Estimating a Stock’s Price-to-Book Ratio from ROE and Growth
Summary
The document demonstrates a fundamental valuation calculation for a pharmaceutical company using expected net income, book equity, a cost of equity, and long-run growth. It first subtracts interest expense from EBIT and applies the corporate tax rate to estimate net income, then divides that estimate by book equity to obtain return on equity. The cost of equity is estimated with a CAPM-style calculation using a government bond yield, an industry beta, and an equity risk premium.
It then applies a stable-growth relationship in which price to book depends on the spread between ROE and growth relative to the spread between required return and growth. The worked example uses historical company context and assumed inputs to arrive at a ratio. The author asks how to source the risk-free rate, equity premium, and expected income in Bloomberg; the excerpt does not answer those data questions. The result depends on the assumptions and on the suitability of stable growth for the company.
Key ideas
- Expected net income is estimated from EBIT after interest expense and taxes.
- Return on equity is calculated by dividing expected net income by book equity.
- The cost of equity uses a bond yield, beta, and assumed equity risk premium.
- The stable-growth price-to-book formula depends on ROE, growth, and required return.
- The example is assumption-dependent and leaves the data sourcing questions unresolved.
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Full text
# Calculating the PB of a stock in practice
# Calculating the PB of a stock in practice
This is a practical problem of calculating the PB of a stock. Here is a example of `Jenapharm`, but I am not sure which terms following can be found in Bloomberg.
Jenapharm was the most respected pharmaceutical manufacturer in East Germany.
Jenapharm, which was expected to have revenues of 230 million DM and `earnings` before interest and taxes of `30` million DM in 1991.
The firm had a book value of assets of 110 million DM, and a `book value of equity` of `58` million DM. The `interest expenses` in 1991 is expected to be `15` million DM. The `corporate tax rate` is `40%`.
The firm was expected to maintain sales in its niche product, a contraceptive pill, and `grow` at `5%` a year in the long term, primarily by expanding into the generic drug market.
The `average beta` of pharmaceutical firms traded on the Frankfurt Stock exchange was `1.05`.
The `ten-year bond rate` in Germany at the time of this valuation was `7%`; the `risk premium for stocks over bonds` is assumed to be `5.5%`.
Calculate the PB:
$$\textrm{Expected Net Income} = (\textrm{EBIT} - \textrm{Interest Expense})*(1-t) $$ $$= (30 - 15) *(1-0.4) = 9$$ $$\textrm{Return on Equity} = \textrm{Expected Net Income / Book Value of Equity}$$ $$ = 9 /58 = 15.52\%$$ $$\textrm{Cost on Equity} = 7\% + 1.05 (5.5\%) = 12.775\%$$ $$\textrm{Price/Book Value Ratio} = (\textrm{ROE} - g) / (r - g) $$ $$= (.1552 - .05) / (.12775 -.05) = 1.35$$
To find the data in `Bloomberg`, I have following questions:
- Which risk free interest rate will we use? 10 year bond of respective currency?
- For Risk premium for stocks over bonds and Expected Net Income, can we directly found those two terms in Company's information?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.