A Discounted Cash Flow Model, Built Step by Step

A handful of inputs decide the answer: this year’s free cash flow, how fast it grows, how long you forecast, the rate you discount at and the growth you assume after that. The rest is arithmetic. It’s easy arithmetic. The trouble is that it looks precise, and a spreadsheet cell reading $31.07 a share starts to feel like a measured fact when it is really a stack of guesses, each one reasonable, multiplied together and carried to the cent.

Start with free cash flow

Free cash flow is the cash left over after running the business and paying for the equipment it needs. Find it on the cash flow statement. Take cash from operations. Subtract capital expenditures. What remains could, in principle, go to owners.

The example needs round numbers. A hypothetical company produces free cash flow of 100, in millions of dollars. Assume it grows 5% a year for three years, so each year is the one before times 1.05.

Discount each year back to today

A dollar in three years is worth less than a dollar now. Today’s dollar can earn a return in the meantime. The later one might never arrive. The discount rate prices both, and at 10% a payment one year out is divided by 1.1, a payment two years out by 1.21, and one three years out by 1.331.

Choosing the rate is the most argued step in valuation. Steady, established businesses get a lower one. Small, cyclical or heavily indebted companies get a higher one, since you want paying for the extra chance that the forecast is wrong, and the gap between those two kinds of rate is where much of the disagreement between analysts valuing the same company comes from.

Add a terminal value

The company doesn’t stop at year three. You need a figure for every year after. The usual shortcut treats cash flow as growing at a slow, steady rate forever. That terminal value equals next year’s cash flow over the discount rate minus long-run growth. Keep the growth rate modest. The example uses 3%.

Look at the split. The terminal value is 1,279.8 of the 1,553.3. That’s about 82%.

So most of the value rests on one guess about growth after year three. Change it from 3% to 2% and the terminal value falls to 115.76 x 1.02 / 0.08 = 1,475.9, which is worth 1,108.9 today and brings the total down to 1,382.4, a drop of 170.9 million or about 11% from a single point of long-run growth that nobody can observe in advance. Show the result as a range.

Divide by diluted shares

The model has valued the business. This hypothetical company has no debt and no spare cash. Its business value and equity value are therefore the same. With net debt, you’d subtract it first.

Then divide by the diluted share count in the annual report. It includes options, restricted stock and convertibles that could turn into shares.

The basic count flatters the result. See fully diluted shares for which securities belong in it. The share dilution calculator shows how quickly extra shares eat into value per share.

What the model gives you

You now have a number you can defend line by line. It still might be wrong in either direction.

Before moving on, put the discount rate and the long-run growth rate in cells of their own and point every formula at them. Try 9% and 11%. Try 2% and 4%. Write down the lowest and highest value per share the model gives, since that spread, more than the middle figure, is what you carry forward when you decide what to pay. Whether $31.07 is a price worth paying is the subject of margin of safety, the next lesson, which turns the estimate into a buy price and then runs the model backward from the market’s own quote.