Valuation modelling

Financial Training Associates Ltd answers the question: “In valuation modelling, where does the terminal value formula come from?” This question was recently posed by a delegate on an FTA Ltd financial modelling course.

1. The terminal value formula. In a discounted cash flow (DCF) valuation model, we can’t forecast forever. Even an Excel spreadsheet has a limit to the number of columns it contains! The terminal value solves this problem by answering the question: “What’s the business worth at the end of the forecast period?” In the final year of an Excel financial model you will usually see a big lump of cash (the terminal value). What we are doing in the model is trying to work out what the company we are valuing is worth at the end of the forecast period, or what it might be able to be sold for.

Many analysts are used to seeing the following formula used to calculate terminal valuation in financial modelling (see the blue box in the slide below, which comes from one of FTA Ltd’s training courses). In the formula, on the top we have next year’s expected free cash flow, divided by [discount rate less long term growth rate]. But where does the terminal valuation formula itself come from?

2. The formula for terminal value is an application of an old valuation formula. The formula is an application of an old valuation methodology called “the dividend discount model” or the “Gordon growth model”, where a business is valued as a stream of its dividends. This model pre-dates discounted cash flow valuation, and the capital asset pricing model on which DCF is based. What we are doing at the back end of our financial model is applying a very old methodology to determine the valuation of the company at the end of the cash flow forecast period.

3. The dividend growth model or the Gordon growth model. The formula for the Gordon growth model is shown below. You can see how the terms match up with the same terms for calculating terminal value.

4. Derivation of the Gordon growth model. The Gordon growth model holds that a company’s valuation is the sum of that company’s discounted forecast dividend payments. For more detail see any good corporate finance textbook or Gordon, M. (1959) “Dividends, earnings and stock prices”, Review of Economics and Statistics, Vol. 41, pp. 99-105.

This long formula is known in maths as a “Geometric series”, where the next term in the series is calculated by multiplying the previous term by a constant. In this case the constant is (1+g)/(1+r).

5. A bit of algebra that you can skip if you wish. If we multiply both sides of the equation by the constant (1+g)/(1+r) we get two different versions of the same long formula.

This second new series is the same as the original, except that the first term is missing from the left hand side. Subtracting the new series from the original, cancels every term in the original but the first.

With a bit of simplification…

Voila – at the bottom we have it: the Gordon growth model! You can see how the terms match up to the same terms used in the terminal value formula.

6. Big sensitivities in financial modelling for valuation. Any analyst who has spent a little bit of time modelling will be able to tell you that big sensitivities on terminal value and hence valuation are the final year cash flow, the long term growth rate, and the discount rate. Making small changes to any of these can result in a very different terminal value. And terminal value can end up accounting for a large proportion of total valuation in a financial model.

To summarise, the terminal value formula used in DCF valuation modelling is an application of a very old (and otherwise now regarded as outdated) valuation methodology, predating the DCF methodology itself. We can put an awful lot of work into modelling intermediate cash flows as accurately as we can, and then try to be very precise about how we discount those cash flows in valuation. But when terminal values (where we are essentially just dividing one quite rough number by another rough number) account for a large proportion of overall valuation, perhaps we should be answering another question. Instead of discounted cash flows, should DCF stand for “Deceit by Computer Fraud”?

About the author: training company financialtrainingassociates.com

Financial Training Associates Ltd is a provider of financial modelling course training and other finance-related courses for accountancy, banking, law and other professionals.