SOLUTIONS TO
EXERCISE AND CASES
For
FINANCIAL STATEMENT ANALYSIS AND SECURITY VALUATION
Stephen H. Penman
CHAPTER ONE
Introduction to Investing and Valuation
Exercises
Drill Exercises
E1.1. Calculating Enterprise Value
Enterprise Value = $1,800 million
E1.2. Calculating Value Per Share
Equity Value = $1,800
E1.3
Buy or Sell?
Value = $850 + $675
= $1,525 million
Value per share = $1,525/25 = $61
Market price
= $45
Therefore, BUY!
Applications
E1.4. Finding Information on the Internet: Dell Computer and General Motors
This is an exercise in discovery. The links on the book’s web site will help with the
search. Here is the link to yahoo finance:
http://finance.yahoo.com
E1.5. Enterprise Market Value: General Mills and Hewlett-Packard
(a)
General Mills
Market value of the equity =
Book value of total (short-term and long-term) debt
=
Enterprise value
Note three points:
(i)
Total market value of equity = Price per share × Shares outstanding.
(ii)
The book value of debt is typically assumed to equal its market value, but
financial statement footnotes give market value of debt to confirm this.
(iii)
The book value of equity is not a good indicator of its market value. The price-tobook ratio for the equity can be calculated from the numbers given:
$20,925/$6,215.8 = 3.37.
(b)
This question provokes the issue of whether debt held as assets is part of enterprise value
(a part of operations) or effectively a reduction of the net debt claim on the firm. The issue arises
in the financial statement analysis in Part II of the book: are debt assets part of operations or part
of financing activities? Debt is part of financing activities if it is held to absorb excess cash
rather than used as a business asset. The excess cash could be applied to buying back the firm’s
debt rather than buying the debt of others, so the net debt claim on enterprise value is what is
important. Put another way, HP is not in the business of trading debt, so the debt asset is not part
of enterprise operations. The calculation of enterprise value is as follows:
Market value of equity = $47 × 2,473 million shares = $116,231 million
Book value of net debt claims:
Short-term borrowing
Long-term debt
$ 711 million
7,688
Total debt
Debt assets
Enterprise value
$8,399 million
11,513
(3,114)
113,117 million
E1.6. Identifying Operating, Investing, and Financing Transactions
(a)
Financing
(b)
Operations
(c)
Operations; but advertising might be seen as investment in a brand-name asset
(d)
Financing
(e)
Financing
(f)
Operations
(g)
Investing. R& D is an expense in the income statement, so the student might be
inclined to classify it as an operating activity; but it is an investment.
(h)
Operations. But an observant student might point out that interest – that is a part
of financing activities – affects taxes. Chapter 9 shows how taxes are allocated
between operating and financing activities in this case.
(i)
Investing
(j)
Operations
CHAPTER TWO
Introduction to the Financial Statements
Exercises
Drill Exercises
E2.1. Applying Accounting Relations: Balance Sheet, Income Statement and Equity
Statement
a. Liabilities = $150 million
b. Net Income = $205 million
c. Ending equity = $32 million
As net income (in the income statement) is $30 million, $2 million was reported as “other
comprehensive income” in the equity statement.
d. Net payout = Dividends + Share repurchases – Share issues
As there were no share issues or repurchases, dividend = $12.
E2.2. Applying Accounting Relations: Cash Flow Statement
Change in cash = $195 million
E2.3. The Financial Statements for a Savings Account
a.
___________________________________________________________________________
BALANCE SHEET
Assets (cash)
$100
INCOME STATEMENT
Owners’ equity
STATEMENT OF CASH FLOWS
Cash from operations
$5
$100
Revenue
$5
Expenses
0
Earnings
$5
STATEMENT OF OWNERS’ EQUITY
Balance, end of Year 0
$100
Cash investment
0
Earnings, Year 1
Cash in financing activities:
5
Dividends (withdrawals), Year 1 (5)
Dividends
(5)
Change in cash
$0
Balance, end of Year 1
$100
b. As the $5 in cash is not withdrawn, cash in the account increases to $105, and owners’
equity increases to $105. Earnings are unchanged.
______________________________________________________________________
BALANCE SHEET
Assets (cash)
$105
INCOME STATEMENT
Owners’ equity
$105
STATEMENT OF CASH FLOWS
Revenue
$5
Expenses
0
Earnings
$5
STATEMENT OF OWNERS’ EQUITY
Cash from operations
$5
Balance, end of Year 0
Cash investment
0
Earnings, Year 1
Cash in financing activities:
$100
5
Dividends (withdrawals), Year 1 (0)
Dividends
(0)
Change in cash
$5
Balance, end of Year 1
$105
______________________________________________________________________
c. With the investment of cash flow from operations in a mutual fund, the financial
statements would be as follows:
_______________________________________________________________________
BALANCE SHEET
INCOME STATEMENT
Assets (cash)
$100
Revenue
$5
Mutual Fund
5
Expenses
0
Equity
$105
Total assets
$105
Total
$105
Earnings
STATEMENT OF CASH FLOWS
$5
STATEMENT OF OWNERS’ EQUITY
Cash from operations
$5
Balance, end of Year 0
Cash investment
(5)
Earnings, Year 1
Cash in financing activities:
$100
5
Dividends (withdrawals), Year 1 (0)
Dividends
(0)
Change in cash
$0
Balance, end of Year 1
$100
E2.4. Preparing an Income Statement and Statement of Shareholders’ Equity
Income statement:
Sales
Cost of good sold
Gross margin
Selling expenses
Research and development
Operating income
Income taxes
Net loss
$4,458
3,348
1,110
(1,230)
(450)
(570)
200
(370)
Note that research and developments expenses are expensed as incurred.
Equity statement:
Beginning equity, 2009
$3,270
Net loss
$(370)
Other comprehensive income
76
Share issues
Common dividends
(294)
680
(140)
Ending equity, 2009
$3,516
($76 is unrealized gain on securities)
Comprehensive income (a loss of $294 million) is given in the equity statement. Unrealized
gains and losses on securities on securities available for sale are treated as other comprehensive
income under GAAP.
Net payout = Dividends + share repurchases – share issues
= 140 + 0 – 680 = - 540
That is, there was a net cash flow from shareholders into the firm of $540 million.
Taxes are negative because income is negative (a loss). The firm has a tax loss that it can carry
forward.
E2.5. Classifying Accounting Items
a. Current asset
b. Net revenue in the income statement: a deduction from revenue
c. Net accounts receivable, a current asset: a deduction from gross receivables
d. An expense in the income statement. But R&D is usually not a loss to shareholders; it
is an investment in an asset.
e. An expense in the income statement, part of operating income (and rarely an
extraordinary item). If the restructuring charge is estimated, a liability is also
recorded, usually lumped with “other liabilities.”
f. Part of property, plan and equipment. As the lease is for the entire life of the asset, it
is a “capital lease.” Corresponding to the lease asset, a lease liability is recorded to
indicate the obligations under the lease.
g. In the income statement
h. Part of dirty-surplus income in other comprehensive income. The accounting would
be cleaner if these items were in the income statement.
i. A liability
j. Under GAAP, in the statement of owners equity. However from the shareholders’
point of view, preferred stock is a liability
k. Under GAAP, an expense. However from the shareholders’ point of view, preferred
dividends are an expense. Preferred dividends are deducted in calculating “net income
available to common” and for earnings in earnings per share.
l.
As an expense in the income statement.
E2.6. Violations of the Matching Principle
a. Expenditures on R&D are investments to generate future revenues from drugs, so are
assets whose historical costs ideally should be placed on the balance sheet and amortized
over time against revenues from selling the drugs. Expensing the expenditures
immediately results in mismatching: revenues from drugs developed in the past are
charged with costs associated with future revenues. However, the benefits of R&D are
uncertain. Accountants therefore apply the reliability criterion and do not recognize the
asset. Effectively GAAP treats R&D expenditures as a loss.
b. Advertising and promotion are costs incurred to generated future revenues. Thus, like
R&D, matching requires they be booked as an asset and amortized against the future
revenues they promote, but GAAP expenses them.
c. Film production costs are made to generate revenues in theaters. So they should be
matched against those revenues as the revenues are earned rather than expensed
immediately. In this way, the firm reports its ability to add value by producing films.
