Calculating the Intrinsic P/E

I am rebuilding a spreadsheet that I use to value equities and am working on the calculation of the Intrinsic P/E, so to help give myself a refresher I am writing it all out for the benefit of my readers, so enjoy!

The intrinsic p/e is the sum of the tangible p/e and the franchise p/e. The tangible p/e assumes the company has no growth or that it will pay out all of its earnings. The franchise p/e represents the present value of future growth and is broken down into two components, the franchise factor and the growth factor.

I will use an example as shown on page 192 of the 2010 CFA Program Curriculum, Level II, Volume 4.

In the example, the company can generate a return on equity of 15% (ROE) and the earnings retention ratio is 0.60% (b). Earnings next year will be $100 million and the required rate of return is 12% (r).

First, let’s calculate the tangible p/e. The tangible p/e is simply 1 divided by the required return. In this case, that is 1/.12=8.33.

Next, we calculate the two components that make up the franchise p/e.  The two components of the franchise p/e are the franchise factor and the growth factor and the franchise p/e is the product of those two numbers.

The franchise factor would be the first component and it “is meant to capture the return levels associated with” new investments. The formula is:

(1/r) – (1/ROE) = (1/.12)-(1/.15) = 1.66667

The second component is the growth factor. “The growth factor captures the present value opportunities for productive new investments.” The formula is:

(b * ROE) / (r-(b*ROE)) = (.6 * .15) / [.12 – (.6*.15)]  = 3

The retention rate (b) multiplied by the ROE is the growth rate (g), so we can simplify the formula as follows:

g = b * ROE = .6 * .15 = .09

and then the growth factor formula is now:

g / (r-g) = .09 / (.12 – .09) = 3

Now, let’s calculate the franchise p/e:

Franchise PE = Franchise Factor x Growth Factor = 1.6667 * 3 = 5.00

The intrinsic p/e is equal to the sum of the tangible p/e and the franchise p/e.

Intrinsic p/e = 8.33 + 5.00 = 13.33.

If the company earned $100,000,000 the intrinsic value would be 13.33*$100,000,000 or $1,333,000,000. There are additional formulas that take into account inflation but I am not covering that here.

There you have it! Everything you wanted to know about the calculation of the intrinsic p/e.