# Using the Price to Earnings Ratio to Derive the Cost of Equity

This article describes how the P/E ratio can be used to derive the cost of capital.  Every time you waste time listening to how the stock market has increased or decreased, you should think either the expected growth rate in profits has changed or, more likely, the cost of capital and the perception of risk has changed.  This page demonstrates some complex issues in using the P/E to estimate the cost of capital after recognising that long-term growth cannot exceed population and productivity growth in the long-run.

## Basic P/E formulas and Deriving the Cost of Capital

Old fashioned DCF formula where the cost of capital could be estimated using the formula:

Value = D1 / (k-g) or (k-g) x Value = D1 or k-g = D1/Value or

k = D1/Value + g

In the case of the P/E formula, a similar derivation can be made:

P/E = (1-g/ROE)/(k-g) or (k-g) = (1-g/ROE)/P/E or

k = (1-g/ROE)/(P/E) + g

## Problems with Estimating High Growth Rates Over Long-term

The set of videos for the cost of capital begins with an introduction to an approach that collects data from finance.yahoo.com and from marketwatch.com on stock prices, historic financial information, interest rates, earnings rates and growth rates. The database evaluates historic market to book ratios relative to projected return on equity to evaluate cost of capital. In addition PE ratios and published growth estimates are used along with assumed transition rates to back into the cost of capital. The CAPM is also computed along with the dividend discount model. The next set of videos explain the theory behind using the market to book ratio and the P/E ratio using simulation and sensitivity analysis. The final set of videos in the set explain details of how to build the data base.

## Using the P/E to Estimate the Cost of Capital

Deriving the cost of capital from the P/E ratio requires a lot of assumptions about long-term ROE versus cost of capital, long-term growth, inflation rates and transition periods. The P/E ratio files and videos use alternative scenario analyses to demonstrate the difficulty. The P/E Analysis file below evaluates the cost of capital with sensitivity and scenario analysis. It demonstrates how to correct the value driver formula P/E = (1-g/ROE)/(k-g) for inflation and changing returns.

This files below evaluates the price to book ratio analysis with regression analysis and shows how to develop the formula: PB = (ROE-g)/(k-g). It shows how you can use the market to book ratio to compute cost of capital and it demonstrates how a regression equation for the market to book ratio can be used to evaluate the cost of capital. If the CAPM is a biased and flawed model, bizarre attempts to adjust the cost of capital for country risk resulting in premiums as much as 11% for some countries. These CAPM derived premiums published by a man named Mr. Damoradan and frequently used have to imply that the real cost of all sorts of products ranging from houses to electricity can be as much as double for so-called risky countries.

• 1. Dow Stocks.xlsm
• 3. Utility Companies.xlsm
• 1. Beer Companies.xlsm
• Price to Earnings Analysis.xlsm

Cost of Capital and PE formula.xlsm

Price to Book Analysis.xlsm