E2.7. Using Accounting Relations to Check Errors
Ending shareholders’ equity can be derived in two ways:
1. Shareholders’ equity = assets – liabilities
2. Shareholders’ equity = Beginning equity + comprehensive income – net dividends
So, if the two calculations do not agree, there is an error somewhere. First make the calculations
for comprehensive income and net dividends:
Comprehensive income = net income + other comprehensive income
= revenues – expenses + other comprehensive income
= 2,300 –1,750 – 90
= 460
Net dividend
= dividends + share repurchases – share issues
= 400 +150 –900
= - 350
Now back to the two calculations:
1. Shareholders’ equity = 4,340 – 1,380
= 2,960
2, Shareholders’ equity = 19,140 + 460 – (-350)
= 19,950
The two numbers do not agree. There is an error somewhere.
Applications
E2.8. Finding Financial Statement Information on the Internet
This is a self-guiding exercise. Students can take it further by downloading financial statements
into a spreadsheet. Go to the links of the book’s web site.
E2.9. Testing Accounting Relations: General Mills Inc.
This exercise tests some basic accounting relations.
(a)
Total liabilities = Total assets – stockholders’ equity = 12,826
(b)
Total Equity (end) = Total Equity (beginning) + Comprehensive
Income – Net Payout to Common Shareholders
6,216 = 5,319 +? – 782
? = 1,679
Net payout to common = cash dividends + stock purchases – share issues = 782
E2.10. Testing Accounting Relations: Genetech Inc.
(a)
Revenue
(b)
ebit
(c)
ebitda
= $4,621.2 million
= $1,136.8 million
=$1,490.0 million
Depreciation and amortization is reported as an add-back to net income to get cash flow from
operations in the cash flow statement.
Long-term assets = $5,980.6 million
Total Liabilities =
Short-term Liabilities
$2,621.2 million
=$1,243.3 million
(c) Change in cash and cash equivalents = Cash flow from operations – Cash used in investing
activities + Cash from financing activities
Change in cash and cash equivalents is given by the changes in the amount is the balance sheet
= $270.1 – 372.2 = -$102.1
So, -$102.1 = $1,195.8 - $451.6 + ?
So
?
= -$846.3 million
That is, there was a cash outflow of $846.3 million for financing activities.
E2.11. Find the Missing Number in the Equity Statement: Cisco Systems Inc.
Total Equity (end) = Total Equity (beginning) + Comprehensive
Income – Net Payout to Common Shareholders
a.
$32,304 = $31,931 + 6,526 -?
?
b.
= $6,153
Net payout to common = cash dividends + stock purchases – share issues
6,153 = 0 + ? – 2,869
= 9,022
E2.12. Find the Missing Numbers in Financial Statements: General Motors
a.
Total Equity (end) = Total Equity (beginning) + Comprehensive
Income – Net Payout to Common Shareholders
-56,990 = -37,094 + ? – 283
? = -19,613
(a loss)
b.
Comprehensive income = Net income + Other comprehensive income
-19,613 = -18,722 + ?
?
= - 891
c.
Net income = Revenue – expenses and losses
-18,722 = ? – 60,895
?
= 42,173
d.
June 30, 2008
Assets
136,046
Liabilities ? = 193,036
Equity
-56,990
December 31, 2007
148,883
? = 185,977
-37,094
E2.13. Mismatching at WorldCom
Capitalizing costs takes them out of the income statement, increasing earnings. But the
capitalized costs are then amortized against revenues in later periods, reducing earnings. The net
effect on income in any period is the amount of costs for that period less the amortization of
costs for previous periods. The following schedule calculates the net effect. The numbers in
parentheses are the amortizations, equal to the cost in prior periods dividend by 20.
1Q, 2001 cost: $780
2Q, 2001 cost:
605
3Q, 2001 cost:
760
4Q, 2001 cost:
920
1Q, 2002 cost:
790
Overstatement of earnings
1Q, 2001
2Q, 2001
3Q, 2001
4Q, 2001
1Q, 2002
$780
$ (39)
$ (39)
$ (39)
$ (39)
605
(30)
(30)
(30)
760
(38)
(38)
920
(46)
790
$780
$566
$691
$813
$637
The financial press at the time reported that earnings were overstated by the amount of the
expenditures that were capitalized. That is not quite correct.
E2.14. Calculating Stock Returns: Nike, Inc.
The stock return is the change in price plus the dividend received. So, Nike’s stock return for
fiscal year 2008 is 12.875/55 = 23.41%.
CHAPTER THREE
How Financial Statements are Used in Valuation
Exercises
Drill Exercises
E3.1. Calculating a Price from Comparables
Average of the two prices = $55 per share
E3.2. Stock Prices and Share Repurchases
Market price per share after repurchase = $1,800/90 = $20
E3.3 Unlevered (Enterprise) Multiples
Market price of equity = 80 × $7 = $560 million
Market value of debt
140
(assumes book value – market value)
Market value of enterprise
$700 million
Book value of shareholders’ equity = $250 - 140 = $110million
a. P/B = 560/110 = 5.09
b. Unlevered P/S = 700/560 = 1.25
c. Enterprise P/B = 700/250 = 2.8
E3.4. Identifying Firms with Similar Multiples
This is a self-guided exercise.
E3.5. Valuing Bonds
For this question, first calculate discount factors for each of five years ahead. You can also get them from present
value tables where the discount factor is given as 1/1.05t. At a 5% required return, the discount factors are:
Year Ahead (t)
1
2
3
4
5
a.
Discount factor (1.05t)
1.05
1.1025
1.1576
1.2155
1.2763
The only cash flow is the $1,000 at maturity
Present value (PV) of $1,000 five years hence = $1,000/1.2763
= $783.51
b.
This is easy. If the coupon rate is the required rate of return, the bond is worth its face value, $1,000. You
can show this by working the problem as in part b, but with an annual coupon of $50.
c.
The yearly cash flows and their present value are:
Year Ahead (t)
Discount factor (1.05t)
Cash Flow
1
1.05
2
1.1025
3
1.1576
4
1.2155
PV
40
40
40
40
38.10
36.28
34.55
32.91
5
1.2763
1, 040
814.86
Total Present Value
$956.70
(Your answers might differ by a couple of cents if you use discount factors to 5 or 6 decimal places.)
E3.6. Applying Present Value Calculations to Value a Building
This is a straight forward present value problem: the required return--the discount rate--is applied to
forecasted net cash receipts to convert the forecast to a valuation:
Present value of net cash receipts of 1.1 million for 5 years
at 12% (annuity factor is 3.6048)
$3.965 million
Present value of $12 million “terminal payoff” at end of 5
years (present value factor is 0.5674)
Value of building
6.809
$10.774
Applications
E3.7
The Method of Comparables: Dell, Inc.
First calculate the multiples for the comparable firms from the price and accounting numbers:
Hewlett-Packard Co.
Gateway Inc.
Sales
Earnings
Book
Value
Market
Value
$45,226
6,080
$ 624
(1,290)
$13,953
1,565
$32,963
1,944
HP:
Price/Sales = 0.73
P/E
= 52.8
P/B
= 2.4
Gateway:
Price/Sales = 0.32
P/E
(not applicable: negative earnings)
P/B
= 1.2
Now apply the multiples to Dell:
Average Multiples
for Comparable
Sales
Earnings
Book value
Average of valuations
* HP only
0.53
52.8*
1.8
Dell’s
Number
x
x
x
31,168
1,246
4,694
Dell’s
Valuation
=
=
=
$16,519 million
65,789
8,449
30,252
With 2,602 million shares outstanding, the estimated value per share
= $30,252/2,602 = $11.63
Difficulties:
-
P/E can’t be calculated for a loss firm
The “comparables” are not exactly like Dell
The calculation assumes the market prices for the “comps” are efficient
Not sure how to weight the three valuation based on sales, earnings and book values;
the valuations differ considerably, depending on the multiple used
E3.8. A Stab at Valuation Using Multiples: Biotech Firms
Multiples of the various accounting numbers for the five firms can be calculated and the average multiple applied to
Genentech’s corresponding accounting numbers. This yields prices for Genentech:
Comparison
Estimated
Firm
Mean
P/B
4.16
Genentech
Value (millions)
$5,610.9
E/P
.0245*
5,077.6
(P-B)/R&D
10.66
4,699.2
P/Revenue
6.05
4,809.0
Multiple
Mean over all values
5,049.2
*Excludes firms with losses.
E/P is used rather than P/E because a very high P/E due to very small earnings can affect the mean
considerably. The mean E/P also excludes the loss firms since Genentech did not have losses.
Research and development (R&D) expenditures are compared to price minus book value. As the R&D
asset is not on balance sheets, its missing value is in this difference. The average ratio of 10.66 is applied to
Genetech’s R&D expenditures to yield a valuation for its R&D asset of $3,350.4 million which, when added to the
book value of the other net assets, gives a valuation of $4,699.2 million for Genentech. This is clearly very rough.
