Why can't the growth rate be higher than the discount rate?
Why can't the discount rate be lower than the growth rate in terminal value?
What is the theoretical reason for it.
Thanks.
Ways to Calculate Terminal Value
Terminal value is an important part in determining company valuation. Before digging in to the theoretical explanation to the above question, here’s a quick review of the calculation. Depending on various factors, you may want to use an exit multiple or perpetual growth method, such as the Gordon Growth Model for determining terminal value in a DCF model.
- Perpetual Growth: Use when company is in its long-term, mature growth phase
- Terminal Value = Last Year Free Cash Flow x ((1 + Terminal Growth Rate) / (WACC - Terminal Growth Rate))
- Exit Multiple: Use when company is not yet in steady growth phase or when market has a good idea of acquisition value (ex: LBO)
For more information on how to find your growth rate and discount rate, check out these posts:
- explains:
Growth rates can exceed the cost of capital for very short periods of time, but we're talking about a growth rate IN PERPETUITY here. Any company whose growth rate exceeds the required rate of return would a) be a riskless arbitrage and b) attract all the money in the world to invest in it. The company would eventually become the entire economy with every human being on earth working for it.
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Nick, growth rates can exceed the cost of capital for very short periods of time, but we're talking about a growth rate IN PERPETUITY here. This is kind of like asking, "why don't trees just keep growing past the clouds?" or "why can't a stock be worth less than zero?" You're just playing with numbers here and have forgotten the underlying reality. Any company whose growth rate exceeds the required rate of return would a) be a riskless arbitrage and b) attract all the money in the world to invest in it. The company would eventually become the entire economy with every human being on earth working for it. Wow! Talk about a conglomerate! Seriously, unless you think this is a likely scenario, it just simply cannot be that the growth rate exceeds the risk. Remember all these formulas are just mathematical APPROXIMATIONS of incredibly complex real world processes. Don't let the tail wag the dog.
Beautiful. Great answer.
If you try to explain theoretically why growth rate can never be greater than the discount rate, you have to keep the assumption in mind that while calculating terminal value, we have assumed the growth to be a stable growth rate and that the firm you are valuing is a going concern.
Now we know that the stable growth rate of the model can never be greater than nominal rate of GDP growth. If the growth rate of a firm is higher than the growth rate of the economy in the long term, then the firm will be bigger in size than the economy which is not feasible
Also, we know that in the long term, real growth rate of economy becomes equal to the real risk free rate. So the nominal growth rate of the economy will be equal to the nominal risk free rate
We know that the discount rate used is calculated by adding a premium to the nominal risk free rate and that the premium will always be positive
From the above two statements, we can argue that since the stable growth of the model is less than the nominal growth rate of GDP, it will also be lesser than the discount rate used in the WACC model