In an article published in the September 2018 issue of Business Valuation Update, Matthew Gold and Matthew Ashby derive a formula that explicitly incorporates the assumed probability of renewal in the valuation of businesses that depend on contracts, licences or permits for their future cash flows.
The formula builds on the Gordon growth model and the formula for the future value of a growing annuity, and has broad application subject to certain conditions being met.
We suggest the mathematical quantification of renewal risk based on an assessment of the probability of contract renewal offers a more intuitive and reliable approach than making subjective adjustments to cash flows, capitalisation multiplies or discount rates to account for the risk of non-renewal.
In the following formulas:
CF0 = Sustainable cash flow into perpetuity
g = Sustainable cash flow growth rate into perpetuity
r = Required rate of return1
P= Probability of contract renewal
n = Length of each contract renewal period
CFnr = Cash flow on realisation
Terminal value adjusted for renewal risk (single-period contract term)
Terminal value adjusted for renewal risk (multiple-period contract term)
The adjusted terminal value formula assumes no realisation cash flows in the event the contract is not renewed. However, there will be cases where a business can realise net cash flows upon winding up operations if the contract or licence is not renewed (e.g. from disposal of property, plant and equipment).
An adjusted terminal value formula can be written to model the non-renewal side of the equation where net cash flows can be realised. For simplicity, it is assumed that cash flows are realised immediately following the non-renewal of the contract (i.e. at t=0), the contract is lost to the business forever if not renewed, and the net cash flow on realisation (CFnr) grows at the same rate (g) as the cash flows from the contract in the adjusted terminal value formula2.
Terminal value of cash flows on non-renewal (multiple-period contract term) – simplified formula
The use of these formulas is subject to the following assumptions and limitations:
The probability of contract renewal is conditional upon the contract being held, and is fixed.
Annual cash flows in real terms are fixed.
In the event the contract is not renewed, it is lost forever.
The formula has the potential to be further developed into a model which incorporates the probability of regaining a contract after it has been lost.
To request a copy of an Excel workbook demonstrating the use of these formulas, please click here.
1 Either WACC or cost of equity depending on the nature of the cash flows.
2 Although it is possible to incorporate a different growth rate
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