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Duration discount rates and the grumpy views of a middle-aged man….

Over the past few years investors have become obsessed with the record low level of interest rates. Interest rates are the fundamental building block of assessing asset values. Lower interest rates mean future cash flows are more valuable. Thus, lower rates mean higher asset values. This sensitivity of asset values to changes in interest rates, called the ‘duration’ by bond investors, is increasing. That is, the lower rates are, the more sensitive asset values become to a further fall in interest rates. By this method, ever increasing asset values can be justified by lower and lower interest rates.

Most discounted cash flow (DCF) valuation models for listed equities or infrastructure assets are based on a period of detailed forecasts (perhaps for 10 or 20 years) and then a terminal value assumption. That is, most models assume companies continue forever and include a terminal value estimate based on a perpetual steady state dividend stream at the end of the explicit forecast horizon. That is, the value of the company/asset implicitly is the value of a perpetual income stream. The chart below shows the value of a $1 per year perpetual at a range of interest rates. Note how the value explodes as interest rates approach zero!

But what if the best mental model isn’t a perpetual? What if the asset/company has a finite life? This might be a certain finite life – eg a PPP. Or it could be an uncertain finite life. That is, a particular business model might produce attractive profits for a while – but at some point, in the future a better mouse trap will be invested and the profits go to zero. For example, horse-drawn cart manufacturers might have made nice steady profits for a while and then those profits ended when the car was invented.

Thus, a better mental model for the value of a company might be the value of an annuity of uncertain length rather than a perpetuity.

This would have big implications for interest rate sensitivity.

While the duration of a perpetuity is unbounded (as the payments go on forever and if interest rates are lower enough its value is infinite) the duration of an annuity is bounded (as it can never be worth more than the simple undiscounted sum of all the payments).

So what?

This matters because perhaps we are:

· overconfident in projecting cash flows and profits long into the future (despite the inherent uncertainty of technological progress and competition)

· overestimating the impact of falling discount rates on valuations

· putting too much focus on short-term yield/growth (ie the flow) and not enough focus on whether the aggregate value of a company is justified by its lifetime future cash flows (ie the stock).

What are some real-life examples in infrastructure? Perhaps consider it through the lens of stranded asset risk – what discount rate is appropriate to apply to a coal terminal, or alternatively gas infrastructure (eg gas pipeline or LNG train)? I highlight these two assets because they have two headwinds – technological and environmental/regulatory risk. What assumptions do you make about the stability of future cashflows? Using gas specifically, will the demand in the future be the same as today? Could hydrogen and/or the switch to storage technologies eviscerate gas demand? I feel reasonably confident about volumes for the next 10 years, but after that I’m much less certain.

When I started working, infrastructure discount rates were 10% plus, what you assumed in years 15 onwards didn’t really matter – it represented a trivial share of overall project net present value. However, at today’s discount rates your views on issues long into the future have a big impact on valuation and investment decisions. That is, in a world of low interest rates, if you mistake an annuity – that is a stranded asset – for a perpetuity – you have made a massive mistake.

But then maybe I am just a grumpy middle-aged man dreaming of the time when bank accounts offered interest rates higher than inflation.


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