estimate of the dividends it will pay out next year, divided by the yield at which investors will be enticed to invest in the company.

This is the most basic incarnation of a group of stock valuation methods called discounted cash flow models.

Discounted Cash Flow Model

The other popular method highlighted was to take a company's net profit and multiply that by a certain number of times to get an estimated value of the stock.

This is known as a price-to-earnings (PE) multiple. The investor determines the PE multiple the company is likely to trade at by taking an average of the PE multiples that similar companies are trading at, or have historically traded at.

This is part of another broad group of stock valuation methods called valuation by multiples.

But this method depends on the prices that other companies are trading at. It is a relative measure, though one that is easy to use - pick a number and multiply it by projected earnings to get your valuation.

Investors looking for a more fundamental measure of value will think about how much cash a company will generate in the foreseeable future, instead of net profit numbers that can distort the real cash flow a company is getting.

We thus return to the first method and drill deeper into the principles underpinning discounted cash flow (DCF) models.

DCF models are used by investment banks and funds to evaluate how much one should actually pay for a company.

They are preferred due to their flexibility. As investment research firm Morningstar writes on their website: "Despite their complexity, valuations based on DCF models are much more flexible than any individual ratio, and they allow an investor to incorporate assumptions about such factors as a company's growth prospects, whether its profit margins are likely to expand or contract, and how risky the company is in general."

Knowing how these models work will enable you to understand why analysts value a stock at a certain price, or why a company is willing to pay so much to acquire another company.

Today, we discuss three scenarios under which a company can be valued using a DCF model: zero growth, slow growth, and a period of fast growth followed by slow growth.

Discounted cash flow models are so named because they predict the cash flows a company will generate, and discount these values to their lower present-day numbers.

The main idea is this - that the value of a business is the present value of all its future cash flows.

A fixed sum of money forever

Recently, a famous braised duck rice coffeeshop along South Buona Vista Road, Lim Seng Lee Duck Rice Eating House, closed down after 45 years. The founder retired due to health reasons and because his children did not want to take over the business.

Let's say the success of the business was due to a secret recipe and a special way of preparing the duck and gravy that can be passed on to the next business owner.

And let's say you - yes, you - want to buy it.

Assume you have no plans to expand the business and no debt to pay off. At the end of each year, you know the business makes a profit of $500,000 in cash.

How did I come up with $500,000? This number is for illustrative purposes only. How to do a cash flow estimate for valuation purposes is briefly mentioned in the article below.

But let's picture this: raking in half a million dollars next year, and the next, and the next, till the end of time.

Sweet deal. What's the selling price?

To value the business, you have to add all these $500,000 payments up.

But the total does not add up to infinity. You won't pay all the money in the world just to own a duck rice shop.

This is because of the time value of money, a topic we discussed before. Getting a sum of money today is better than getting the same sum 20 years from now, because you can invest the sum of money today and grow it to become much more 20 years later.

For example, you can grow $107,000 today to become $500,000 in 20 years' time, assuming an 8 per cent interest rate. In other words, the $500,000 cash flow 20 years from now is only worth $107,000 today.

To figure out how much you should pay for the business, you have to value the perpetually-$500,000-generating duck rice shop at today's prices.

That means you have to discount each cash flow in the future to its present value, before adding everything up.

You are essentially adding up a stream of decreasing payments over time that eventually dwindles to near zero. For example, the $500,000 cash flow the business will generate 100 years from now is only worth $227 today. (See Table 1)

How do you add up an infinite number of payments, discounted to their present-day value? The mathematical shortcut to use is called a perpetuity calculation, named after the financial product that pays you the same sum of money forever.

To calculate the value of a perpetuity, you simply divide the payment stream a year by your selected interest rate, called the discount rate and otherwise known as your cost of capital.

The cost of capital represents the price investors are willing to pay to invest in a certain business or project.

It is the rate of return investors will earn on an enterprise that carries a similar risk.

Determining the cost of capital can be another complicated calculation. But for now, let us assume your cost of capital is 8 per cent.

To value the business, you simply divide the cash flow you get every year, $500,000, by 8 per cent, and get $6.25 million.

Notice this calculation is the same as the first stock valuation method we introduced two weeks ago. If you get a dividend payment of $500,000 every year from a business forever, and you need an 8 per cent return from your investment, you will be willing to pay a maximum of $6.25 million for the business.

