A Look At The Fair Value Of Purplebricks Group plc (LON:PURP)

In this article we are going to estimate the intrinsic value of Purplebricks Group plc (LON:PURP) by taking the expected future cash flows and discounting them to today's value. This will be done using the Discounted Cash Flow (DCF) model. Don't get put off by the jargon, the math behind it is actually quite straightforward.

We generally believe that a company's value is the present value of all of the cash it will generate in the future. However, a DCF is just one valuation metric among many, and it is not without flaws. For those who are keen learners of equity analysis, the Simply Wall St analysis model here may be something of interest to you.

Check out our latest analysis for Purplebricks Group

The calculation

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 ten years of cash flows. 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.

Generally we assume that a dollar today is more valuable than a dollar in the future, 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

	2022	2023	2024	2025	2026	2027	2028	2029	2030	2031
Levered FCF (£, Millions)	UK£2.60m	UK£7.90m	UK£12.5m	UK£13.8m	UK£14.9m	UK£15.8m	UK£16.5m	UK£17.0m	UK£17.5m	UK£17.8m
Growth Rate Estimate Source	Analyst x1	Analyst x1	Analyst x1	Est @ 10.8%	Est @ 7.83%	Est @ 5.76%	Est @ 4.31%	Est @ 3.29%	Est @ 2.58%	Est @ 2.08%
Present Value (£, Millions) Discounted @ 6.5%	UK£2.4	UK£7.0	UK£10.3	UK£10.8	UK£10.9	UK£10.8	UK£10.6	UK£10.3	UK£9.9	UK£9.5

("Est" = FCF growth rate estimated by Simply Wall St)
Present Value of 10-year Cash Flow (PVCF) = UK£92m

We now need to calculate the Terminal Value, which accounts for all the future cash flows after this ten year period. The Gordon Growth formula is used to calculate Terminal Value at a future annual growth rate equal to the 5-year average of the 10-year government bond yield of 0.9%. We discount the terminal cash flows to today's value at a cost of equity of 6.5%.

Terminal Value (TV)= FCF₂₀₃₁ × (1 + g) ÷ (r – g) = UK£18m× (1 + 0.9%) ÷ (6.5%– 0.9%) = UK£322m

Present Value of Terminal Value (PVTV)= TV / (1 + r)¹⁰= UK£322m÷ ( 1 + 6.5%)¹⁰= UK£171m

The total value is the sum of cash flows for the next ten years plus the discounted terminal value, which results in the Total Equity Value, which in this case is UK£263m. The last step is to then divide the equity value by the number of shares outstanding. Compared to the current share price of UK£0.8, the company appears about fair value at a 11% discount to where the stock price trades currently. Remember though, that this is just an approximate valuation, and like any complex formula - garbage in, garbage out.

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. Part of investing is coming up with your own evaluation of a company's future performance, so try the calculation yourself and check your own 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 Purplebricks Group 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 6.5%, which is based on a levered beta of 1.053. 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.

Moving On:

Valuation is only one side of the coin in terms of building your investment thesis, and it ideally won't be the sole piece of analysis you scrutinize for a company. DCF models are not the be-all and end-all of investment valuation. Preferably you'd apply different cases and assumptions and see how they would impact the company's valuation. For example, changes in the company's cost of equity or the risk free rate can significantly impact the valuation. For Purplebricks Group, there are three relevant items you should assess:

1. Risks: For instance, we've identified 2 warning signs for Purplebricks Group that you should be aware of.
2. Future Earnings: How does PURP'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 Solid Businesses: Low debt, high returns on equity and good past performance are fundamental to a strong business. Why not explore our interactive list of stocks with solid business fundamentals to see if there are other companies you may not have considered!

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

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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. We aim to bring you long-term focused analysis driven by fundamental data. Note that our analysis may not factor in the latest price-sensitive company announcements or qualitative material. Simply Wall St has no position in any stocks mentioned.
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