Lesson 6 of 6
Discounted cash flow against NPV
A DCF and an NPV use the same arithmetic and answer different questions. The difference is one subtraction at the end, and it changes a number into a decision.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- A discounted cash flow converts future cash into a value today. Net present value subtracts what that value costs to acquire.
- The terminal value, what everything after the forecast is worth, is usually most of the answer.
- One point added to the perpetual growth rate can move the total value by ten percent.
The discounting in a DCF and an NPV is identical arithmetic. The difference is one subtraction at the end: NPV takes the value and subtracts the cost to acquire it, which turns a number into a decision.
Where the value sits: forecast years against the terminal value
Nearer
- Forecast years 1 to 5$379.132%
- Terminal value$791.768%
Furthest out
Total$1,170.8
Three inputs, all estimates
| Input | What it is | Measured or estimated |
|---|---|---|
| Cash flows | Free cash flow to the firm: operating profit after tax, plus depreciation, less capital expenditure and less the increase in working capital, forecast for five or ten years. | Estimated |
| Discount rate | What the money could earn elsewhere at the same risk. | Estimated |
| Terminal value | What everything after the forecast is worth, usually a perpetuity growing at a low rate. | Estimated |
The terminal value is one cash flow divided by the gap between two estimates, so it moves fastest.
One point of growth, a large swing in the total
One percentage point on a growth rate the five-year forecast never discusses moved the total value by 10.4 percent. The terminal value is one number divided by the gap between two estimates, so as that gap narrows the answer moves fast.
The cap on the growth rate
A company growing faster than the whole economy forever eventually becomes the economy. Damodaran's practical rule is to cap the perpetual growth rate at the risk-free rate, which already carries expected inflation and growth. Nothing in a spreadsheet objects to a higher number: it just returns a bigger value that looks like a finding, and the assumption behind it is one cell nobody re-reads. The same warning runs the other way. Adding a premium to the discount rate for small size or illiquidity, with no procedure behind the number, makes the answer whatever the analyst wanted it to be.
The fork that is a common error
Free cash flow to the firm
- Discounted at the weighted average cost of capital.
- Returns enterprise value; subtract net debt to reach equity value.
Free cash flow to equity
- Discounted at the cost of equity alone.
- Returns equity value directly, nothing subtracted after.
Both are correct, and mixing them produces a number that still looks like a valuation.
Check yourself
What is the one arithmetic difference between a DCF value and an NPV?
- NPV uses a higher discount rate
- NPV subtracts the cost to acquire the cash flow stream from the DCF value
- DCF only works for whole companies
Show the answer
Answer: B.
The discounting is identical in both. NPV takes that present value and subtracts what the stream costs to acquire, turning a value into a decision.In a typical two-stage model, where does most of the total value usually sit?
- In the first forecast year
- In the terminal value
- Split evenly across all years
Show the answer
Answer: B.
The terminal value stands in for every year after the explicit forecast, and it is usually the majority of the total, which is why the terminal assumptions matter more than the forecast years.Free cash flow to the firm should be discounted at what rate?
- The cost of equity
- The weighted average cost of capital
- The risk-free rate
Show the answer
Answer: B.
Cash flow to the firm belongs with the weighted average cost of capital, which reflects both debt and equity holders. Mixing this with the cost of equity is a common error.Sources
- Berkshire Hathaway shareholder letter, 2000: reduces every valuation to three questions, how certain the cash is, when it arrives and how much, and the risk-free rate.
- Damodaran, Investment Valuation and The Dark Side of Valuation, on the terminal growth cap and on forecasting a path to a mature margin instead of abandoning the model.
What this leaves out
- This lesson does not cover the mechanics of forecasting cash flows, which carries most of the real work.
- The terminal treatment shown is the perpetuity growth method; the exit multiple method moves the same problem elsewhere.
- The worked examples use round invented numbers so the arithmetic can be checked. Nothing here is any company's filed figures.
- Nothing here is advice about any security.