Franchise P/E

What Is Franchise P/E?

Franchise P/E (price-to-earnings) is the present value of new business opportunities available to a business. When added together, a firm's tangible P/E (sometimes called base P/E) and franchise P/E equal its intrinsic P/E. Franchise P/E is a function of the excess return on those new investments (the franchise factor) relative to the size of the opportunity (the growth factor).

Understanding Franchise P/E

Franchise P/E is mainly determined by the differences between the return on the new business opportunity and the cost of equity. Companies with high franchise P/E ratios are those that are able to continually capitalize on core strengths. Their franchise value measures their capacity to expand over time through investments that provide above-market returns. Companies that increase their asset turnover or widen their profit margin, will increase their Franchise P/E and its observed P/E ratio.

A firm’s equity value or market value is the sum of its tangible value and franchise value. Breaking down the P/E ratio results in two major components, the tangible P/E (the base P/E of a firm with constant earnings), and the franchise factor, which captures the returns associated with new investments. Franchise factor contributes to the P/E ratio in the same way that franchise value contributes to share value.

Calculating Franchise P/E

The formula for franchise P/E is:

Franchise P/E Formula

$\begin{aligned}&\text{Franchise } \frac{P}{E}\\&\quad=\text{(observed) intrinsic }\frac{P}{E}\\&\qquad-\text{tangible }\frac{P}{E}=\text{franchise factor}\\&\qquad\times\text{growth factor}\\&\textbf{where:}\\&\text{Intrinsic }P/E=\text{Tangible }P/E\\&\quad+\text{franchise }P/E\\&\text{Tangible }P/E=\text{Firm's static value}\\&\text{Franchise }P/E=\text{Firm's growth value}\\&\text{Franchise factor (FF)}=\text{Incorporates the}\\&\quad\text{required return on new investments}\\&\text{Growth factor (G)=Factors in the present}\\&\quad\text{value of the excess return from new}\\&\quad\text{investments}\end{aligned}$​Franchise EP​=(observed) intrinsic EP​−tangible EP​=franchise factor×growth factorwhere:Intrinsic P/E=Tangible P/E+franchise P/ETangible P/E=Firm’s static valueFranchise P/E=Firm’s growth valueFranchise factor (FF)=Incorporates therequired return on new investmentsGrowth factor (G)=Factors in the presentvalue of the excess return from newinvestments​

Franchise Factor Formula

$\textit{franchise factor}=\frac{1}{r}-\frac{1}{\textit{ROE}}$franchise factor=r1​−ROE1​

Growth Factor (G)

$\begin{aligned}G=\textit{growth factor}=\frac{g}{r-g}&\\g=\textit{ROE}\times b=\textit{ROE}\frac{1}{d}&\\d=\frac{D_1}{E_1}=\frac{1-g}{\textit{ROE}}&\end{aligned}$G=growth factor=r−gg​g=ROE×b=ROEd1​d=E1​D1​​=ROE1−g​​​

These can further be modified:

• Intrinsic leading P/E = P₀ / E₁ = (1 - b) / (r - g) = (1 / r) + [1 / r - 1 / ROE]*g / (r - g)
• Intrinsic trailing P/E = P₀ / E₀ = (1 / r) + [1 / r - 1 / ROE + (1 - g / ROE)]*g / (r - g)

Using Franchise P/E

Using the franchise factor the impact on a company's price-earnings ratio (P/E ratio) per unit growth in new investment can be calculated. For example, a franchise factor of 3 would indicate that the P/E ratio of a company would increase by three units for every unit of growth in the company's book value. The franchise factor can be calculated as the product of annual investment returns in excess of market returns and the duration of the returns.

A higher asset turnover ratio increases the franchise P/E ratio, one of the components of the intrinsic P/E value. This is according to Du Pont analysis, which breaks up return on equity into three basic components: net profit margin, asset turnover, and the equity multiplier.

DuPont Analysis = Net Profit Margin * Asset Turnover * Equity Multiplier

$\begin{aligned}\textit{DuPont Analysis}&=\textit{Net Profit Margin}\\&\quad\times\textit{Asset Turnover}\\&\quad\times\textit{Equity Multiplier}\end{aligned}$DuPont Analysis​=Net Profit Margin×Asset Turnover×Equity Multiplier​

Thus we can use the DuPont equation:

• ROE (↑) = NI/E = NI/revenue * revenue/A (↑) * A/E
• g (↑) = ROE (↑) * (1-d)
• Intrinsic P/E = (1/r) + (((1/r) - (1/ROE(↑)))* g(↑)/(r-g(↑)))
• = (1/r) + (((1/r) - (1/ROE)(↓))* (g/(r-g))(↑))
• = intrinsic P/E (↑)

And when firms pay out more dividends, a firm's intrinsic P/E value decreases:

• d (↑)
• g (↓) = ROE * (1-d(↑))
• Intrinsic P/E = (1/r) + (((1/r) - (1/ROE))* g(↓)/(r-g(↓)))
• = (1/r) + (((1/r) - (1/ROE))* (g/(r-g))(↓))
• = intrinsic P/E (↓)