Discounted cash flow calculator

A discounted cash flow model says something simple: a business is worth the cash it will hand its owners, and cash arriving later is worth less than cash arriving now. Everything else is bookkeeping around those two ideas.

The model projects free cash flow forward for five years at a growth rate you choose, then stops pretending it can forecast individual years and lumps everything after that into a single terminal value. Each of those amounts is discounted back to today at a rate that stands in for what the money could have earned elsewhere, adjusted for risk. Add them up, add the cash on the balance sheet, subtract the debt, and divide by the share count.

The output is not a price. It is what your assumptions imply, which is a different and more useful thing: change one input and watch what happens.

FCF(t)  = FCF(0) x (1 + g)^t          for t = 1..5
TV      = FCF(5) x (1 + gt) / (d - gt)
PV      = sum of FCF(t) / (1 + d)^t  +  TV / (1 + d)^5
Equity  = PV + cash - debt
Value per share = Equity / diluted shares

A company generating $1,000m of free cash flow, with $500m of cash, $200m of debt and 100m shares. You assume 8% growth, a 10% discount rate and 2.5% terminal growth.

1. 1Year 1 free cash flow is 1,000 x 1.08 = $1,080m, and so on to $1,469m in year 5.
2. 2Terminal value is 1,469 x 1.025 / (0.10 - 0.025) = $20,081m.
3. 3Discounted back, the five years are worth $4,734m and the terminal value $12,469m.
4. 4Equity value is 4,734 + 12,469 + 500 - 200 = $17,502m.

• Compare the per-share figure to the current price. A value well above the price means your assumptions are more optimistic than the market's, not that the stock is cheap.
• The terminal value usually accounts for well over half the total. That is normal, and it is also the reason a DCF is more sensitive to the discount rate and terminal growth than to anything you assume about the next five years.
• Treat one run as one opinion. The useful exercise is running it three times with pessimistic, central and optimistic inputs and seeing how wide the range is.

• Setting terminal growth at or above the discount rate. The formula divides by the gap between them, so as they converge the value runs away to infinity. No business grows faster than its cost of capital forever.
• Using a starting free cash flow from an unusual year. One large asset sale or one deferred capex programme distorts every projected year after it.
• Running a DCF on a company with negative free cash flow. Projecting a negative number forward at a positive growth rate compounds the negativity and produces a confident answer to a meaningless question.
• Treating the output as precise. Two reasonable people can pick inputs a couple of points apart and arrive at values that differ by half.

What each of these inputs actually is, where it comes from in a filing, and where it misleads.