12-1
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in whole or in part.
CHAPTER 12
VALUATION: CASH-FLOW-BASED APPROACHES
Solutions to Questions, Exercises, Problems, and Teaching Notes to Cases
12.1 Free Cash Flows. Cash flows are free if they are unencumbered and available to
be distributed to financial claims, such as debt, preferred, noncontrolling interests,
and common equity shares. Cash flows are not free if it is necessary for the firm
to use the cash to maintain working capital, invest in productive capacity, or make
other strategic investments. Free cash flows available for debt and equity
stakeholders include cash flows to satisfy all debt, preferred, noncontrolling, and
common equity claims. They differ from the free cash flows that are available to
common equity shareholders, which include only free cash flows that can be paid
to common shareholders, the residual claimants of the firm, after debt, preferred,
and noncontrolling interest claims have been satisfied.
12.2 Free Cash Flows Valuation Approach. The theory behind the free cash flows
valuation approach is that these cash flows are ultimately distributable to common
equity shareholders. These free cash flows are value-relevant to common equity
shareholders, even though the shareholders do not receive them directly, because
they are the cash flows that will ultimately be paid to investors through dividends
and stock repurchases. Free cash flows valuation, like dividends valuation, is a
liquidation valuation concept.
12.3 Valuation Approach Equivalence. Valuation based on dividends and valuation
based on the free cash flows for common equity shareholders should yield
identical value estimates because they are opposite sides of the same coin. The
dividends approach values cash flows as they are distributed to shareholders. The
free cash flows approach values cash flows as they are generated. Over the life of
the firm, all of the free cash flow generated by the firm will be paid out to the
shareholders in some form of dividends (periodic quarterly or annual dividends,
share repurchases, or liquidating dividends).
12.4 Measuring Value-Relevant Free Cash Flows. When the firm borrows cash by
issuing debt, it increases free cash flows for common equity shareholders that
period. That period, the firm has more cash that it can use to pay out dividends or
repurchase shares. In some future periods, of course, the firm will have to use cash
to repay the debt. When the firm uses cash to repay debt, it obviously reduces the
amount of free cash flows for common equity shareholders that period.
Chapter 12
Valuation: Cash-Flow-Based Approaches
12-2
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in whole or in part.
12.5 Measuring Value-Relevant Free Cash Flows. When the firm uses marketable
securities to manage operating liquidity and then uses cash to purchase
marketable securities, it decreases the amount of free cash flows that can be
distributed to common equity shareholders that period. In subsequent periods,
when the firm sells the securities for cash, it increases the free cash flows for
common equity shareholders.
12.6 Valuation When Free Cash Flows Are Negative. Healthy, growing, profitable
firms commonly project negative free cash flows for equity shareholders for a
number of years as they invest cash in acquiring assets and growing the business.
The free cash flows valuation approach is useful even when cash flows are
negative. To obtain positive valuations of firms when they are expected to
generate negative free cash flows over the next five years, the analyst must extend
the forecast horizon to a point in the future when the free cash flows will turn
positive. The current negative cash flows are intended to yield positive cash flows
in the future, which the valuation model should capture.
12.7 Using Different Free-Cash-Flows-Based Approaches. Analysts should use free
cash flows for all debt and equity stakeholders when valuing the operating assets
of an entity or all financial claims on the entity. In settings such as those, the
analyst is interested in all of the cash flows the assets will generate to meet debt
and equity claims. Such settings might arise when the analyst is considering a
takeover or an asset acquisition of a target firm, the divestiture of a subsidiary or
division, or a leveraged buyout. The analyst should use free cash flows for equity
shareholders in settings where he or she is interested in the equity value of the
firm rather than the value of all assets or financial claims on the enterprise. Thus,
in valuing shares of stock, the analyst can just focus the valuation on free cash
flows to equity.
12.8 Appropriate Discount Rates. The analyst should use a required rate of return on
equity capital as a discount rate when valuing the equity in a firm or a share of
common stock. In settings in which the analyst is valuing cash flows that will be
distributable to debt, preferred, noncontrolling interests, and common equity
claimants, the analyst should use a weighted-average cost of capital as a discount
rate. In such settings, the weights used to compute the weighted-average cost of
capital must be consistent with the proportionate claims on the cash flows;
otherwise, the analyst will determine an inconsistent estimate of enterprise value.
12.9 Free Cash Flows and Discount Rates. Firms that are financed with all common
equity capital (no debt, preferred, stock, or noncontrolling interests) are obvious
examples of when free cash flows to equity shareholders and free cash flows to all
debt and equity stakeholders will be identical. For such firms, the required rate of
return on equity and the weighted-average cost of capital should be identical too
because the weight on equity is 100%.