The average of the values based on the mean multiples is $5,049.2 million. Genetech’s actual traded value
in April 1995 was $5,637.6 million.
E3.9. Pricing Multiples: General Mills, Inc.
P/E =
P S
1
× = 1.6 ×
= 16.84
S E
0.095
E3.10. Measuring Value Added
(a) Buying a stock:
Value of a share =
2
=
0.12
$
Price of a share
Value lost per share
16.67
19.00
$
2.33
(b) Value of the investments:
Present value of net cash flow of
$
3.890 million
$1M per year for five years (at 9%)
Initial costs
2.000
Value added
$
1.890 million
E3.11. Forecasting Prices in an Efficient Market: Weyerhaeuser Company
This tests whether you can forecast future prices, ex-dividend, using the no-arbitrage relationship between
prices at different points in time.
The T-Bill rate at the end of 1995 was 5.5%.
So the CAPM cost of capital = 5.5% + (1.0 × 6.0%) = 11.5% (using an 6% risk premium).
(a)
P1997 = ρ 2 P1995 = 1.1152 × 42 = 52.22
This is the cum-dividend price
(b)
P1997 = ρ 2 P1995 − ρd 1996 − d 1997
= (1.1152 x 42) - (1.115 × 1.60) - 1.60 = 48.83
E3.12. Valuation of Bonds and the Accounting for Bonds, Borrowing Costs, and Bond
Revaluations
The purpose of this exercise is to familiarize students with the accounting for bonds.
The cash flows and discount rates for each bond are as follows:
2007
2008
2009
40
2010
2011
2012
40
40
40
40
Coupon
1000
1.08
1.1664
1.2597
1.3605
Redempt.
1.4693 Discount rate
(a) Present value of cash flows = value of bond = $840.31.
(b) (1)
(2)
Borrowing cost = $840.31 × 8% = $67.22 per bond
This is the way accountants calculate interest (the effective interest method): $67.22 per bond will be
recorded as interest expense. This will be made up of the coupon plus an amortization of the bond discount. The
amortization is $67.22 - $40.00 = $27.22. This accrual accounting records the effective interest of $67.22, not the
cash flow.
(c) (1)
As the firm issued the bonds at 8%, it is still borrowing at 8%. Of course, if the firm issued new debt at the
end of 2009, its borrowing cost would be 6%.
(2) Interest expense for 2009 will be $69.40 per bond. This is the book value of the bond at the end of 2008
times 8%: $867.53 × 8% = $69.40. The book value of the bond at the end of 2008 is $840.31 + $27.22 =
$867.53, that is, the book value at the beginning of 2008 plus the 2008 amortization.
(d)
The future cash flows at the end of 2009 are:
2010
2011
40
1.08
1.06
2012
40
40
1.1664
1.1236
1.2597
1.1910
Coupon
1000
Redemption
Original Discount rate
New discount rate
Present value of remaining cash flows at 8% discount rate = $896.92
Present value of remaining cash flows at 6% discount rate = 946.55
Price appreciation
$ 49.63
(1) The bonds are marked to market so they are carried at $946.55 at the end of 2009. Note that bonds are marked
to market only if they are assets, not if they are liabilities. Debtor Corporation’s carrying amount would not be
affected by the change in yield.
(2) The interest income in the income statement will be as before, $69.40 per bond. However, an unrealized gain of
$49.63 per bond will appear in other comprehensive income to reflect the markup. (Unrealized gains and losses on
securities go to other comprehensive income rather than the income statement. See Accounting Clinic III.)
Note that, if Debtor Corporation had sold the bonds at the end of 2009 (for $946.55 each), it would have realized
a loss of $49.63 per bond which would be reported with extraordinary items in the income statement. If it
refinanced at 6% for the last three years, it would lower borrowing costs that, in present value terms, would equal
the loss.
E3.13. Share Issues and Market Prices: Is Value Generated or Lost By Share Issues?
This exercise tests understanding of a conceptual issue: do share issues affect shareholder value per share? The
understanding is that issuing shares at market price does not affect the wealth of the existing shareholders if the
share market is efficient: New shareholders are paying the “fair” price for their share. However, if the shares are
issued at less than market price, the old shareholders lose value.
(a)
Shares outstanding after share issue = 188 million
Price per share after issue
= $55
Like a share repurchase, a share issue does not affect per share value as long as the shares are issued at the
market price. Old shareholders can’t be damaged or gain a benefit from the issue. Of course, if the market
believes that the issue indicates how insiders view the value of the firm, the price may change. But this is
an informational effect, not a result of the issue. Old shareholders would benefit if the market were
inefficient, however. If shares are issued when they are overvalued in the market, the new shareholders pay
too much and the old shareholders gain.
The idea that share issues don't generate value (if at market prices) is the same idea that dividends don't
generate value. Share issues are just dividends in reverse.
(b)
Shares outstanding after exercise
200 million
Price per share
$60.10
The (old) shareholders lost $1.90 per share through the issue: issue of shares at less than market causes
“dilution” of shareholder value.
E3.14. Stock Repurchases and Value: Dell, Inc.
This exercise makes the same conceptual point as the previous exercise on stock issues: stock repurchases
(which are reverse stock issues) don't create value, if the market price is at fair value.
There is no effect on the price per share at the date of repurchase. The total value of the company (price
per share x shares outstanding) would drop by $335 million, the amount of cash paid out. But the number of shares
outstanding would also drop by 7.5 million leaving the price per share unchanged.
Price per share before repurchase
=
$4,004M/179M
= $22.37
Total value of the equity before repurchase =
$22.37 × 2,239M
= $50,086M
Total value of the equity after repurchase
=
$50,086M − $4,004M = $46,082M
Shares outstanding after repurchase
=
2,239M − 179M
Price per share after repurchase
= $46,082/2,060
= 2,060M
= $22.37
Note: the announcement of a share repurchase might affect the price per share if the market inferred that the
management thinks the shares are underpriced. That is, the repurchase might convey information. But the actual
repurchase itself will not affect the per-share price. If the shares are not priced efficiently in the market, value will
be gained (or lost) for shareholders who do not participate in the repurchase.
E3.15. Dividends, Stock Returns, and Expected Payoffs: Weyerhaeuser Company
If no dividends are to be paid, the expected 1997 price would be higher by the amount of the terminal value
of the dividends.
Terminal value in 1997 of 1996 dividend
=
Terminal value in 1997 of 1997 dividend
=
$1.60 × 1.115
=
$1.784
1.600
$3.384
Ex-dividend price, 1997
$48.83
Cum-dividend price
$52.214
Stock repurchases have no effect on per-share price so the expected price would be the cum-dividend price
of $52.22.
This conclusion ignores any “signaling effect” from the announcement of the stock dividend and any
differences in tax effects between capital gains at dividends.
E3.16. Betas, the Market Risk Premium, and the Equity Cost of Capital: Sun Microsystems
a)
The CAPM equity cost of capital is given by
Cost of capital = Risk-free rate + (Beta × Market risk premium)
= 4.0% + (1.38 × ?)
Market Risk
Cost of
Premium
Capital
4.5%
6.0%
7.5%
10.21%
12.28%
14.35%
9.0%
16.42%
b)
Market Risk
Beta
Cost of Capital
1.25
1.55
1.25
1.55
1.25
1.55
1.25
1.55
9.63%
10.98%
11.5%
13.30%
13.38%
15.63%
15.25%
17.95%
Premium
4.5%
6.0%
7.5%
9.0%
c)
Lowest cost of capital:
9.63%
Highest cost of capital:
17.95%
Forecasted price in June 2000 = $0.54 × 20 = $10.80
Present value at 9.63% discount rate (no dividends) = $10.80 = $9.85
1.0963
Present value at 17.95% discount rate (no dividends) = $10.80 = $9.16
1.1795
E3.18. Implying the Market Risk Premium: Procter & Gamble
The CAPM cost of capital is given by
Cost of Capital = Risk-free rate + (Beta × Market risk premium)
7.9% = 4.0% + (0.65 × ?)
