FOOL SCHOOL
Valutation: Discounted Cash Flow

February 21, 2003

Discounted cash flow (DCF to its friends) is the topic of the final article in this mini-series on valuation. Here is how it works. Suppose you can invest a sum of money now, at a rate of 10% per annum, and you are promised £1 in a year's time. How much would you need to invest now? The answer is 90.9 pence. But the answer doesn't come off the top of your head. The best way to work out the algebra is to start with the future value of £1 and work backwards.

If we substituted x for 0.909, the formula rewritten would look like this:

To extend that out for two years, keeping the interest rate the same, how much would you need to invest now to receive £1 in two years' time. The answer is 82.6p and is calculated like this:

A scientific calculator can be used to work these out as well. A company is ultimately worth the sum of all the cash it can generate over its lifetime. If we were to say that Frederick's Folly PLC will be in existence for 10 years, and in that time it will generate free cash flow of £1m, how much would you be prepared to pay for that company now?

There are a number of important variables that determine what valuation a discounted cash flow model will spit out. The first is the free cash flows -- in this case, £1m. Frederick's Folly's cash flow statement in year one could look like this:

£57,000 is the free cash flow the company intially has at its disposal. It can choose to distribute it to shareholders as a dividend, it can keep some to invest back in the business or it can use it to buy back its own shares in an attempt to enhance shareholder value.

Let's say that we reckon Frederick's Folly can grow its free cash flow by 10% compounding per annum for the next 10 years. The next year's free cash flow is £62,700. Following that through to year 10, free cash flow in that year is £147,800. Adding up all the free cash flow amounts for each of the 10 years, we get a total amount generated of £1m (rounded up a bit).

Does that mean the company is worth £1m? The answer is no, because we haven't taken into account the time value of money. We are also making an assumption that at the end of year 10, the company will cease to exist, which in the case of most publicly quoted companies is not true.

This is where we introduce the discount factor. It is the amount by which you are prepared to discount each year's free cash flows to calculate their present value. If you were investing your money into something as safe as a 100% government-guaranteed bond, you would use a discount factor equivalent to the current rate of return on that bond. Let's say that is 6%. Using that discount rate, the £62,700 free cash flow generated in year one is discounted back to a present value of £59,200.

In year 2, the present value of the free cash flow would be £61,400, and so on out to year 10, where the sum of the discounted free cash flows equals £702,800. Using a 6% discount factor, and assuming Frederick's Folly can grow its free cash flow at 10% for 10 years (at which stage the company is liquidated), you would say the fair value of the company right now would be around £700,000. You go ahead and offer Frederick £500,000, he accepts, and you're off to the races.

The discount factor very much affects the valuation of a company using a discounted cash flow model. If I were to raise the rate to 12%, the value of the company now becomes £517,000-- quite a difference. As you can see, the use of the discount factor can substantially affect an investor's perception of a company's valuation.

When looking at publicly quoted companies, an appropriate discount factor would often be higher than the 6% we've used in the above example. Like any of the valuation models we've looked at in this series, it works best when used on a company with a predictable earnings stream. Investors can still calculate a valuation on companies with less-than-predictable earnings, but they would need to be conservative in their growth rate percentages, or their discount factor, or both. There is a chance that your company will not be able to execute its business plan as well as you may have thought, and there's a chance that your company's prospects could be adversely affected by increased competition.

The bond rate varies depending on the underlying rate and direction of interest rates. A higher discount factor is appropriate when interest rates are higher. At the moment we are seeing interest rates at relatively low levels, but this may not be the case in the future. Investors, therefore, will need to vary the discount rate accordingly.

One other complication to bear in mind is the residual value of the company. In the Frederick's Folly example, we assumed that the company would cease to exist after year 10. As we said earlier, this rarely happens in real life, and long-term investors will want to focus on companies that have good economics over an extended period of time -- ideally 100 years or more (only joking... not quite that long, maybe only 50 years).

To give a valuation to the rest of the company after year 10, it is appropriate to work out a long-term growth rate for the company. Most people will assume that the company would continue to grow at the rate of inflation, or perhaps marginally higher. Some analysts say it is appropriate to capitalise the 10-year free cash flow by the difference between the discount factor and the long-term growth rate. For example, if you said the discount factor was 12% and your long-term growth rate was 5%, the capitalisation rate would be 7%.

The discount factor in year 10 using a 12% rate is 0.322. If the future free cash flow is £155,200, capitalising that at a rate of 7% would give a residual worth of £2,217,600 (£155,200/7%). Discount that back to present using 0.322, and it gives you a present value of that residual of £714,000. This is then added to the discounted value for the first 10 years, in the same method we looked at earlier, and voila -- you have a total discounted cash flow valuation for your company.

As we said before, this valuation tool works best when you are looking at companies with a predictable earnings stream. It also works well when you are looking at more mature companies. Fast growing companies won't generate much in the way of free cash flow, because they are investing it back into the business. That's not to say they are bad investments and can't be valued -- it's just that a discounted cash flow calculation is not the most appropriate tool.

More on valuation
1. Price to earnings
2. PEG
3. Price to sales
4. Dividend yield
5. Return on equity
6. Adjusting for goodwill
7. Uses of return on equity
8. Balance sheet basics
9. Discounted cash flow