Calculating the Discounted Cash Flow Valuation

Calculating a Discounted Cash Flow (DCF) Valuation relies on assumptions about cash flows the firm expects to generate, the growth rate of the firm, the inflation rate of the country, and the amount of risk we expect (or alternatively, the amount of extra return we want on our cash investment to compensate for the risk we expect). All of these variables need to be forecast a long way into the future.

Before anyone suggests that with so many assumptions about the firm’s future that the valuation might be inaccurate or that the DCF valuation method might be inferior to others for SMBs, let me reinforce the message that ‘two businesses in the same industry with exactly the same financial statements at the same time can face very different futures, and thus have different valuations’. This simple statement shows that whereas Net Asset Value or a Multiple/comparable approach would both value the businesses equally, only the DCF forces us to consider the future cash flows and the level of risk/uncertainty around them, and only the DCF method would help us choose between the two otherwise equal businesses.

Let’s get stuck in: I’m going to keep things as simple and as broad today as possible, with further depth and refinement in future articles.

Forecasting something into the far future is tricky. For SMBs the trick is to break our forecasts down into 2 periods: an initial period where we forecast growth and cash flows year by year (and where we expect the business to grow faster than the economy), then a second period where it grows more or less at the same speed as the economy. Typically this first period is 3-5 years, and the second period is everything thereafter. To make things easy we employ a mathematical trick of treating the second period as a single lump sum that we then discount back to present along with the other years. This means that we only have to calculate 3-5 years of specific cash-flows with the rest being sorted out by some simple maths. Suddenly the DCF Valuation is not so daunting!

The formula for each of the first few years (the ‘high-growth’ period) would look like this:

PV=(CF1/(1+r))+ (CF2/(1+r)^2)+ (CF3/(1+r)^3)

Where CF1 = Cash Flow in year 1, CF2 = Cash flow in year 2 etc, and r is the discount rate.

What about the cash flows that come after 3 years, i.e. 4 years to infinity? Here we use a formula (derived from the Gordon growth model) that allows us to treat this as a single cash flow in year 4.

FV=CF*(1+g)/(r-g)

CF with the subscript t+1 means that we are using next years cash flow forecast, not the prior years actual cash. g is the growth rate in % that we predict in the long term.

So if we have projected cashflow in year 3 of R1000, a growth rate of 3%, and a discount rate of 20% then we’d use FV=(1000*(1+3%))/(20%-3%)=103/0.17=R6058, which would reflect cumulative effect of all cash flows from year 4 onwards.

The important points here is that (1) we add the growth rate of 3% to the cashflows expected in year 3 to get to what we expect in year 4, then (2) we divide this by the discount rate less the growth rate to get to the ‘in perpetuity’ calculation. Lastly, since this lump sum now sits 4 years out, we must discount it along with the cash flows we expect in years 1 to 3.

So putting these together we end up with something that looks like this:

PV=(CF1/(1+r)^1)+ (CF2/(1+r)^2)+ (CF3/(1+r)^3)+ {CF3*(1+g))/(r-g)}/(1+r)^4)

If we have expected cash flows of R700, R850, and R1000 in each of year 1,2 and 3 then the model works out like this:

PV=(700/1+20%)+(850/(1+20%)^2)+(1000/(1+20%)^3)+(6058/(1+20%)^4)

PV=583.3+590.2+578.7+2921.5

PV=4673.69

There you have it – a DCF valuation at last!

 

In the coming weeks we are going to unpack and repack this further, with the main focus on being how to use the DCF valuation as both a means of setting price in negotiations, and as the single number that shows you how the decisions you are making in your business today affect its long-term value.

 

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  • Kevin Scott

    The infinity explanation here is really helpful, as it’s often ignored. Really great, thanks.

    • Gareth Ochse

      Glad we could help…thanks Kevin.