LOS 29.h: Calculate and interpret the justified price-to-earnings ratio (P/E), price-to- book ratio (P/B), and price-to-sales ratio (P/S) for a stock, based on forecasted
fundamentals.
CFA® Program Curriculum: Volume 4, page 395–396
4.20+3.75+4.75+4.30 4
0.14+0.12+0.16+0.14 4
PROFESSOR’S NOTE
We organized the material related to these two LOS by ratio. We start with the formula for the justified price multiple. If you know the formula, you know the fundamental factors. Notice that the LOS ask us to “describe” all of the justified price multiples plus the dividend yield, but only to
“calculate” three: P/E, P/B, and P/S.
Justified P/E Multiple
As we said earlier, the justified P/E price multiple is a P/E ratio with the “P” in the numerator equal to the fundamental value derived from a valuation model. The best way to analyze the fundamental factors that affect the P/E ratio is to use the single-stage Gordon growth model:
V0= =
where:
V0 = fundamental value D0 = dividend just paid
D1 = dividends expected to be received at end of Year 1 r = required return on equity
g = dividend growth rate
If we express D0 as the product of current earnings per share (E0) and the payout ratio (D0 / E0) and express the retention rate as b, the previous formula becomes trailing P/E:
justified trailing P/E = = =
Recognizing that E1 = E0 (1 + g) and D1 = D0 (1 + g), the leading P/E is calculated as:
justified leading P/E = = = PROFESSOR’S NOTE
Remember that if earnings are expected to grow, E1 will be greater than E0, and the justified leading P/E (P0 / E1) will be smaller than the justified trailing P/E (P0 / E0 ) because you’re dividing by a larger number when you are calculating leading P/E. In fact, trailing P/E will be larger than leading P/E by a factor of (1 + g): justified trailing P/E = justified leading P/E × (1 + g).
By examining the formulas for justified (leading and trailing) P/E, we can conclude that the fundamental factors that affect P/E are expected growth rate and required return (which is related to risk). The justified P/E ratio is:
Positively related to the growth rate of expected cash flows, whether defined as dividends or free cash flows, all else equal.
Inversely related to the stock’s required rate of return, all else equal.
EXAMPLE: Calculating justified P/E ratio for Comtronics again
Shares of Comtronics are selling for $30. The mean analyst earnings per share forecast for next year is $4, and the long-run growth rate is 5%. Comtronics has a dividend payout ratio of 60% and a required return of 14%. Calculate the justified leading P/E ratio.
D0×(1+g) (r−g)
D1
(r−g)
P0
E0
D0×(1+g)/E0 r−g
(1−b)×(1+g) r−g
P0
E1
D1/E1
r−g 1−b
r−g
Answer:
justified leading P/E = = = 6. 67 times
This is the same answer we got when we calculated Comtronics’ P/E the “long way” in the example at the beginning of this topic review.
EXAMPLE: Calculating justified P/E ratio
A stock has a payout ratio of 40%. The shareholders require a return of 11% on their investment, and the expected growth rate in dividends is 5%. Calculate the trailing and leading P/E multiple based on these forecasted fundamentals.
Answer:
justified trailing P/E = = = 7.00
justified leading P/E = = = 6.67 or
justified trailing P/E = 6.67 × (1.05) = 7.00
Justified P/B Multiple
Using the sustainable growth relation of g = ROE × b and observing that E1 = B0 × ROE, we can also derive the justified P/B from the Gordon growth model as:
justified P/B ratio = where:
ROE = return on equity r = required return on equity
g = expected growth rate in dividends and earnings
We can draw two useful conclusions from this formula concerning the fundamentals that influence the P/B ratio:
P/B increases as ROE increases, all else equal.
The larger the spread between ROE and r, all else equal, the higher the P/B ratio. This makes sense if you remember that ROE is the return on the firm’s investment projects and r is the required return. The larger the spread, all else equal, the more value the firm is creating through its investment activities and the higher its market value as represented by V0.
We can then use fundamental forecasts of ROE, r, and g to find a value for this ratio.
EXAMPLE: Calculating justified P/B ratio
A firm’s ROE is 14%, its required rate of return is 8%, and its expected growth rate is 4%. Calculate the firm’s justified P/B based on these fundamentals.
1−b r−g
0.60 0.14−0.05
(1−b)×(1+g) r−g
0.40 ×1.05 0.11−0.05
1−b r−g
0.40 0.11−0.05
ROE−g r−g
Answer:
justified P/B ratio = = = 2. 5
Justified P/S Multiple
Since net profit margin (PM0) is equal to E0/S0, we can also restate the Gordon growth model as:
justified =
Net profit margin (E0/S0) thus influences P/S directly as well as indirectly through its effect on the sustainable growth rate, g:
g = retention ratio × net profit margin ×( )×( ) This means that the P/S ratio will increase, all else equal, if:
Profit margin increases.
Earnings growth rate increases.
We can also do a little algebra and solve for P/S as a function of trailing P/E, which might be an easier formula to remember:
justified = (E0/S0) ×[ ] = net profit margin × justified trailing P/E
EXAMPLE: Calculating justified P/S ratio
A stock has a dividend payout ratio of 40%, a return on equity (ROE) of 8.3%, an EPS of $4.25, sales per share of $218.75, and an expected growth rate in dividends and earnings of 5%. Shareholders require a return of 10% on their investment. Calculate the justified P/S multiple based on these fundamentals.
Answer:
The ratio E0/S0 is the profit margin. In this example, the profit margin is ($4.25 / $218.75) = 0.0194.
Therefore, we get:
= = 0.163 times
Justified P/CF Multiple
The justified price to cash flow based on fundamentals can be calculated by finding the value of the stock using a DCF model and dividing the result by the chosen measure of cash flow.
For example, equity value using the single-stage FCFE model is:
V0=
P/CF will increase, all else equal, if:
Required return decreases.
Growth rate increases.
ROE−g r−g
0.14−0.04 0.08−0.04
P0
S0
(E0/S0)×(1−b)×(1+g) r−g
sales assets
assets shareholders’ equity
P0
S0
(1−b)×(1+g) r−g
P0 S0
0.0194 × 0.4 × 1.05 0.10−0.05
FCFE0×(1+g) r−g
Justified EV/EBITDA Multiple
The justified EV/EBITDA based on fundamentals is simply the enterprise value based on a forecast of fundamentals divided by EBITDA forecast based on fundamentals. The ratio is:
Positively related to the growth rate in FCFF and EBITDA.
Negatively related to the firm’s overall risk level and weighted average cost of capital (WACC).
Justified Dividend Yield
The dividend yield relative to fundamentals may be expressed in terms of the Gordon growth model as:
=
Dividend yield is:
Positively related to the required rate of return.
Negatively related to the forecasted growth rate in dividends. This implies that choosing high dividend yield stocks reflects a value rather than a growth investment strategy.