Need help in understanding perpetuity valuation formula

[ilovejesus215]

The net present value of a perpetuity is calculated as

PV = C / (r-g)

where C is the cash flow in the first period, r is the market interest rate (or discount rate) and g is the growth rate of the cash flow. Importantly, the formula doesn't work if the growth rate is higher than the interest rate. What I don't understand is that if this formula (and the related one for growing annuities) is pretty fundamental and supposedly very useful, then why would it be limited to only when an investment grows below the discount rate?

Here's an example from Fundamentals of Corporate Finance. They use the formula to calculate the price of a stock. You can see how the value of the stock and value of its dividend both grow at 6% a year when the interest rate is 11%. But isn't the whole point of investing in the stock market to at least equal the market interest rate if not do better than it?

I must be misunderstanding something pretty fundamental here, but I don't know what it is.

 

[marc22039]

@ilovejesus215 the reason the formula caps at the market interest rate, is that the calculation stems from calculating the amount of money required for the market to maintain the payments indefinitely. If the payments grow faster than the market, then the payouts need an infinite amount of money since the market can't sustain the lump sum.

If you have an investment with payouts growing at above market rates forever, that investment's worth is potentially infinite.

Does that make sense?

 

[ilovejesus215]

@marc22039 I see. That makes sense for perpetuities. And I just realized that the reason I was confused about the same thing for annuities is because I saw the same C/(r-g) term in the annuities formula and just assumed it would cause the same problem. But in working out an example I can see that even if r

 

[marc22039]

@ilovejesus215 glad to be of assistance

 

[forsakennowforgiven]

@ilovejesus215 There is a really good lecture series from MIT by prof Andrew Lo that has been mentioned here before. The entire series is worth watching, and he does a great job building up to the perpetuity formula, highly recommend it. You can skip to minute 30 to see it here:

And the lecture slides are here:

https://ocw.mit.edu/courses/sloan-s...eo-lectures-and-slides/MIT15_401F08_lec02.pdf

 

[ilovejesus215]

@forsakennowforgiven Thanks for that.