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# Calculating The Fair Value Of Sotheby’s (NYSE:BID)

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Does the February share price for Sotheby’s (NYSE:BID) reflect it’s really worth? Today, I will calculate the stock’s intrinsic value by estimating the company’s future cash flows and discounting them to their present value. I will be using the discounted cash flows (DCF) model. Don’t get put off by the jargon, the math behind it is actually quite straightforward. If you want to learn more about discounted cash flow, the basis for my calcs can be read in detail in the Simply Wall St analysis model. Please also note that this article was written in February 2019 so be sure check out the updated calculation by following the link below.

### What’s the value?

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. To start off with we need to estimate the next five years of cash flows. For this I used the consensus of the analysts covering the stock, as you can see below. I then discount this to its value today and sum up the total to get the present value of these cash flows.

#### 5-year cash flow estimate

 2019 2020 2021 2022 2023 Levered FCF (\$, Millions) \$124.80 \$146.20 \$181.30 \$188.90 \$200.90 Source Analyst x2 Analyst x2 Analyst x1 Analyst x1 Analyst x1 Present Value Discounted @ 12.01% \$111.42 \$116.53 \$129.01 \$120.01 \$113.95

Present Value of 5-year Cash Flow (PVCF)= US\$591m

We now need to calculate the Terminal Value, which accounts for all the future cash flows after the five years. For a number of reasons a very conservative growth rate is used that cannot exceed that of the GDP. In this case I have used the 10-year government bond rate (2.7%). In the same way as with the 5-year ‘growth’ period, we discount this to today’s value at a cost of equity of 12%.

Terminal Value (TV) = FCF2023 × (1 + g) ÷ (r – g) = US\$201m × (1 + 2.7%) ÷ (12% – 2.7%) = US\$2.2b

Present Value of Terminal Value (PVTV) = TV / (1 + r)5 = US\$2.2b ÷ ( 1 + 12%)5 = US\$1.3b

The total value is the sum of cash flows for the next five years and the discounted terminal value, which results in the Total Equity Value, which in this case is US\$1.9b. To get the intrinsic value per share, we divide this by the total number of shares outstanding, or the equivalent number if this is a depositary receipt or ADR. This results in an intrinsic value of \$39.97. Relative to the current share price of \$40.89, the stock is fair value, maybe slightly overvalued at the time of writing.

### The assumptions

The calculation above is very dependent on two assumptions. The first is the discount rate and the other is the cash flows. You don’t have to agree with my inputs, I recommend redoing the calculations yourself and playing with them. Because we are looking at Sotheby’s as potential shareholders, the cost of equity is used as the discount rate, rather than the cost of capital (or weighed average cost of capital, WACC) which accounts for debt. In this calculation I’ve used 12%, which is based on a levered beta of 1.276. This is derived from the Bottom-Up Beta method based on 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. For BID, I’ve compiled three pertinent aspects you should further examine:

1. Financial Health: Does BID 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.
2. Future Earnings: How does BID’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.
3. Other High Quality Alternatives: Are there other high quality stocks you could be holding instead of BID? Explore our interactive list of high quality stocks to get an idea of what else is out there you may be missing!

PS. The Simply Wall St app conducts a discounted cash flow for every stock on the NYSE every 6 hours. If you want to find the calculation for other stocks 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. On rare occasion, data errors may occur. Thank you for reading.