# DCF Series: Finding the present value of future FCFs

In this post, we use the cost of capital we found from the last post to discount the future Free Cash Flow of a company to find the present value of future free cash flows.

This is part of the DCF Valuation series; if you haven't read any of the previous posts, start here.

The exercise of finding the present value of a company (which is the whole point of this series), we've already said that we just need to predict the future Free Cash Flow for the company — all the way into the future, and discount it to today.

However, we can't predict future FCF forever, all the way into 'infinity'. What we do instead, is to approach this in two distinct steps:

1. Model predictions for 5 or 10 years (usually projecting revenue first, and finding FCF accordingly

2. Calculate a 'terminal value' for the company

… and then simply add the two (discounting where necessary) to find the total present value of the company.

## Discounting FCF into the present

To discount FCF to the present, we're working in reverse — trying to find the present value (or $\text{PV}$) that would grow (at the rate of WACC) to become the FCF at the target year.

$$\text{PV}_\text{year 1} = \frac{\text{FCF year}_1}{1 + \text{WACC}}$$

$$\text{PV}_\text{year 2} = \frac{\text{FCF year}_2}{(1 + \text{WACC})^2}$$

$$\text{PV}\text{year n} = \frac{\text{FCF}\text{year n}}{(1 + \text{WACC})^n}$$

That's all there is to it. Now we just add them all up to get the net present value of the next 10 years of FCF.

Example: Calculating Net Present Value for 10 years of $SFIX's future FCF Coming back to the example we've been using throughout this series, you'll recall that $$\text{WACC}_\text{overall} = 17.37%$$$ .

We'll now calculate the Net Present Value of Stitch Fix ($SFIX) for the 10 year FCF forecast we did earlier: YearFCFPV of FCF 0 (Current)$12,670$12,670 1$56,152$$\frac{56,152}{1 + 0.1737} = 47,842$$$2$66,259$$\frac{66,259}{(1 + 0.1737)^2} = 48,098$$$3$82,824$51,225 4$107,671$56,738 5$129,205$58,009 6$160,596$61,431 7$192,715$62,808 8$231,258$64,215 9$277,509$65,654 10$319,135$64,329 Total-$580,350

There we have it. The net present value of the future FCF's for $SFIX is the sum of the present value for all of the year's FCFs, resulting in$580,350.

Next, we'll consider the 'Terminal Value' (or value of the firm beyond the 10 years we forecast).

## Finding the Terminal Value

The Terminal Value is the value that we assign to a company beyond the forecast period — and into perpetuity. As you can imagine, this can represent the bulk of a company's forecase, so we need to make sure we do this right!

There are a few approaches we can take, and the choice of which one we make largely depends on whether we think the company has a lasting competitive advantage:

ApproachApplies to
Value Driver ModelFirms that maintain a competitive advantage over time (e.g. Coca Cola)
Convergence ModelMost Firms
Perpetuity Growth Model❌ Should not be used1
Exit MultipleCan be used to provide an alternative measure of firm value

This is for companies where the competitive advantage erodes over time. We can assume that the Return on Invested Capital (ROIC) converges to (or equals) the Cost of Capital (WACC).

To calculate the terminal value, we use:

$$\text{Terminal Value}_\text{Year 10} = \frac{\text{NOPAT}}{\text{WACC}}$$

where $$NOPAT$$$is the Net Operating Profit After Tax. Essentially, $$NOPAT = \text{Operating Income}*(1 - \text{Tax Rate})$$$.

Of course, we'd still need to discount the resulting value to find the present value by dividing by $$(1 + \text{WACC})^\text{10}$$$(assuming we made a 10 year forecast). For$SFIX, this is a simple process. We've already projected $$\text{Operating Income}$$$in 2030E to be$478,755. Assuming a 25% corporate tax rate at that time, we can find NOPAT:

$$NOPAT_\text{Year 10} = 478,755 * 0.75 = 359,066$$

And now, we calculate Terminal Value (TV) using:

$$\text{TV}_\text{Year 10} = \frac{\text{NOPAT}}{\text{WACC}} = \frac{359,066}{17.37%} = 2,067,161$$

Finally, we discount that to the present to arrive at the present value:

$$\text{TV}_\text{present} = \text{TV}_10 * (1 - \text{WACC})^\text{10} = 2,067,161 * (1 - 17.37)^\text{10} = 306,726$$

Usually, you'll find that the Terminal Value you get is much larger than the sum of the cash flows during the projected period. In our case, it's the opposite.

### Exit Multiple

I often use this method to 'check my work'. The exit multiple approach assumes the business is sold for a multiple of some metric (e.g., EBITDA) based on currently observed comparable trading multiples for similar businesses.

For example, this could be $$\text{Terminal Value} = EBITDA * Multiple$$$Other industry-specific metrics can be used, but EBITDA is a popular metric for this model. Since this measure is based on the EBITDA in Year 10, we'd need to discount it back to find the present value. Now that we've found the Terminal Value, the final step is to put everything together and (finally!) find out what the company is worth! Head on to the next post to see how. 1. Estimates the terminal value based on an assumed perpetual growth rate for a business (e.g. $$2.5%$$$) — into perpetuity, which is baseless. The formula, if you're curious is, $$\frac{\text{Final FCF} * (1 + g)}{WACC - g}$$\$ (and requires discounting to present value from the date of the final FCF year)