Chapter 12
Valuation: Cash-Flow-Based Approaches
12-3
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in whole or in part.
12.10 Calculating Free Cash Flows.
Free cash flows for 3M for 2006 through 2008 were as follows: (amounts in
millions; allow for rounding)
a. Free cash flows for all debt and equity stakeholders:
2008 2007 2006
Cash Flow from Operating Activities …… $4,118 $4,363 $3,896
Interest Paid (net of taxes):
2008: (1 – 0.35) × $215 ………………… 140
2007: (1 – 0.35) × $210 ………………… 137
2006: (1 – 0.35) × $122 ………………… 79
Change in Cash Required for Liquidity … 47 (449) (375)
Free Cash Flow from Operations to All
Debt and Equity Stakeholders ………… $4,305 $ 4,051 $ 3,600
Fixed Assets Acquired ……………………….. $(1,384) $(1,319) $(1,119)
Acquisition of Businesses …………………… (1,306) 358 321
Other Investing Activities …………………… 291 (406) (662)
Cash Flow for Investing Activities ………. $(2,399) $(1,367) $(1,460)
Free Cash Flows to All Debt and
Equity Stakeholders ……………………… $ 1,906 $ 2,684 $ 2,140
b. Free cash flows for common equity shareholders:
2008 2007 2006
Cash Flow from Operating Activities …… $4,118 $4,363 $3,896
Change in Cash Required for Liquidity … 47 (449) (375)
Cash Flow for Investing Activities ………. (2,399) (1,367) (1,460)
Increase (Decrease) in Short-Term
Borrowing …………………………………… 361 (1,222) 882
Increase (Decrease) in Long-Term Debt .. 676 2,444 253
Free Cash Flows to Common Equity
Shareholders ………………………………… $2,803 $3,769 $3,196
c. 3M’s uses of free cash flows for common equity shareholders:
2008 2007 2006
Common Stock Repurchases ………………. $1,405 $2,389 $1,820
Dividend Payments ……………………………. 1,398 1,380 1,376
Free Cash Flows to Common Equity
Shareholders ………………………………… $2,803 $3,769 $3,196
Chapter 12
Valuation: Cash-Flow-Based Approaches
12-4
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in whole or in part.
12.11 Calculating Free Cash Flows.
Free cash flows for Dick’s Sporting Goods for fiscal years ending in 2009, 2008,
and 2007 were as follows: (amounts in thousands)
a. Free cash flows for all debt and equity stakeholders:
2009 2008 2007
Cash Flow from Operating Activities …… $ 159,676 $ 262,968 $139,609
Interest Paid (net of taxes):
2009: (1 – 0.40) × $8,021 ……………… 4,813
2008: (1 – 0.40) × $12,314 ……………. 7,388
2007: (1 – 0.40) × $9,286 ……………… 5,572
Cash required for liquidity ………………….. (24,530) 85,635 (99,378)
Free Cash Flow from Operations to All
Debt and Equity Stakeholders ………… $ 139,959 $ 355,991 $ 45,803
Cash Flow for Investing Activities ………. $ (144,194) $ (435,296) $ (130,486)
Free Cash Flows to All Debt and
Equity Stakeholders ……………………… $ (4,235) $ (79,305) $ (84,683)
b. Free cash flows for common equity shareholders:
2009 2008 2007
Cash Flow from Operating Activities …… $ 159,676 $ 262,968 $ 139,609
Cash Required for Liquidity ……………….. (24,530) 85,635 (99,378)
Free Cash Flow from Operations for
Common Equity Shareholders ……….. $ 135,146 $ 348,603 $ 40,231
Cash Flow for Investing Activities ………. $ (144,194) $ (435,296) $ (130,486)
Construction Allowance Receipts ………… 11,874 13,282 17,902
(Decrease) Increase in Short-Term
Borrowing …………………………………… (9,927) 4,785 8,829
(Decrease) in Long-Term Debt and
Capital Leases ……………………………… (6,793) (1,058) (184)
Free Cash Flows to Common Equity
Shareholders ………………………………… $ (13,894) $ (69,684) $ (63,708)
c. Dick’s Sporting Goods sources of free cash flows from common equity
shareholders:
2009 2008 2007
Proceeds from Sale of Common Stock …. $ 13,894 $ 69,684 $ 63,708
Free Cash Flows from Common Equity
Shareholders ………………………………… $ 13,894 $ 69,684 $ 63,708
Chapter 12
Valuation: Cash-Flow-Based Approaches
12-5
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in whole or in part.
d. The free cash flows to all debt and equity capital stakeholders for Dick’s
Sporting Goods vary dramatically over 2007 to 2009. In 2007, the firm grew
by investing in new store assets but financed most of that growth with cash
from operations, construction allowances, short-term debt, and equity issues.
