#### First World Problems – Calculating Cost of Equity for Value Investors by SG Value Investor, The Value Edge

While the concept of cost of equity is widely used, I personally find several issues with current form which I will raise in the course of this post.

### What is cost of equity?

Nothing beats a Wikipedia definition – in finance, cost of equity is the return a firm theoretically pays to its equity holders as compensation for the risk of investing. While a firm’s present cost of debt is relatively easy to determine from observation of interest rates in the capital markets, its current cost of equity is unobservable and must be estimated.

### How is cost of equity derived?

There are currently 2 ways to calculate the cost of equity for a firm. The first is from the Capital Asset Pricing Model where the cost of equity is equal to the beta of a firm multiplied by a risk premium plus the risk free rate. The second and less used method is based on the Gordon’s growth model where cost of equity is the expected dividend for next year divided by current price plus expected growth rate of future dividends.

### When is cost of equity used?

Cost of equity is often used as a discount rate for valuation of companies. In particular, all discounted cash flow (DCF) and discounted dividend models (DDM) will need to determine the cost of equity in order to find the present value of future forms of cash flow.

### What’s the issue?

Firstly, value investors will reject the notion of beta as an appropriate proxy for a firm’s risk because it is a mere function of price and nothing else. In a paper written by Bruce Grantier, Benjamin Graham is quoted in the following words.

Beta is a more or less useful measure of past price fluctuations of common stocks. What bother me is that authorities now equate the beta idea with the concept of risk. Price variability yes; risk no. Real investment risk is measured not by the percent that a stock might decline in price in relation to the general market in a given period but by the danger of a loss of quality and earnings power through economic changes or deterioration in management.

Cost of equity calculated based on beta will not be rigorous enough for a value investor, and this includes most of the calculations by data aggregators such as Bloomberg etc. Gordon’s growth model is a function of price and suffers from the same problem.

The fundamental risk of a company for a business owner does not change whether the company is public or private. This leads us to the second issue – current derivations are not applicable to private companies because they do not a share price. This raises further doubt on the validity of current derivations.

We therefore conclude that an appropriate derivation of cost of equity should be one that is based on earnings return instead of the current share price return. It makes some sense then, and since discounting is defined as “how much money would have to be invested currently, at a given rate of return, to yield the cash flow in future”, that cost of equity should be equal to return on equity (ROE). However, this would mean that based on current DCF and DDM models, when 2 firms have the same earnings but different ROEs, the one with the higher ROE will be accorded a lower ‘price’ and hence lower value. This seems to be the conventional understanding. Now, if you remember the definition for discounting above, then the ‘price’ should actually represent the amount of money that would have to be invested currently to receive the same amount of earnings. In that regard, it would make sense to have a lower value.

To conclude, this seems to run counterintuitive against conventional practice and I will be more than happy if anyone can point out a logical flaw. Nevertheless, there is no denying that current calculations of cost of equity do not satisfy the requirements of a value investor. This is indeed an area for future examination.

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