Today we'll do a simple run through of a valuation method used to estimate the attractiveness of Armstrong World Industries, Inc. (NYSE:AWI) as an investment opportunity by taking the expected future cash flows and discounting them to today's value. This is done using the Discounted Cash Flow (DCF) model. It may sound complicated, but actually it is quite simple!

Remember though, that there are many ways to estimate a company's value, and a DCF is just one method. If you want to learn more about discounted cash flow, the rationale behind this calculation can be read in detail in the Simply Wall St analysis model.

Check out our latest analysis for Armstrong World Industries

### Crunching the numbers

We are going to use a two-stage DCF model, which, as the name states, takes into account two stages of growth. The first stage is generally a higher growth period which levels off heading towards the terminal value, captured in the second 'steady growth' period. In the first stage we need to estimate the cash flows to the business over the next ten years. Where possible we use analyst estimates, but when these aren't available we extrapolate the previous free cash flow (FCF) from the last estimate or reported value. We assume companies with shrinking free cash flow will slow their rate of shrinkage, and that companies with growing free cash flow will see their growth rate slow, over this period. We do this to reflect that growth tends to slow more in the early years than it does in later years.

A DCF is all about the idea that a dollar in the future is less valuable than a dollar today, so we need to discount the sum of these future cash flows to arrive at a present value estimate:

#### 10-year free cash flow (FCF) estimate

2020 | 2021 | 2022 | 2023 | 2024 | 2025 | 2026 | 2027 | 2028 | 2029 | |

Levered FCF ($, Millions) | $249.6m | $290.1m | $323.0m | $351.2m | $375.6m | $397.0m | $416.0m | $433.4m | $449.6m | $465.1m |

Growth Rate Estimate Source | Analyst x2 | Analyst x1 | Est @ 11.33% | Est @ 8.75% | Est @ 6.94% | Est @ 5.68% | Est @ 4.8% | Est @ 4.18% | Est @ 3.74% | Est @ 3.44% |

Present Value ($, Millions) Discounted @ 10% | $226.9 | $239.8 | $242.7 | $239.9 | $233.2 | $224.1 | $213.5 | $202.2 | $190.7 | $179.3 |

*("Est" = FCF growth rate estimated by Simply Wall St)* **Present Value of 10-year Cash Flow (PVCF)**= $2.2b

After calculating the present value of future cash flows in the intial 10-year period, we need to calculate the Terminal Value, which accounts for all future cash flows beyond the first stage. The Gordon Growth formula is used to calculate Terminal Value at a future annual growth rate equal to the 10-year government bond rate of 2.7%. We discount the terminal cash flows to today's value at a cost of equity of 10%.

**Terminal Value (TV)** = FCF_{2029} × (1 + g) ÷ (r – g) = US$465m × (1 + 2.7%) ÷ (10% – 2.7%) = US$6.6b

**Present Value of Terminal Value (PVTV)** = TV / (1 + r)^{10} = $US$6.6b ÷ ( 1 + 10%)^{10} = $2.53b

The total value, or equity value, is then the sum of the present value of the future cash flows, which in this case is $4.73b. To get the intrinsic value per share, we divide this by the total number of shares outstanding. **This results in an intrinsic value estimate of $97.1**. Relative to the current share price of $95.5, the company appears about fair value at a 1.6% discount to where the stock price trades currently. Valuations are imprecise instruments though, rather like a telescope - move a few degrees and end up in a different galaxy. Do keep this in mind.

### The assumptions

We would point out that the most important inputs to a discounted cash flow are the discount rate and of course the actual cash flows. If you don't agree with these result, have a go at the calculation yourself and play with the assumptions. The DCF also does not consider the possible cyclicality of an industry, or a company's future capital requirements, so it does not give a full picture of a company's potential performance. Given that we are looking at Armstrong World Industries as potential shareholders, the cost of equity is used as the discount rate, rather than the cost of capital (or weighted average cost of capital, WACC) which accounts for debt. In this calculation we've used 10%, which is based on a levered beta of 1.22. Beta is a measure of a stock's volatility, compared to the market as a whole. We get our beta from the industry average beta of globally comparable companies, with an imposed limit between 0.8 and 2.0, which is a reasonable range for a stable business.

### Next Steps:

Valuation is only one side of the coin in terms of building your investment thesis, and it shouldn’t be the only metric you look at when researching a company. The DCF model is not a perfect stock valuation tool. Rather it should be seen as a guide to "what assumptions need to be true for this stock to be under/overvalued?" If a company grows at a different rate, or if its cost of equity or risk free rate changes sharply, the output can look very different. For Armstrong World Industries, I've put together three pertinent aspects you should further research:

**Financial Health**: Does AWI have a healthy balance sheet? Take a look at our free balance sheet analysis with six simple checks on key factors like leverage and risk.**Future Earnings**: How does AWI's growth rate compare to its peers and the wider market? Dig deeper into the analyst consensus number for the upcoming years by interacting with our free analyst growth expectation chart.**Other High Quality Alternatives**: Are there other high quality stocks you could be holding instead of AWI? Explore our interactive list of high quality stocks to get an idea of what else is out there you may be missing!

PS. Simply Wall St updates its DCF calculation for every US stock every day, so if you want to find the intrinsic value of any other stock just search here.

*We aim to bring you long-term focused research analysis driven by fundamental data. Note that our analysis may not factor in the latest price-sensitive company announcements or qualitative material.*

*If you spot an error that warrants correction, please contact the editor at editorial-team@simplywallst.com. This article by Simply Wall St is general in nature. It does not constitute a recommendation to buy or sell any stock, and does not take account of your objectives, or your financial situation. Simply Wall St has no position in the stocks mentioned. Thank you for reading.*