Chapter 14
Valuation: Market-Based Approaches
14-11
in whole or in part.
c. The value-to-book ratio computations for each scenario are as follows:
Dividend Years of
Cost of Equity Payout Excess VB
Scenario ROCE Capital Percentage Earnings Ratio
A 0.20 0.13 0.30 10 1.64
B 0.18 0.13 0.30 10 1.44
C 0.14 0.13 0.30 10 1.08
book ratio:
1. The value-to-book ratio is
• positively related to ROCE.
of ROCE over the cost of equity capital.
2. A particular percentage change in ROCE results in a greater-than-
proportional change in the value-to-book ratio.
3. A particular percentage decrease in the cost of equity capital results in a
proportional decrease in the value-to-book ratio.
4. A particular percentage change in the dividend payout rate results in a
less-than-proportional change in the value-to-book ratio.
5. A particular percentage change in the length of the period in which a firm
the value-to-book ratio.
6. In terms of sensitivity of the value-to-book ratio to percentage changes in
an underlying variable, the underlying variables rank from largest to smal-
lest impact as follows:
a. ROCE
Chapter 14
Valuation: Market-Based Approaches
14-12
in whole or in part.
A 10% decrease in each of the four underlying variables for Scenario B above
(while holding the other variables constant) results in the following:
a. ROCE: 11.8% decrease in the value-to-book ratio
ratio
d. Dividend Payout Percentage: 0.7% increase in the value-to-book ratio
14.21 Market Multiples and Reverse Engineering Share Prices.
a. Following the CAPM, Enron faces a required rate of return on equity capital
of 12.8% at the end of 2000. This rate is computed as follows:
b. At year-end 2000:
(1) Market-to-book = $62,530 million/$11,470 million = 5.45.
(2) Price-earnings, based on 2000 reported earnings per share = $83.00 per
liable proxies for market expectations.
(3) Enron will maintain a 40% dividend payout rate.
CAPM discount rate is appropriate.
These first-pass assumptions yield a value of $10.60 per share, much lower
Chapter 14
Valuation: Market-Based Approaches
14-13
in whole or in part.
Year +1 Year +2 Year +3 Year +4 Year +5
Long
Run
EPS $1.31 $1.44 $1.59 $1.74 $1.92 $1.98
BVps (Lagged) $15.25 $16.02 $16.87 $17.80 $18.83 $19.96
Normal EPS $1.95 $2.05 $2.16 $2.28 $2.41 $2.56
To solve for the implied expected return on Enron shares, we re-run the above computa-
as shown in the following computations:
Year +1 Year +2 Year +3 Year +4 Year +5
Long
Run
EPS $1.31 $1.44 $1.59 $1.74 $1.92 $1.98
BVps (Lagged) $15.25 $16.02 $16.87 $17.80 $18.83 $19.96
Normal EPS $0.67 $0.71 $0.74 $0.79 $0.83 $0.88
Chapter 14
Valuation: Market-Based Approaches
14-14
in whole or in part.
Note: You should be careful to avoid creating the appearance of hindsight bias. As
noted in the problem, these analyses and conclusions do not depend on foresight that
Enron would declare bankruptcy in late 2001.
of 3.0%, you quickly realize that increasing Enron’s long-run earnings growth will
drive the share price down. This occurs because the analysts’ earnings forecasts imply
that Enron will create negative residual income during 2001–2005; so faster growth in
2006 and beyond will simply destroy more value faster.
In this problem, we estimate cost of equity capital for Coca-Cola and use the
value-to-book valuation approach to estimate Coca-Cola’s share value and make a
recommendation on Coca-Cola stock based on this analysis. We also examine the
value-earnings ratio, the price-earnings ratio, price differentials, and reverse
engineering.
price was $35.48.
Part I—Computing Coca-Cola’s Value-to-Book Ratio Using the Value-to-Book
Valuation Approach
Chapter 14
Valuation: Market-Based Approaches
14-15
in whole or in part.
b., c., d., e., f., g., h., and i.
