Time Value of Money question

confuising

Take a company with nearly guaranteed cash flows, very low growth, and concrete assets. Something like Con Edison would. Intuitively, it's pretty clear that we're demanding a discount on the cash flows of the firm because it's trading at a P/E of ~14. Unless you think their monopoly will end in 14 years, you're paying for >14 years of potential for amount less than that because of how that cash flow, while very low risk, is into the future.

The only real thing that you need to take from the Wikipedia example is that P / E = 1 / i, which solves to P = E / i, which is the form of the Gordon Growth Model and the perpetuity formula.

The confusing thing about the P/E ratio is that it's backwards. Usually you think about the cash flow of something as a percentage of the price. For example, in real estate, the "cap rate" is the Net Operating Income divided by the Market Value of the building. That's going to give you a percentage. In fixed income, the "yield" on a bond is the coupons and principal divided by the price. Again a percentage, or, a "rate." Yields are just effective average rates, and rates are just measures of return on invested capital. Because we like multiples so much, we flip the two over when talking about equities. (it's actually a lot easier to work with the numbers and compare E/P, but no matter). So if cashflow / Investment = some rate of return, then obviously Investment/cashflow = 1/same rate or return. As singularity says above, from there it's pretty easy to get to the basic form of a perpetuity.

The reason all this stuff is related to the time value of money is because the what the Gordon growth model is discounting a future stream of cash to arrive at a Present Value. (the summation of the infinite series E1/(1+i) + E2/(1+i)^2 + E3/(1+i)^3... is E/i. Convenient!) This is the reason why $100 per year forever at 10% is only worth $1000 and not infinity forever dollars.

2 comments (having not read the Wiki article, bear in mind)

• P contains embedded assumptions about discount rates. i.e. assume value is derived from a DCV (explicitly) then you are discounting cash flows and assuming a terminal value, perpituity value at some distant point (say year 6). Then you the result value will have some relationship to earnings in year 1. If earnings are expected to grow then you P/E should reflect a multiple greater than the 1/d, and the opposite will be true if earnings are higher now than they will be in the future.

• This is perhaps more interesting in my view. P/B is an explicit comparison of internal and external interest rates. i.e., a P/B of 1 shows that the market is generally using the same discount rates as the company (with B representing a PV of the future CFs of all the assets and libilities of the company and P implicitly representing the same calculation but dones at the require rate of return of the market.