? = 6.0%
CHAPTER FOUR
Cash Accounting, Accrual Accounting, and Discounted Cash Flow Valuation
Exercises
Drill Exercises
E4.1. A Discounted Cash Flow Valuation
2009
Cash flow from operations
Cash investment
Free cash flow
Discount rate (1.10)t
PV of cash flows
Total PV to 2012
Continuing value*
PV of CV
a. Enterprise value
Net debt
b. Value of equity
* Continuing value =
2010
$1,450
$1,020
$ 430
2011
1,576
1,124
452
1.10
2012
1,718
1,200
518
1.21
1.331
391
374
389
$1,154
8,979
6,746
$7,900 million
759
$7,141 million
518 × 1.04
= 8,989
1.10 − 1.04
E4.2. A Simple DCF Valuation
= $8,600 million
E4.3. Valuation with Negative Free Cash Flows
Calculate free cash flow from the forecasts of cash flow from operations and cash investments. Your will see that
free cash flow is negative in all years except 2009:
2009
2010
2011
2012
Cash flow from operations
730
932
1,234
1,592
Cash investments
673
1,023
1,352
1,745
Free cash flow
57
( 91)
( 118)
( 153)
If you calculate the present value of these free cash flows (with any discount rate), you’ll get a negative price. Prices
can’t be negative (with limited liability). The continuing value must be greater than 100% of the price, but we have
no way to calculate it. One would have to extend the forecast horizon.
E4.4. Calculate Free Cash Flow from a Cash Flow Statement
Cash flow from operations reported
Interest payments
$1,342
Interest receipts
876
Net interest payments
Tax at 35%
Cash flow from operations
Cash investments reported
$6,417
Purchase of short-term investments (4,761)
Sale of short-term investments
547
Free Cash Flow
$5,270
466
163
303
5,573
2,203
3,370
Applications
E4.5. Calculating Cash Flow from Operations and Cash Investment for Coca-Cola
Cash from operations = $7,258 million
Coke’s free cash flow was = $190.
E4.6. Identifying Accruals for Coca-Cola
Accruals are the difference between net income and cash flow from operations:
Accruals
= -$1,169 million
That is, accruals were negative, yielding net income below cash flow from operations.
E4.7. Converting Forecasts of Free Cash Flow to a Valuation: Coco-Cola Company
Unlike the case in Exercise E 4.3, the free cash flows here are positive:
________________________________________________________________________
2004
2005
2006
Cash flow from operations
Cash investments
Free cash flow
5,929
618
5,311
6,421
1,496
4,925
5,969
2,258
3,711
2007
7,258
7,068
190
However, although positive, the free cash flow are declining over the four years. If cash flows from operations and
cash investments were declining at about the same rate, we might conclude that the firm indeed was in a state of
decline: declining cash flows from the business lead to declining investments. However, cash flows from operations
are increasing and cash investment is increasing at a faster rate: Coke is investing heavily. While free cash flow is
declining over these years, one would thus expect it to increase in future years as cash from the rising investment
here comes in. These cash flow are not a good indication of future free cash flows (and nor is the $190 million of
free cash flow in 2007 a good base to calculate a continuing value.)
The exercise is a good example of why free cash flow does not work, in principle: Investment (which is made to
generate cash flows actually decreases free cash flow, so rising investment relative to cash flow from operations
(lower free cash flow) typically means higher free cash flow later.
E4.8. Cash Flow and Earnings: Kimberly-Clark Corporation
Part a.
Adjust cash flow from operations for after-tax net interest payments and cash investment for net investments in
interest-bearing assets:
Cash flow from operations
Free cash flow
$3,071.0
$2,572.0
Note: As cash interest receipts are not reported (as is usual), use interest income from the income statement.
Part b.
Accruals = $(1,169.4)
E4.9. A Discounted Cash Flow Valuation: General Mills, Inc.
a. The exercise involves calculating free cash flows, discounting them to present value, then adding the present
value of a continuing value. For part (a) of the question, the continuing value has no growth:
2005
2006
Cash flow from operations
2,014
2,057
Cash investment in operations
300
380
Free cash flow (FCF)
1,714
1,677
Discount rate
1.09
1.1881
Present value of FCF
1,572
1,411
Total of PV to 2009
5,419
Continuing value (CV)
PV of CV
12,885
Enterprise value
18,304
Net debt
6,192
Equity value
12,112
2007
2,095
442
1,653
1.2950
1,276
2008
2,107
470
1,637
1.4116
1,160
18,189
Value per share on 369 million shares = $32.82
1,637
= 18,189
0.09
18,189
PV of CV =
= 12,885
1.4116
CV (no growth) =
b. With growth of 3% after 2009, the continuing value is:
CV =
1,637 × 1.03
= $28,102
1.09 − 1.03
The present value of the continuing value is $28,102/1.4116 = $19,908.
Do the valuation is as follows:
Total of PV to 2009
Continuing value (CV)
PV of CV
Enterprise value
Net debt
Equity value
5,419
28,102
19,908
25,327
6,192
19,135
Value per share on 369 million shares = $51.86.
E4.10. Free Cash Flow for General Motors
2009
Appropriate free cash flow calculation:
2005
Cash flow from operations reported
Net interest
Tax at 36%
Cash investment reported
Net investment in debt securities
$3,676
$4,059
1,461
$(179)
(1,618)
2,589
$6,274
(1,797)
Free cash flow
2004
$12,108
$3,010
1,084
1,926
$14,034
(24,209)
( 592)
$4,477
(24,801)
$(10,767)
Mistakes by analyst:
1.
Includes net sales of marketable (debt) securities as cash investment in operations rather than sales of
these securities to satisfy a cash shortfall. In both years, there is more sales (liquidations) of these
securities than purchases, reducing reported cash investment.
2.
Treats the liquidation of investments in companies (of $1,367 million in 2005) as good news because it
increases free cash flow. Selling off investments increases current cash flow but reduces future free
cash flows.
3.
Treats increased sales of finance receivables (of $27,802 million in 2005) as increasing free cash flow
(and thus as good news). Sales of finance receivables merely speed the receipt of cash. Booking the
receivables from customers is what adds value.
4.
Treats the decrease in bookings of finance receivables (from a $31,731 million increase in 2004 to a
$
15,843 million increase in 2005) as good news.
E4.11. Cash Flows for Wal-Mart Stores
a.
Wal-Mart is an expanding company with opportunities to invest in new stores throughout the world. While
it generates considerable cash flow from operations, cash investments routinely exceed cash from
operations. So free cash flow is negative. This is a firm like General Electric in Exhibit 4.2. DCF analysis
will not work for this firm.
b.
The difference between earnings and cash from operations is due net interest (after-tax) and accruals.
The difference between earnings and free cash flows is due to net interest (after
tax), accruals and investments in operations.
c.
DCF will not work. Negative free cash flows yield negative values.
E4.12. Accruals and Investments for PepsiCo
The question in this exercise tests accounting relation 4.12:
Accruals = -$ 842 million
The second question modifies the investing section of the cash flow statement according to equation 4.11:
Cash investments reported
Purchases of investments
$1,007
Sales of investments
38
Cash investment in operations
$2,330 million
969
$1,361 million
E4.13. Accrual Accounting Relations
(a)
Cash = $373 million
(b)
Change in payable = $45 million
(c)
PPE = $181 million
E4.14. An Examination of Revenues: Microsoft
Cash revenue = $35.430 billion
CHAPTER FIVE
Accrual Accounting and Valuation: Pricing Book Values
Exercises
Drill Exercises
E5.1. Calculating Return on Common Equity and Residual Earnings
Set up the pro forma as follows:
2009 2010
Eps
Dps
Bps
20.00
ROCE
RE (10% charge)
3.00
0.25
22.75
15.00%
1.00
2011
2012
3.60
0.25
26.10
15.83%
1.325
4.10
0.30
29.90
15.71%
1.49
a.
The answer to the question is in the last two lines of the pro forma
b.
As forecasted residual earnings are positive, the shares of this firm are worth a premium over book value.
E5.2. ROCE and Valuation
As expected ROCE is equal to the required return, expected residual earnings are zero. So the shares are worth their
book value per share. Book value per share = $3,200/500 = $6.40.
E5.3. A Residual Earnings Valuation
This question asks you to convert a pro forma to a valuation using residual earnings methods. First complete the pro
forma by forecasting book values from earnings and dividends. Then calculate residual earnings from the completed
pro forma and value the firm.
2010E
Earnings
Dividends
Book value
388.0
a.
2012E
2013E
2014E
629.0
349.0
5,505.0
660.4
367.0
5,780.0
385.4
12.4%
111.7
12.0%
99.7
12.0%
104.7
12.0%
109.9
8.9%
-10.7%
5.0%
5.0%
5.0%
5.0%
5.0%
570.0
115.0
4,583.0
ROCE
Residual earnings
(10%)
Growth in RE
Growth in Book value
Discount factor 1.110
PV of RE
2011E
599.0
160.0
4,993.0
9.0%
-43.0
5,243.0
1.210
-39.1
1.331
92.3
1.464
1.611
74.9
Forecasted book values, ROCE, and residual earnings are given in the completed pro forma above. Book
value each year is the prior book value plus earnings and minus dividends for the year. So, for 2011 for
example,
Book value = 4583 +570 –160 = 4,993.