Exhibit 14.A presents the excerpts from FSAP for the valuation of Coca-Cola
based on projected residual ROCE and the value-to-book approach. The first
rows of the table present the computations for Coca-Cola’s projected residual
using the free cash flows to equity model in Chapter 12 and the residual in-
come model in Chapter 13.
Chapter 14
Valuation: Market-Based Approaches
14-16
in whole or in part.
Exhibit 14.A
Value-to-Book Model Valuation for Coca-Cola
(Problem 14.22)
Continuing
RESIDUAL INCOME VALUATION 1 2 3 4 5 Value
Market-to-Book Approach Year +1 Year +2 Year +3 Year +4 Year +5 Year +6
Comprehensive Income Available for Common Shareholders 8,648.5 9,094.5 9,542.9 10,014.4 10,510.1 10,825.4
Book Value of Common Shareholders’ Equity (at t–1) 32,790.0 34,367.0 35,693.3 36,998.9 38,276.6 39,525.4
Sum 5.55
Adjust to mid-year discounting 1.038
Implied Market-to-Book Ratio 5.763
Times Beginning Book Value of Equity 32,790.0
Chapter 14
Valuation: Market-Based Approaches
14-17
in whole or in part.
b. and c.
Projected residual ROCE amounts for Coca-Cola in Years +1 to +6 are
shown in Exhibit 14A.
equity.
e. The data in the exhibit indicate that projected residual ROCE in Year +6 will be
19.9%). Using the 7.50% required rate of return on common equity from Solu-
f. We compute Coca-Cola’s value-to-book ratio as of the end of 2012 with the
following three steps: (1) The total sum of the present value of all future resi-
g. Coca-Cola’s market-to-book ratio as of the end of 2012 equals 4.84 [($35.48
value)/4,469 million shares].
i. The share value estimate of $42.28 per share is identical to the share value
estimate obtained using the free cash flows to equity model in Chapter 12 and
the residual income model in Chapter 13.
Part II—Analyzing Coca-Cola’s Share Price Using the Value-Earnings Ratio,
Price-Earnings Ratio, Price Differentials, and Reverse Engineering
j. Our Year +1 earnings per share based on projected comprehensive income
available for common shareholders in Year +1 of $8,648.5 million divided by
Chapter 14
Valuation: Market-Based Approaches
14-18
k. Using the Year +1 earnings-per-share forecast of $1.935 from Solution j
above, and the $35.48 share price at the end of 2012, Coca-Cola’s price-
ratios in Solutions g above.
l. Note: This question requires students to assume a 1% long-run growth rate
(rather than 3% for the other parts). We make this change because with a 3%
risk-free discount rate and a 3% long-run growth rate, the perpetuity value of
m. Reverse engineering Coca-Cola’s share price at the end of 2012 to solve for
the implied expected rate of return yields 8.372%, which is higher than the
n. Reverse engineering Coca-Cola’s share price at the end of 2012 to solve for
the implied expected long-run growth yields a growth rate of 1.676%. We
solve for this growth rate by assuming that value equals price and that our
earnings forecasts through Year +5 are reliable proxies for the market’s ex-
Chapter 14
Valuation: Market-Based Approaches
14-19
14.23 Analysis of Comparable Companies Using Market Multiples.
a. The following table uses data and analyses for PepsiCo from this chapter and
the data and analyses for Coca-Cola from the previous problem to compare
these two competitors on the following dimensions:
dollar amounts in millions PepsiCo Coca-Cola
1. Cost of Equity Capital (R
E
) 7.50% 7.50%
2. ROCE for 2012 28.6% 28.0%
3. Projected ROCE for Year +1 27.2% 26.4%
4. Book Value of Common Shareholders’ Equity $22,417 $32,790
5. Market Value of Common Shareholders’ Equity $105,656 $158,560
the market at the end of 2012. These comparisons are consistent with the conclusion
that both shares are underpriced in various ways, as follows:
versus 26.4%, respectively).
(2) Price differentials suggest that both firms’ share prices have been deeply dis–
counted for risk by the market.