15.5 Relative Multiples

We don’t compare to sales (use equity) because of leverage from p/h’s liability

Stock price can fluctuate so use an average price

Multiples can vary significantly even over short periods of time

Assumptions

Constant \(ROE\), \(\rho\), and \(k\)

15.5.1 Price to Earnings

\[\begin{equation} \dfrac{P_0}{E_1} = \dfrac{1 - \rho}{k - \underbrace{\rho \times ROE}_{g}} \tag{15.6} \end{equation}\]
  • If \(ROE > k\) \(\Rightarrow\) Keep a high \(\rho\)

Proof. Formula above is based on the DDM

Start with (15.2) and \(\mathrm{E}[Div_1] = E_1 (1-\rho)\)

\(g = \rho \times ROE\)

If the shares are priced fairly then \(P_0 = V_0\)

Plug all the above in and we’ll have (15.6)

Remark. P:E Ratio

  • Forward or leading P/E = consensus forecast earnings for next year

  • Trailing P/E = last year’s actual; Can be distorted by unusual events

  • Price = value of the firm derived from any of the methods

  • Earnings = \(NI\); Either forward or trailing

  • By default, apply the ratio to next year’s earnings per formula

Alternative use of P:E

  • Validating assumptions: reasonability check on the forecast

  • Shortcut to valuation: if you think company will grow similar to the industry

  • Terminal value: use the other method for the forecast horizon then P/E for the terminal value

15.5.2 Price to Book

\[\begin{equation} \dfrac{P_0}{BV_0} = 1 + \dfrac{ROE - k}{k - g} \tag{15.7} \end{equation}\]

  • \(BV_0 =\) equity @ t = 0

  • Useful for firms with substantial holdings in marketable securities

Proof. Above formula is based on AE method

Start with (15.4) and (15.5)

Assume book value grow at constant rate \(g\) and the \(ROE\) is constant and we have:

\(BV_t = BV_0(1+g)^t\)

Plug in to the formulas and using the geometric series

15.5.3 Transaction Multiples

Pros:

  • Based on transaction price of knowledgeable or sophisticated parties, which makes the valuation more meaningful

  • Not subject to random market fluctuations, should have been valued by careful analysis

  • Transactions done by people/experts involved in the companies – would have best estimate of values

Cons:

  • Companies tend to overpay

    • Control premium, and other reason M&A overpay

  • IPO’s are under priced

  • Financials used to value the transaction could be different from the information being used now (forecast is different)

  • Economic conditions @ transaction \(\neq\) economic conditions now

15.5.4 Relative Valuation for Multi-line firms

Use multiples from pure play peers (monoline firms) to estimate by division

Or compare multiples from diversified insurers

  • Choose firms with similar business, \(ROE\), claims paying rating, \(\beta\)