Earning Power and Price Earnings Ratio (PER)

In first place we see that the PER that the XYZ share should have is the inverse of the hoped for earning power by the shareholder (1/K). The higher the K, the lower the PER we are willing to pay will be. Since we know the K will increase if the interest rates in the market go up and if the risk premium or the perception of the risk we have as far as the company is concerned. That is why bad news about the XYZ Company at least will make the risk premium increase the investors ask for, and therefore, K will increase with which the PER we are willing to pay will go down, and therefore, the price will also go down (unless the benefits increase). In our example, if the solicited K by investors is of 15 for 100 the PER should be of 1/0,15 = 6,6.

But this PER comes modified to the lowering or rising by the F factor or factor of creation of value we are going to interpret in the following:

F = 1 – g/ROE over 1- g/k

So that F is positive and the PER increases depends on that the ROE is higher than the earning power solicited by the shareholders. In other words, the company needs to make more than what the shareholders have asked for. To try to explain this: The shareholders have invested an amount in a company that is equal to their own equity; in this case it is of 100 million dollars. They are hoping to obtain a profit or earning power of 15 for 100. If the earning power that the company produces over the inverted amount (ROE) is of 15 for 100, the equity (price of the share) will not vary in value. They will continue being worth 100 million dollars. But if the company is able to generate a profit of say for example, 20 for 100, it is evident that the equity will increase in value, since they are obtaining extra earning power above that which they hoped for when they invested. 

To look at it with numbers let us suppose that the growth g is always of 10 for 100, and let us calculate the value of the factor F, for various types of earning power or ROE.

  • For a ROE of 10 for 100, F is worth 1,5 and the PER should be 1/K x F = 1/0,15 x 1,5 = 10
  • For a ROE of 15 for 100, F = 1,0. The PER would be of 6,6.
  • For a ROE of 12 for 100, F = 0,5. The PER would be of 6,6 x 0,5 = 3,3.

By this we see that when the ROE is higher than the profit solicited by the shareholder (K) the PER will increase. If the ROE is equal to K, the PER will be the same to 1/K. And if the ROE is less than the K, the company will be destroying value and the shares will have a PER under 1/K.