Download Chapter 2

Module 4.3
Stock Valuation – estimating growth and
discount rates, plus a look at comparables
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
9.2 Estimates of Parameters

The value of a firm depends upon its growth
rate, g, and its discount rate, R.

Where does g come from?
g = Retention ratio × ROE
(eq 9.8)
Payout Ratio = dividend per share / earnings per share
Retention Ratio = 1 – dividend payout ratio
9-1
Digging into ROE


Please read this wikipedia link:
https://en.wikipedia.org/wiki/Return_on_equity
ROE is typically described as the product of three other
ratios: net margin, asset turnover, and leverage. Net margin
and asset turnover are typically deemed decent measures of
managerial skill.
æ NetIncome öæ Sales öæ Assets ö NetIncome
ROE = ç
֍
֍
÷=
è Sales øè Assets øè Equity ø
Equity

So, not ROEs are created equally. Warren Buffet likes firms
that improve ROE by improving net margin and asset
turnover (the first two ratios).
9-2
Where Does R Come From?
Asset pricing models like the CAPM (coming
soon) or from our dividend growth model
 The discount rate can be broken into two parts.

The dividend yield
 The growth rate (in dividends)


In practice, there is a great deal of estimation
error involved in estimating R AND g.

If g is estimated from ROE, and ROE is based on accounting numbers,
then you know there is a lot room for error!
9-3
Using dividend growth model
(DGM) to Find R

Start with the DGM:
D0 (1+ g) D1
P0 =
=
R-g
R-g
Rearrange and solve for R, shows R as sum of dividend
yield and growth rate :
D0 (1+ g)
D1
R =
+g =
+g
P0
P0
Dividend yield
growth rate
9-4
9.3 Growth Opportunities
Growth opportunities are opportunities to
invest in positive NPV projects.
 The value of a firm can be conceptualized as
the sum of the value of a firm that pays out
100% of its earnings as dividends plus the net
present value of the growth opportunities.

EPS
P=
+ NPVGO
R
9-5
NPVGO Model: Example
Consider a firm that has forecasted EPS of $5, a
discount rate of 16%, and is currently priced at
$75 per share.

We can calculate the value of the firm as a cash cow.
EPS $5
P0 =
=
= $31.25
R
.16

So, NPVGO must be: $75 - $31.25 = $43.75
9-6
9.4 Comparables


Comparables are used to value companies based
primarily on multiples.
Common multiples include:


Price-to-Earnings
Enterprise Value Ratios
9-7
Price-Earnings Ratio

The price-earnings ratio is calculated as the current
stock price divided by annual EPS.

The Wall Street Journal uses last 4 quarter’s earnings
Price per share
P/E ratio =
EPS
9-8
PE and NPVGO
EPS
P=
+ NPVGO
R

Recall,

Dividing every term by EPS provides the following description
of the PE ratio:
1 NPVGO
PE = +
R
EPS

So, a firm’s PE ratio is positively related to growth
opportunities and negatively related to risk (R)
9-9
Enterprise Value Ratios


The PE ratio focuses on equity, but what if we want the value of
the firm?
Use Enterprise Value:


Like PE, we compare the value to a measure of earnings. From
a firm level, this is EBITDA, or earnings before interest, taxes,
depreciation, and amortization.


EV = market value of equity + market value of debt - cash
EBITDA represents a measure of total firm cash flow
The Enterprise Value Ratio = EV / EBITDA
9-10
Common Stock Market Reporting
52 WEEKS
YLD
VOL
NET
HI
LO STOCK SYM DIV % PE 100s CLOSE CHG
21.89
9.41 Gap Inc GPS 0.34 3.1 8 88298 11.06 0.45
Gap has
been as high
as $21.89 in
the last year.
Gap pays a
dividend of 34
cents/share.
Gap ended trading at
$11.06, which is up 45
cents from yesterday.
Given the current
price, the dividend
yield is 3.1%.
Gap has been as
low as $9.41 in
the last year.
Given the current
price, the PE ratio is
8 times earnings.
8,829,800 shares traded
hands in the last day’s
trading.
9-11