The starting book value (in 2009) is 4,310. Residual earnings for each year is earnings charged with the
required return in book value. So, for 2011,
RE is 570 – (0.10 × 4,583) = 111.7.
b.
Forecasted growth rates in book value and residual earnings are given above.
c.
The growth rate in residual earnings is 5% after 2012. Assuming this growth rate will continue into the
future, the valuation is a Case 3 valuation with the continuing value calculated at the end of 2012:
Book value, 2006
Total present value of RE to 2012 (from last line above)
Continuing value (CV), 2012:
4,310.0
128.1
104.7
= 2094.0
1.10 − 1.05
Present value of CV: 2094/1.331
1,573.3
Value of the equity, 2009
6,011.4
Per share value (on 1,380 million shares)
d.
4.36
The premium is 6,011.4 – 4,310 = 1,701.4, or 1.23 on a per-share basis.
The P/B ratio is 6,011.4/4,310 = 1.39.
E5.4. Residual Earnings Valuation and Target Prices (Easy)
This problem applies the residual earnings model and its dividend discount equivalent.
Develop the pro forma as follows:
2009
2010
3.90
1.00
24.90
2011
3.70
1.00
27.60
RE (0.12)
1.26
.71
Discount rate
1.12
1.2544
1.125
.57
Eps
Dps
Bps
(a)
22.00
PV
(b)
Total PV
1.70
Value
23.70
(c)
2012
3.31
1.00
29.91
0
2013
3.59
1.00
32.50
0
2014
3.90
1.00
35.40
0
As residual earnings are expected to be zero after 2014, the equity is expected to be worth its book
value of $35.40.
(d)
As aside:
The expected premium at 2014 is zero because subsequent residual income is expected to be zero.
Note that the dividend discount formula can be applied because we now have a basis for calculating its terminal
value. The terminal value is the expected terminal price, and this can be calculated at the end of 2011 because, at
this point, expected price equals book value.
T
V0E = ∑ ρ − t d t + TV T / ρ T
t =1
The TV2011 is given by the expected 2011 book value:
TV2011 = 27.60
So the calculation goes as follows:
2009
2010
2011
Dps
1.00
1.00
PV
Total PV of divs. 1.69
TV
PV of TV
Value
.89
.80
27.60
22.00
23.69
E5.5. Residual Earnings Valuation and Return on Common Equity
(a)
Set the current year as Year 0.
Earnings, Year 1 = 15.60 × 0.15 = 2.34
Residual earnings, Year 1 = 2.34 – (0.10 × 15.60)
= 0.78
This RE is a perpetuity, so
V0 = B 0 +
RE 0
0.10
= 15.60 +
0.78
= 23.40
0.10
P B = 23.40 15.60 = 1.5
(b)
No effect:
future payout does not affect current price (unless you have a tax story) and future
dividends don’t affect current book value.
P/B is still 1.5
E5.6.
Using Accounting-Based Techniques to Measure Value Added for a Project
(a)
Time line:
0
Depreciation
Book value
150
Earnings (15%)
RE (0.12)
PV of RE
Total PV of RE
Value of Project
1
30
120
22.5
4.5
4.02
2
30
90
18
3.6
2.87
3
30
60
13.5
2.7
1.92
4
30
30
9
1.8
1.14
5
30
0
4.5
0.9
0.51
10.47
160.47
The investment added $10.47 million over the cost.
(b)
Time line
0
Earnings
Depreciation
Cash from operations
t
PV of cash flow (1.12t)
Total PV of cash flow
Cost
NPV
The NPV is the value added.
160.47
150.00
10.47
1
2
3
4
5
22.5
30.0
52.5
18.0
30.0
48.0
13.5
30.0
43.5
9.0
30.0
39.0
4.5
30.0
34.5
46.88
38.27
30.96
24.79
19.58
E5.7. Using Accounting-Based Techniques to Measure Value Added for a Going Concern
(a)
Time line:
0
1
2
3
4
5
6
7
150
150
30
270
150
60
360
150
90
420
150
120
450
150
150
450
150
150
450
150
150
450
Earnings (15%)
52.5
30.0
22.5
100.5
60.0
40.5
144.0
90.0
54.0
183.0
120.0
63.0
217.5
150.0
67.5
217.5
150.0
67.5
217.5
150.0
67.5
RE (0.12)
4.5
8.1
10.8
12.6
13.5
13.5
13.5
PV of RE
4.0
6.5
7.7
8.0
Investment
1
Depreciation
Book value2
Revenue
Depreciation
Total of PV of RE
26.2
Continuing value3
112.5
PV of CV
71.5
Value
247.7
150
97.7
Lost
Value added
1.
Depreciation is $30 million per year for each project in place
2.
Book value (t) = Book value (t-1) + Investment (t) – Depreciation (t)
3.
CV =
13.5
= 112.5
0.12
The value of the firm is $247.7 million. The continuing value is based on a forecast of residual earning of 13.5 in
year 5 continuing perpetually with no growth. This is a Case 2 valuation.
(b)
The value added is $97.7 million
(c) The value added is greater than 15% of the initial investment because there is growth in investment: value is
driven by the rate of return of 15% (relative to a cost of capital of 12%) but also by growth.
E5.8. Creating Earnings and Valuing Created Earnings
a.
Earnings = Revenues – Expenses
= $440 - $360 = $80
Earnings in the text example were $40. Clearly earnings have been created,
by expensing $40 of the investment in the prior period and thus reducing
Year 1expenses by $40.
b.
ROCE = $80/$360 = 22.22%
Residual earnings = $80 – (0.10 × 360) = 44
c.
Value = $360 +
$44
= $400
1.10
Even though earnings have been created, the calculated value is the same as that
in the text (before earnings were created).
E5.9. Reverse Engineering
With a P/B ratio of 2.0 and a price of $26, the book value per share is $13. Thus,
Residual earnings (2010) = $2.60 – (0.10 × 13.0) = $1.30
Reverse engineering solves for g in the following model:
$26 = $13 +
1.30
1.10 − g
The solution is g = 1.0. That is, the growth rate is zero: The market expects residual earnings to continue at $1.30
per share after 2010.
Applications
E5.10. Residual Earnings Valuation: Black Hills Corp
The pro forma for the exercise is as follows:
1999
Eps
Dps
Forecast Year
____________________________________
2000
2001
2002
2003 2004
2.39
3.45
1.06
1.12
2.28
1.16
2.00
1.22
1.71
1.24
Bps
9.96
ROCE
RE (11% charge)
Discount rate (1.11)t
Present value of RE
Total present value of RE to 2004
3.78
Continuing value (CV)
Present value of CV
Value per share
13.74
a.
b.
11.29
13.62
14.74
24.0% 30.6% 16.7%
1.294 2.208
0.782
0.379
1.110 1.232 1.368
1.166 1.792 0.572
15.52
15.99
13.6% 11.0%
0.003
1.518
1.685
0.250
0.002
0.0
0.00
ROCE and residual earnings are in the pro forma
If ROCE is to continue at 11% after 2004, then residual earnings are expected to be zero. The continuing
value is zero. The value is $13.74 per share – a Case 1 valuation.
As the CV = 0, the target price is equal to forecasted bps of $15.99 at 2004.
c.
E5.11. Valuing Dell, Inc.
a. The pro forma for 2009 and 2010 and the value it implies is as follows:
2008
EPS
DPS
BPS
RE (10%)
Discount rate
PV of RE
Total PV to 2010
Continuing value
2009
1.47
0.00
3.283
1.289
1.10
1.172
1.813
2010
1.77
0.00
5.053
1.442
1.21
1.192
2.364
1.442 × 1.04
1.10 − 1.04
24.99
PV of continuing value
20.66
Value per share
24.84
Note: BPS at eh end of fiscal-year 2008 = $3,735/2,060 shares = $1.813.
b.
The growth rate is calculated by reverse engineering:
P2008 = $20.50 = 1.813 +
1.289 1.442
1.442 × g
+
+
1.10
1.21 1.21(1.10 − g )
The solution for g = 1.025 (or a 2.5% growth rate)
E5.12 Sellers Wants to But
a.