In 2008, the firm used a large amount of cash from operations, cash on hand,
and issued equity to acquire Golf Galaxy and Chick’s Sporting Goods and to
finance growth in new stores. In the fiscal year ending in 2009, Dick’s used
primarily cash from operations to finance growth in stores. In each of these
three years, the free cash flows to all debt and equity capital stakeholders
differ from the free cash flows to common equity shareholders because Dick’s
Sporting Goods is relying more heavily on equity than debt for external
capital. Note: Most of Dick’s equity issues are to employees through stock
purchase plans and stock option exercises.
e. In each of these three years, Dick’s Sporting Goods produces negative free
cash flows for common shareholders, but this does not imply that Dick’s
Sporting Goods is destroying the value of common equity. To the contrary,
Dick’s Sporting Goods is raising additional equity capital through stock
offerings and is investing in acquisitions and opening new stores, which
should create shareholder value in the long run.
12.12 Valuing a Leveraged Buyout Candidate. (dollar amounts in millions)
May Department Stores:
a. Levered Unlevered
Equity = Equity
Beta Beta
0.88 = X[1 + (1 – 0.35)($4,658/$6,705)]
X = 0.61
b. Revised Equity Beta:
X = 0.61[1 + (1 – 0.35)(0.75/0.25)]
X = 1.80
Revised Cost of Equity Capital:
X = 0.042 + (1.80 × 0.05)
X = 0.132
c. Revised Weighted-Average Cost of Capital:
(0.75)(1 – 0.35)(0.10) + (0.25)(0.132) = 0.04875 + 0.033 = 0.08175
()
EquityofValueMarket
DebtofValueMarket
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Chapter 12
Valuation: Cash-Flow-Based Approaches
12-6
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in whole or in part.
d. Free Present Value Factor Present
Year Cash Flow at 8.175% Value
13 $798 0.92443 $ 738
14 $861 0.85457 736
15 $904 0.78999 714
16 $850 0.73029 621
17 $834 0.67510 563
18 $884 0.62408 552
19 $919 0.57691 530
20 $947 0.53332 505
21 $985 0.49301 486
22 $1,034 0.45575 471
After Year 22 $20,580a 0.45575 9,379
Total Present Value ……………………………………………………………. $15,295
a$20,580 = $1,034 × [1.03/(0.08175 – 0.03)]
e. The firm will finance the $15,295 purchase price with $11,471 (0.75 ×
$15,295) of debt and $3,824 (0.25 × $15,295) of equity. The annual interest
cost of the debt is $1,147 (0.10 × $11,471) pretax and $746 (0.65 × $1,147)
after tax. The free cash flows projected for the first ten years appear sufficient
to service annual cash payments. However, there is little cushion if free cash
flows fall short of projections, particularly during the early years. Also, there is
little excess cash flow to repay principal amounts annually if lenders require it.
12.13 Valuing a Leveraged Buyout Candidate. (dollar amounts in thousands)
Experian:
a.
Equity Beta = Asset Beta
0.86 = X[1 + (1 – 0.35)($366.5/$4,436.8)]
X = 0.82
b. X = 0.82[1 + (1 – 0.35)(0.60/0.40)]
X = 1.62
c. The after-tax cost of debt capital of Experian is 6.5% (0.65 × 10%). The cost
of equity capital of Experian is 12.3% [4.2% + (1.62)(5.0%)]. The weighted-
average cost of capital is 8.82% [(0.60)(6.5%) + (0.40)(12.3%)].
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Chapter 12
Valuation: Cash-Flow-Based Approaches
12-7
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in whole or in part.
d. Free Present Value Factor Present
Year Cash Flows at 8.82% Value
6 $52,300 0.91895 $ 48,061
7 $54,915 0.84447 46,374
8 $57,112 0.77602 44,320
9 $59,396 0.71312 42,357
10 $62,366 0.65532 40,870
After Year 10 $1,714,249a 0.65532 1,123,382
Total Present Value …………………………………………………………. $ 1,345,364
a$1,714,249 = $62,366 × [1.05/(0.0882 – 0.05)]
e. At a total purchase price of $1,345,364, debt will total $807,218 (0.6 ×
$1,345,364) and common equity will total $538,146 (0.4 × $1,345,364).