If the going price for the duck rice coffeeshop was $10 million, you would laugh and walk away. This is because you know you can invest that $10 million in another business and get an 8 per cent return a year, or $800,000. That is superior to the $500,000 a year you get from this deal.

Conversely, if the price of the business was just $5 million, you would jump at the opportunity. If the business yields $500,000 a year, you are getting a return of 10 per cent. This is superior to the 8 per cent you get elsewhere.

Getting a steadily growing sum

The owner of the duck rice coffeeshop takes you aside and says, hey, it is unrealistic to assume my duck rice business will only pay $500,000 a year forever.

He is more optimistic than that. More and more customers will come to eat at his shop, which he can deal with over time through improved technology and productivity changes. In short, his profit will keep increasing.

Let's say the profit from the business can grow at the rate of 2 per cent a year. Again, determining this growth rate requires another potentially tricky calculation, so we shall just assume it for now.

The shop's profit of $500,000 this year will thus grow to $510,000 next year. And $520,200 in the next. And so on, until the end of time.

How much is this business worth?

The mathematical calculation used here is called the Gordon growth model.

The model states that the value of a business that gives a steadily increasing cash payment every year is simply next year's cash payment divided by the difference between the cost of capital and the growth rate.

In this case, the duck rice business will be worth $510,000 / (0.08 - 0.02) = $8.5 million. The growth assumption of 2 per cent added more than $2 million to the value of the business.

Of course, if your growth assumptions are higher, the business will be worth even more.

With a growth assumption of 6 per cent, the business will be worth a whopping $530,000 / (0.08 - 0.06) = $26.5 million. Growth assumptions make a big difference.

Growth spurt and maturity

The growth rate of a business cannot exceed your cost of capital, or the equation will not make sense as the denominator becomes negative.

But sometimes, companies can grow at 30 per cent a year - a phenomenal rate that far outstrips any normal cost of capital assumption.

This is when we need to tweak our valuation model.

Suppose the owner had grander plans for the business, before poor health forced him to retire. He wanted to expand his business to other parts of the island and build his own duck rice empire.

As a result, he enthusiastically projects his earnings to grow by 30 per cent a year as he progressively invests, recoups his cost of investment, and thus conquers the palates of another area.

Based on his reading of the Singapore market, he thinks this growth spurt can last for five years.

So, next year, the business will earn $650,000. Year two, $845,000. By year five, whoever owns the business will be raking in $1.86 million a year. No business can grow at a 30 per cent rate forever. After five years, let's assume this duck rice enterprise has established a dominant position in the market. Thereafter, it will keep up a relatively sedate 2 per cent pace of growth a year forever.

The appropriate valuation model to use is known as the two-stage model.

The first stage calculates the present value of the cash flow the business throws out during its growth spurt. To do so, you discount every year's cash flow to its present value, for five years in this case.

The second stage calculates the present value of the cash flow of the business after the growth spurt, when cash flows are assumed to either not grow at all or grow at a slower pace forever. The value of the business at this stage is calculated by either a perpetuity or Gordon growth model. Alternatively, one can use an earnings multiple.

This process is known as calculating the terminal value of a company.

In our duck rice shop example, the present value of the five cash flow payments during the growth spurt adds up to $4.5 million.

Using a Gordon growth model to calculate terminal value, we end up with a value of $31.6 million for the business at Year 5. After discounting, the present value is $21.5 million. (See Table 2)

The total valuation of the duck rice business, assuming a five-year expansion plan, is thus $26 million.

Summary

We have described three ways to value a company that has a predictable cashflow stream.

For most companies, however, the reality is that cash flow streams are uncertain and might even fall for a few years. The DCF model might not be suitable for cyclical companies where it is difficult to forecast with any certainty how fast they will grow.

Many assumptions for revenue growth and profit margins have to be made. You need to think about the fundamentals of the company, the industry, and the company's position in the business cycle.

To make sure your assumptions are not off the mark, use various methods to arrive at the company's intrinsic value. Build in a generous margin of safety - the more risky the company, the greater the margin of safety. For example, give another 30 per cent discount to the intrinsic value you calculated to make sure you are not paying too much for the stock relative to other options.

After all, duck rice isn't everything. Maybe chicken rice is cheaper and more delicious.

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