The Pro Forma:
2006
Eps
Dps
Bps
12.67
2007
2.98
0.60
15.05
2008
3.26
0.70
17.61
Residual earnings (10%)
1.713
1.755
The current book value per share = Book value/Shares outstanding
= $26,909/2,124
= $12.67
Reverse engineer Seller’s price:
$50 = 12.67 +
1.713
1.755
+
1.10
1.10 x (1.10 - g)
g = 1.0555 (a 5.55 % growth rate)
A.
Getting to eps growth rates for 2009 and 2010:
RE growing at 5.55%
Prior Bps
Prior Bps x 0.10
Eps (1) + (2)
Eps growth rate
Dps (at 2008 payout ratio)
Bps
Prior Bps x 0.10
Eps (1) + (3)
Eps growth rate
2009
1.852
17.61
2010
1.955
1.761
(2)
3.613
0.776
10.83%
%
20.447
2.045
10.71%
%
= $23.62
The first building block is the book value
Market price
The three components are diagramed as follows:
(3)
4.00
E5.13. Building Blocks for a Valuation: General Electric Co.
b.
(1)
=
$10.47
36.00
Book
Value
Value from
Short-term
Forecasts
Value from
Growth
c. Reverse engineer the model:
= $36.00
The solution is g = 1.0698, or approximately a 7% growth rate.
d. For 2007:
Earnings2007 = (12.30 × 0.10) + 0.886 = $2.116 per share
EPS growth rate for 2007 = 2.116/1.96, which is a 7.96% growth rate
For 2008:
Earnings2008 = (13.358 × 0.10) + 0.948 = $2.284 per share
Earnings growth rate for 2008 = 2.284/2.2116, which is a 7.94% growth rate
E5.14. Reverse Engineering Growth Forecasts for the S&P 500 Index
(a)
With a P/B ratio is 2.5, investors are paying $2.50 for every dollar of book value in the S&P 500 companies. With
an ROCE of 18%, the current residual earnings on a dollar of book value is:
RE0 = (0.18 – 0.10) × 1.0
= 0.08
That is, 8 cents per dollar of book value. The value of an asset (with a constant growth rate is mind) is calculated as:
V0 = B0 +
RE 0 × g
ρ−g
(One always capitalizes the one-year-ahead amount, which is the current residual earnings, RE0, growing one year at
10%.) So, for every dollar of book value worth $2.50,
2.50 = 1.0 +
0.08 × g
1.10 − g
Solving for g,
g = 1.044 (a 4.4% growth rate)
A good benchmark growth rate for the market as a whole is the GDP growth rate. This has historically been an
average of about 4.0%. So, if history is an indication of the future, a 4.4 % implied growth rate suggests that the
S&P 500 stocks, as a portfolio, are a little overpriced.
What does a growth rate of 4.4% for residual earnings mean? If the S&P 500 firms can maintain an ROCE of
18%, then investment in net assets must grow by 4.4%. Alternatively, if ROCE were to improve, a growth in
residual earnings of 4.4% can be maintained with a lower growth rate. Is a 4.4% growth rate for residual earnings
reasonable? What is the prospect for ROCE for the market as a whole? Is the market appropriately priced?
(Analysis in Part II of the book will help answer these questions.)
(b)
See the last paragraph. With a constant ROCE, the growth in residual earnings is determined by the growth in net
assets (book value). Remember, residual earnings is driven by two factors:
1.
Profitability of net assets: ROCE
2.
Growth in net assets
E5.15. The Expected Return for the S&P 500
a. Book value on January 1, 2008
Forward ROCE for 2008
= 564.62
= 12.85%
a.
The reverse engineering problem:
= 1,468
The following formula solves for the expected return (see equation 5.7 in Ch. 5):
= 7.403%
b. Required return = 4% + 5% = 9%
Do not buy, for the expected return is less than the required return.
c. Although the level of the index is not given, one can still work the problem based on the
price-to-book of 5.4. For every $1 of book, the price is 5.4, so the reverse engineering
problem can be set up as:
? = 7.515%
The following “weighted average” formula solves for the expected return (see equation 5.7a
in Ch. 5):
Expected return = 7.5%
If the required return is 9%, this expected return indicates that the S&P 500 stocks are
overvalued. All the more so when one appreciates that a 23% ROCE used as an input is quite
a bit above the historical ROCE of 18%. A 23% ROCE means a high residual earnings base
to apply a 4% growth rate to.
E5.16. Valuing Dividends or Return on Equity: General Motors Corp.
a.
P/B = 0.57;
ROCE = 1.41%
b.
Yes; the required return is not stated, but any reasonable return is far greater than 1.41 percent. As GM is
expected to earn an ROCE far below its required return, it should have a P/B well below 1.0.
c.
The analyst makes a mistake in focusing on the dividend (yield). An unprofitable firm will drop its
dividend – as GM has done in the past in bad times – and GM does not look profitable. The dividend they
have been paying is not a good indicator of value. A firm can pay a high dividend in the short run, but if
fundamentals give a different message, follow the fundamentals. The dividend yield (dividend/price) is
high because price is low, because of poor prospects.
E5.17. Residual Earnings Valuation and Accounting Methods
a.
Inventory in the balance sheet is carried at historical cost but is written down to market value if market
value is less than cost. The carrying amount of inventory on the balance sheet becomes cost of good sold
when the inventory is sold. So, a write-down of $114 million in 2009 means cost of goods sold in 2010 will
be $114 million lower, and (assuming no change in the forecasts of sales) earnings will be $114 million
higher, that is, $502 million. The book value at the end of 2009 is $114 million lower, or $4,196 million.
So,
ROCE = 11.96
This is an increase over the 9% (388/4,310) before the impairment.
b.
Refer to the answer to Exercise 5.3. With earnings of $502 million forecasted for 2010, residual earnings is
now 502 – (0.10 × 4,196) = $82.4 million. The present value of this RE is $82.4/1.10 = $74.9 million. As
the present value of RE for 2010 prior to the impairment was $-39.1 million, the change in the PV of RE in
the valuation is $114 million. As this is the change in the 2009 book, value the valuation remains
unchanged.
The full pro forma under the changed accounting is below:
2010E
Earnings
Dividends
Book value
502.0
570.0
115.0
4,583.0
ROCE
Residual earnings
Growth in RE
Growth in Book value
Discount factor 1.110
PV of RE
2011E
599.0
160.0
4,993.0
11.96% 12.4%
82.4
5,243.0
2013E
2014E
629.0
349.0
5,505.0
660.4
367.0
5,780.0
385.4
12.0%
111.7
12.0%
99.7
-10.7%
5.0%
8.9%
1.210
74.9
2012E
1.331
92.3
12.0%
104.7
5.0%
5.0%
1.464
109.9
5.0%
5.0%
1.611
74.9
Note that the pro forma is unchanged after 2010 as 2010 book values are the same as before.
The valuation now runs as follows:
Book value, 2009
Total present value of RE to 2012 (from last line above)
Continuing value (CV), 2012:
4,196.0
242.1
104.7
= 2094
1.10 − 1.05
Present value of CV: 2094/1.331
1,573.3
Value of the equity, 2009
6,011.4
Per share value (on 1,380 million shares)
4.36
This is the same valuation as before.
c.
The taxes will affect 2010 earnings and 2009 book values by the after-tax amount of the impairment:
After-tax effect on 2010 earnings = $74.1
After-tax effect on book value in 2009 = $74.1
Accordingly,
ROCE, 2010 = 10.91%
As both 2010 earnings and 2009 book values are affected by the same amount, the value of the equity is unchanged
(following the same calculation as in b).
E5.17. Impairment of Goodwill
(a) As the asset is at fair value (the acquisition price) on the balance sheet, it is expected to earn at the required
return on book value: Residual earnings is projected to be zero. (Fair value in an acquisition always prices
the acquisition to earn at the required rate of return.)
(b) The book value must be marked down to fair market value under FASB Statement No. 142. The book value
at the end of 2009 before the write down, is 301 + 79 = 380 (the depreciated amount of the tangible assets
plus the good will).
Forecasted earnings for 2010 on this book value (at the forecasted ROCE of 9%) is
380 x 0.09 = 34.2
For a 10% required return, the book value that yields residual earnings in 2010 equal
Accordingly, the amount of impairment = 380 – 342 = 38.
CHAPTER SIX
Accrual Accounting and Valuation: Pricing Earnings
Drill Exercises
E6.1 Forecasting Earnings Growth and Abnormal Earnings Growth
The calculations are as follows:
2009
AEG
2010
2011
0.325
0.165
20.0%
20.83%
13.89%
14.58%
(a)
Ex-div growth rate (from line 1)
Cum-div growth rate (from line 2)
- 3.625/3.00 for 2010
- 4.125/3.60 for 2011
(b) AEG is in pro forma above
(c) Normal forward P/E = 1/0.10 = 10.