Annual interest expense on the debt will be $80,722 pretax and $52,469 after
tax (0.65 × $80,722). The projected free cash flows will be insufficient during
Year 6 to service the debt and slightly more than sufficient after Year 6. The
buyout firm might attempt to use zero coupon debt for a portion of the
borrowing, attempt to lower the purchase price, or make operational changes
to increase the free cash flows.
12.14 Applying Various Present Value Approaches to Valuation. (dollar amounts in
millions; allow for rounding)
Wedgewood Products:
a. The after-tax cost of debt is 6.0% [(1 – 0.40)(10.0%)]. The weighted-average
cost of capital is 10.8%[(0.40)(6.0%) + (0.60)(14.0%)].
b. Free Present Value Factor Present
Year Cash Flows at 10.8% Value
8 $ 2,100 0.90253 $ 1,895
9 $ 2,268 0.81456 1,847
10 $ 2,449 0.73516 1,800
11 $ 2,645 0.66350 1,755
12 $ 2,857 0.59883 1,711
After Year 12 $ 110,199a 0.59883 65,990
Total Present Value …………………………………………………………. $ 74,998
a
c. The $74,998 purchase price will be financed with $29,999 (0.40 × $74,998) of
debt and $44,999 (0.60 × $74,998) of common equity. The pretax interest cost
on the debt is $3,000 (0.10 × $29,999). The cash flows are as follows:
$110,199
0.08 0.108
1.08
$2,857 =
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Chapter 12
Valuation: Cash-Flow-Based Approaches
12-8
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in whole or in part.
Year 8 Year 9 Year 10 Year 11 Year 12
Free Cash Flows to All
Debt and Equity
Stakeholders ……………. $ 2,100 $ 2,268 $ 2,449 $ 2,645 2,857
Interest Cost ………………. (3,000) (3,000) (3,000) (3,000) (3,000)
Tax Savings from Interest
at 40% ……………………. 1,200 1,200 1,200 1,200 1,200
Free Cash Flows to Com-
mon Shareholders…….. $ 300 $ 468 $ 649 $ 845 $ 1,057
d. The present value of the free cash flows for common equity shareholders at
the 14.0% cost of equity capital is as follows:
Free Present Value Factor Present
Year Cash Flows at 14.0% Value
8 $300 0.87719 $ 263
9 $468 0.76947 360
10 $649 0.67497 438
11 $845 0.59208 500
12 $1,057 0.51937 549
Total Present Value for Year 8 to Year 12 …………………………. $ 2,110
Required Present Value from Continuing Value …………………. 42,889
Total Value of Equity………………………………………………………. $44,999
The undiscounted continuing free cash flow as of the end of Year 12 is
$82,579 ($42,889/0.51937). This undiscounted value implies a multiple on
Year 12 free cash flow of 78.13 ($82,579/$1,057). We can solve the
continuing value model, (1 + g)/(r – g), for a multiple of 78.13 and an r of
14.0% to obtain a growth rate, or value of g, of 12.5616%.
e. The growth in free cash flows to all debt and equity capital stakeholders is 8%
and in free cash flows to common equity shareholders is 12.5616%. Free cash
flows for common equity shareholders grow faster because free cash flows to
all debt and equity capital stakeholders grow over time but the interest cost net
of taxes remains the same. Thus, each dollar of growth in free cash flows to
all debt and equity capital stakeholders increases free cash flows to common
equity shareholders in an equal amount. Because free cash flows to common
equity shareholders are a smaller dollar amount than the amount of free cash
flows to all debt and equity capital stakeholders, the growth rate in free cash
flows to common equity shareholders is larger.
Chapter 12
Valuation: Cash-Flow-Based Approaches
12-9
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in whole or in part.
f. Present Value of Free Cash Flows to All Debt and Equity Capital Stakeholders
at Unlevered Cost of Equity:
Free Present Value Factor Present
Year Cash Flow at 11.33% Value
8 $2,100 0.89823 $1,886
9 $2,268 0.80682 1,830
10 $2,449 0.72471 1,775
11 $2,645 0.65096 1,722
12 $2,857 0.58471 1,670
After Year 12 $92,659a 0.58471 54,178
Total Present Value …………………………………………………………. $63,061
a
Present Value of Tax Savings from Interest Deductions
The annual tax savings from interest deductions is $1,200 (0.40 × $3,000).