(d) As AEG is forecasted to be greater than zero, then one would expect the forward
P/E to be greater than 10. Equivalently, as the cum-dividend earnings growth rate
is expected to be greater than the required return of 10%, the P/E should be
greater than the normal P/E
E6.2 P/E Ratios for a Savings Account
a. = $257
b. = 26
(This is the normal P/E for a 4% required return.)
= 25
(This is the normal forward P/E for a required return of 4%.)
E6.3. Valuation From Forecasting Abnormal Earnings Growth
This exercise complements Exercise 5.3 in Chapter 5, using the same forecasts. The
question asks you to convert a pro forma to a valuation using abnormal earnings growth
methods. First complete the pro forma by forecasting cum-dividend earnings and normal
earnings. Then calculate abnormal earnings growth and value the firm.
2010E
2011E
2012E
2013
2014
Earnings
388.0
Dividends
115.0
Reinvested dividends
Cum-div earnings
Normal earnings
Abnormal earn growth
570.0
160.0
11.5
581.5
426.8
154.7
599.0
349.0
16.0
615.0
627.0
-12.0
629.0
367.0
34.9
663.9
658.9
5.0
660.45
385.40
36.70
697.15
691.90
5.25
Growth rates:
Earnings growth
Cum-div earn growth (AEG)
Growth in AEG
46.91%
49.87%
5.09%
7.89%
5.00%
10.83%
5.00%
10.83%
5.0%
Discount rate
PV of AEG
1.100
140.64
1.210
-9.92
Note that the AEG for 2011 and 2012 are discounted back to the end of 2010.
a. Forecasted abnormal earnings growth (AEG) is given in the pro forma above.
AEG = 581.5 – 426.8 = 154.7.
Cum-dividend earnings = 570.0 + (115 × 10%) = 581.5
Normal earnings is prior year’s earnings growing at the required rate. So, for 2011,
Normal earnings = 388 × 1.10 = 426.8
Abnormal earnings growth can also be calculated as
AEG = (cum-div growth rate – required rate) × prior year’s earnings
So, for 2011,
AEG = (0.4987 – 0.10) × 388 = 154.7
b. The growth rates are given in the pro forma.
The growth rate of AEG after 2012 is 5%. Assuming this rate will continue into
Value per share on 1,380 million shares
4.36
This is a Case 2 valuation. If you worked exercise E5.3 using residual earnings
methods, compare you value calculation with the one here.
c. The forward P/E = 6,013.6/388 =15.5. The normal P/E is 1/0.10 = 10.
E6.4. Abnormal Earnings Growth Valuation and Target Prices
This exercise complements Exercise 5.4 in Chapter 5, using the same forecasts.
Develop the pro forma to forecast abnormal earnings growth (AEG) as follows:
Eps
3.90
Dps
Reinvested dividends (12%)
Cum-dividend earnings
Normal earnings (12%)
2010
2011
2012
2013
2014
3.70
1.00
3.31
1.00
0.12
3.82
4.368
3.59
1.00
0.12
3.43
4.144
3.90
1.00
0.12
3.71
3.707
1.00
0.12
4.02
4.021
-0.548
-0.714
0.003
-0.001
Abnormal earnings growth
(a) See bottom line of pro forma for answer.
(b) As AEG is forecasted to be zero after 2012, the valuation is based on forecasted
AEG up to 2012:
= $23.68
Note that this is the same value as obtained using residual earnings methods in
Exercise 5.4.
(c) The expected trailing P/E for 2014 must be normal if abnormal earnings growth is
Expected to continue to be zero after 2014. The normal trailing P/E for a required
return of 12% is 1.12/0.12 = 9.33.
With a normal trailing P/E of 9.33,
= $36.387
As the dividend is expected to be $1.00, the 2014 value (ex-dividend) is $35.387.
E6.5.
Dividend Displacement and Value
(a)
Firm B will have higher earnings in 2011 because it will pay no dividend
in 2010. Firm A’s 2011 earnings will be displaced by its 2010 dividend.
= 18.90
(Assumes retained earnings are invested at the cost of capital.)
(b)
Anticipated future dividends don’t affect current price (unless payment
reduces investment in value-generating projects). Firm A’s shareholders
expect to earn the earnings of Firm B’s shareholders by reinvesting the
dividend at the cost of capital. So, cum-dividend earnings are the same for
both firms.
E6.6. Normal P/E Ratios
The normal trailing P/E ratio is
1+ required equity return
required equity return
The normal forward P/E is the trailing P/E – 1.0
The schedule for the trailing P/E is as follows. Subtract 1.0 to get the forward P/E.
8%
13.50
9%
12.11
10%
11.00
11%
10.09
12%
9.33
13%
8.69
14%
8.14
15%
7.67
16%
7.25
Applications
E6.7. Calculating Cum-dividend Earnings Growth Rates: Nike
The pro forma is as follows:
2009
2010
Eps
3.90
4.45
Dps
Reinvestment of 2009 dividend at 10%
0.92
0.092
Cum-dividend eps
4.542
Cum-dividend eps growth rate (4.542/3.90 –1)
Ex-dividend eps growth rate (4.45/3.90 - 1)
16.46%
14.10%
E6.8. Calculating Cum-dividend Earnings: General Mills
Earnings on prior
Cumdividend eps
Year
year’s reinvested
Eps
Dps
dividends
2004
2005
2006
2007
2008
2.82
3.34
3.05
3.30
3.86
1.10
1.24
1.34
1.44
1.57
E6.9. Residual Earnings and Abnormal Earnings Growth: IBM
0.11
0.124
0.134
0.144
3.45
3.174
3.434
4.004
The pro forma for the forecast is as follows:
2002
2003
2004
2005
2006
2007
Eps
4.32
5.03
5.58
6.20
6.88
Dps
0.60
0.67
0.74
0.83
0.92
Bps
13.85 17.57 21.93 26.77 32.14 38.10
Reinvested dividends at 12%
0.072
0.080
0.089
0.100
Cum-dividend earnings
5.102
5.660
6.289
6.980
Normal earnings
4.838
5.634
6.250
6.944
Abnormal earnings growth
0.264
0.026
0.039
0.036
Residual earnings
2.658
2.922
2.948
2.987
3.023
0.264
0.026
0.039
0.036
Change in residual earnings
The answers to parts a, b and c of the question are in the last three lines of the pro forma.
E6.10. A Normal P/E for General Electric?
a.
Forward P/E = $26.75/ $2.21
= 12.10
b. Earnings forecast for 2009
2008 dividend reinvested: $1.24 x .09
Cum-dividend earnings for 2009
AEG (2009)
$2.30
0.1116
$2.4116
= 2.4116 – (1.09 × 2.21)
= 0.0027 or 0.27 cents per share
This is close to zero, indicating that the forward P/E should be normal. Put another
way, the cum-dividend earnings growth for 2009 = 2.4116/2.21 – 1 = 9.1% which
is close to the required return; thus the P/E should be normal.
E6.11. Plotting Earnings Implied Growth Rates for the S&P 500
The S&P example is the text reverse engineered to the growth rate from forecasts of
earnings for two years ahead. The pro forma with these forecasts (given in the chapter) is:
Earnings
Dividends (31% payout)
Reinvested dividends at 9%
Cum-dividend earnings
Normal earnings ($53 ×1.09)
AEG
2004
2005
$53.00
16.43
$58.20
1.479
$59.679
57.770
$ 1.909
With the forecast of forward earnings and AEG for 2005, we are ready to reverse
engineer for a market price of 1000:
The solution for g is 1.039, that is, a 3.9 percent growth rate.
Using implied AEG growth rate, g = 1.039, we can calculate implied earnings growth
rates for years from 2006 to 2011 as following. This reverse engineers the AEG formula:
Earnings forecast = Normal earnings forecast + AEG Forecast
- Forecast of earnings from prior year’s dividends
That is,
Earningst = (ρ × Earningst-1) + AEGt – (ρ-1)dividendst-1
So, moving ahead to 2006,
Earnings forecast for 2006
The calculations for 2006 – 2010 are:
Year
2006
Earnings
63.797
Dividends (payout= 31%)
19.777
Dividends reinvested (at 9%)
1.624
Cum-dividend earnings
65.421
Normal earnings
63.438
Abnormal Earnings Growth
1.983
(AEG)
Implied earnings growth rate
9.62%
Implied cum dividend growth rate 12.41%
$63.797
2007
69.820
21.644
1.780
71.600
69.539
2008
76.296
23.652
1.948
78.244
76.103
2009
83.259
25.810
2.129
85.387
83.163
2010
90.740
28.129
2.323
93.063
90.752
2.060
2.141
2.224
2.311
9.44% 9.28% 9.13% 8.99%
12.23% 12.07% 11.92% 11.78%
Next we can plot the sequence of the implied earnings growth rates as in Figure 6.2.