Use the 10% cost of debt to discount these tax savings to a present value of
$12,000 ($1,200/0.10).
The total present value of $75,061 ($63,061 + $12,000) differs from the
value of $74,998 determined in Solution b due to the rounding of various
intermediate calculations.
12.15 Valuing the Equity of a Privately Held Firm.
Massachusetts Stove Company:
a.
Best-Case Likely Case Worst-Case No-Gas-Case
Cash Present Cash Present Cash Present Cash Present
Year Flow Value Flow Value Flow Value Flow Value
8 $73,967 $65,141 $47,034 $41,421 $3,027 $2,666 $162,455 $143,069
9 52,143 40,441 –3,120 –2,420 –84,800 –65,769 132,708 102,926
10 213,895 146,097 135,939 92,850 48,353 33,027 106,021 72,416
11 315,633 189,860 178,510 107,377 36,605 22,019 81,840 49,228
12 432,232 228,971 220,010 116,548 10,232 5,420 60,007 31,788
13 518,678 241,974 242,011 112,903 10,232 4,773 60,007 27,994
14 622,414 255,725 266,212 109,376 10,232 4,204 60,007 24,654
15 746,897 270,250 292,833 105,956 10,232 3,702 60,007 21,712
16 896,276 285,598 322,117 102,642 10,232 3,260 60,007 19,121
17 1,075,532 301,826 354,328 99,435 10,232 2,871 60,007 16,840
After 17 33,326,344a 9,352,254 4,351,397
b
1,221,117 75,513c 21,191 442,856
d
124,277
Total $11,378,137 $2,107,205 $37,364 $634,025
a$33,326,344 = $1,075,532 × [1.10/(0.1355 – 0.10)]
b$4,351,397 = $354,328 × [1.05/(0.1355 – 0.05)]
c$75,713 = $10,232 × (1/0.1355)
d$442,856 = $60,007 × (1/0.1355)
$92,659
0.08 0.1133
1.08
$2,857 =
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Chapter 12
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in whole or in part.
b. The most likely scenario provides a value for MSC that is more than three
times larger than if the firm does not add gas stoves. The wood-stove market
appears to be in decline, whereas the gas stove market is growing. If the
probability of the most likely scenario is approximately 30% or more, the
expected value of adding gas stoves exceeds the value of not adding gas
stoves, regardless of the probability of the best- and worst-case scenarios.
12.16 Free-Cash-Flows-Based Valuation. This is an extensive integrated problem
that illustrates the topics of Chapter 12 using The Coca-Cola Company. This
problem provides students with a parallel application of the techniques of Chapter
12 to a company that is very similar to PepsiCo. This problem should help
students understand the application of the cash-flows-based valuation techniques
of this chapter by seeing them applied in parallel with Coca-Cola. This problem
also will be used to demonstrate the valuation approaches in Chapters 13 and 14.
Note that these analyses have been prepared using FSAP. The FSAP file
containing these analyses is available for download by instructors (not students)
from the book’s website for instructors. Go to instructor’s resources page at
www.cengage.brain.com.
In this problem, you must estimate cost of equity capital for Coca-Cola and
use both free-cash-flows-based valuation approaches to estimate Coca-Cola’s
share value. The problem also requires a bit of sensitivity analysis and making a
recommendation about Coca-Cola stock based on this analysis. The market equity
beta for Coca-Cola at the end of 2012 is 0.75. Coca-Cola has 4,469 million shares
outstanding at the end of 2012, at which time the KO share price was $35.48.
Part I.—Computing Coca-Cola’s Share Value Using Free Cash Flows to
Common Equity Shareholders
a. Following the CAPM, Coca-Cola faces a required rate of return on equity
capital of 7.50% at the end of 2012. This rate is computed as follows:
E[RKO] = E[RF] +
β
KO × E[RM – RF]
= 3.0% + (0.75 × 6.0%)
= 7.50%
b., c., d., and e.
Exhibit 12.A presents the excerpts from FSAP for the valuation of Coca-Cola
based on projected free cash flows to common equity. The first rows of the
table present the computations for Coca-Cola’s projected free cash flows for
common equity shareholders for Years +1 through +5. The right-most column
contains the projected free cash flows for common equity shareholders in
Year +6 based on the projected Year +6 financial statements, assuming 3.0%
long-run growth. The remaining rows of the table include discounting the free
cash flows for Years +1 through +5 to present value, computing continuing
value, and computing share value. The share value estimate is $42.28. You
can also assign students the dividends valuation model in Chapter 11 or
demonstrate to them that the model will lead to an identical value estimate.