11.00%
BUY
10.50%
EPS growth rate
10.00%
9.62%
9.50%
9.44%
9.28%
9.13%
9.00%
8.99%
SELL
8.50%
8.00%
2006
2007
2008
2009
2010
E6.12. Challenging the Level of the S&P 500 with Analysts’ Forecasts
The required return = 10%
To develop the pro forma for the implied growth rate, first apply the forward P/E ratio to
get an earnings forecast for 2006, then convert the PEG ratio to an earnings forecast for
2007:
Forward P/E = Price/Earnings2006
Treat the 1271 as dollars to get earnings in dollars:
$1,271/Earnings2006 = 15
Thus Earnings2006 = $84.73
PEG =
Forward P / E
= 1.47
Growth Rate for 2007
Thus, for a forward P/E of 15, the 2007 growth rate for 2007 earnings is 10.2%.
Thus, 2007 earnings forecasted is $84.73 × 1.102 = $93.37
a. The pro forma to calculate abnormal earnings growth (AEG) is as follows:
Earnings
Dividends (payout = 27%)
Reinvested dividends (at 10%)
Cum-dividend earnings
Normal earnings ($84.73 x 1.10)
AEG
2003
2004
84.73
22.88
93.37
2.288
95.658
93.203
2.455
b. If cum-dividend earnings are expected to grow at the required rate of return, 10%, after
2006, the P/E should be normal:
= 847.3
The normal P/E is appropriate if (cum-dividend) earnings are expected to grow at a rate
equal to the required return, 10%. The P/E based on analysts forecast (15) is higher than
this because the market sees earnings growing at a higher rate. Is this assessment
reasonable?
c. Applying the abnormal earnings growth (AEG) pricing model with the long-term
growth rate for AEG of 4%:
= 1256
d. The S&P 500 index is appropriately priced (approximately) at 1271. This will not
always be the case. The estimated level can different from the actual level for a number
of reasons:
1. Analysts’ forecasts are too optimistic relative to how the rest of the market sees it.
2. The market agrees with analysts’ forecasts for 2006 and 2007, but sees the longterm growth rate at less than 4%.
3. The market requires a higher or lower required return than 10%
4. The market is mispriced.
With respect to point 1, sell-side analysts’ forecasts are often overly optimistic,
particularly two-year ahead forecasts on which the AEG is calculated.
This exercise is dangerous when both the market and analysts are too optimistic (as in the
bubble). Then you have to challenge the price with your own forecasts. Notice that the
next exercise works with actual earnings numbers, not analysts’ forecasts.
E6.13. Valuation of Microsoft Corporation
a. The Pro Forma
Eps forecasted
Dps
Dps reinvested at 9%
Cum-dividend earnings
Normal earnings: 1.44 x 1.09
AEG
2007
1.44
0.40
2008
1.67
0.036
1.706
1.5696
0.1364
[Analysts’ consensus forecasts are from Yahoo Finance on 10/09/06]
Valuation with a margin of safety (that avoids speculation about growth):
= $33.58
[Allow for rounding error]
Implication: The market sees AEG declining in the future (because the market price
of $27.20 is less than the no-growth value). The question that the fundamental
investor has to answer: Is it the case that Microsoft can no longer grow AEG? Are the
growth days over?
b.
Normal P/E for a 9% required return = 1/0.09 = 11.111
c.
Analysts' eps growth rate for 2008 =
PEG =
1.67
- 1 = 15.97%
1.44
18.89
= 1.18
15.97
While the standard PEG ratio is based on eps growth rates, it is better
calculated with a cum-dividend growth rate:
PEG =
18.89
= 1.02
18.47
E6.14. Inferring Implied EPS Growth Rates: Kimberly-Clark Corporation
Price, March 2005
a.
$64.81
Trailing P/E =
64.81 + 1.60
= 18.24
3.64
Forward P/E =
64.81
= 17.01
3.81
Normal trailing P/E =
1.089
= 12.24
0.089
Normal forward P/E =
1
= 11.24
0.089
b.
Calculate AEG for 2006:
2004
2005
2006
Eps
3.64
3.81
4.14
Dps
1.60
1.80
1.96
Dividends reinvested at 8.9%
0.1602
Cum-dividend earnings
4.3002
Normal eps (3.81 x 1.089)
4.1491
Abnormal earnings growth (AEG)
0.1511
P = 64.81 =
1 
0.1511 
3.81
+
0.089 
1.089 - g 
g = 1.012 (1.2% growth rate )
c.
2005
2006
2007
2008
2009
2010
Eps
Dps
3.81
1.80
4.14
1.96
2.14
2.33
2.54
2.77
0.1529
0.1547
0.1566
0.1585
(0.1744)
(0.1905)
(0.2074)
(0.2261)
Normal earnings
4.5085
4.8863
5.2822
5.6970
Eps
4.4870
4.8505
5.2314
5.6294
8.38%
8.10%
7.85%
7.61%
AEG
0.1511
(growing at 1.2%)
Reinvested dividends
(at 8.9%)
Eps growth rate
8.66%
Note: Normal earnings are the earnings in the prior year growing at 8.9%. So, for 2008,
normal earnings = $4.487 x 1.089 = 4.8863.
d.
The market was pricing approximately the same growth rates as forecasted by analysts.
Put another way, the market was pricing KMB based on consensus analysts’ forecasts.
e.
Yes, as analysts were forecasting the same growth rates as those implied in the market
price, they are saying that the market price is reasonable. The 2.6 rating – a HOLD – has
integrity.
(If you are following the Continuing Case in the text, some of this material will be
familiar to you.)
E6.15. Using Earnings Growth Forecasts to Challenge a Stock Price: Toro Company
a. With a required return of 10%, the value from capitalizing forward earnings is
Value2002 = $5.30/0.10 = $53
With a view to part d of the question, forward earnings explain most of the current
market price of $55. If one can forecast growth after the forward year, one would be
willing to pay more that $53.
b. First forecast the ex-dividend earnings based of analysts’ growth rate of 12%. Then
add the earnings from reinvesting dividends at 10%.
2003
2004
2005 2006 2007 2008
Eps growing at 12%
5.30
5.936
6.648 7.446 8.340 9.340
Dividends
0.53
0.594
0.665 0.745 0.834 0.934
Dividends reinvested at 10%
0.053
0.059 0.067 0.075 0.083
Cum-dividend earnings
5.989
6.707 7.513 8.415 9.423
c. Abnormal earnings growth (AEG) is cum-dividend earnings minus normal growth
earnings. Normal earnings is earnings growing at the required return of 10%:
Cum-dividend earnings
5.989
6.707 7.513 8.415 9.423
Normal earnings
5.830
6.530 7.313 8.191 9.174
Abnormal earnings growth (AEG)
0.159
0.177 0.200 0.224 0.249
d. With abnormal earnings growth forecasted after the forward year, the stock should be
worth more than capitalized forward earnings of $53, the approximate market price. (One
would have to examine the integrity of the analysts’ forecasts, however.)
The growth rate forecast for AEG for 2005-2008 is 12% (allow for rounding error
in calculating this growth rate from the AEG numbers above). This cannot be sustained if
the required return is 10%, but there is plenty of short-term growth to justify a price
above $55. (Of course, one can call the analysts’ forecasts into question.)
E6.16. Abnormal Earnings Growth and Accounting Methods
The revised pro forma is as follows:
2010E
2011E
2012E
2013E
2014E
Earnings
502.0
Dividends
115.0
Reinvested dividends
Cum-div earnings
Normal earnings
Abnormal earn growth
570.0
160.0
11.5
581.5
552.2
29.3
599.0
349.0
16.0
615.0
627.0
-12.0
629.0
367.0
34.9
663.9
658.9
5.0
660.45
385.40
36.70
697.15
691.90
5.25
Growth rates:
Earnings growth
Cum-div earn growth (AEG)
Growth in AEG
13.55%
15.84%
5.09%
7.89%
5.00%
10.83%
Discount rate
PV of AEG
1.100
26.64
1.210
-9.92
5.0%
10.83%
5.0%
(a) Forecasted earnings for 2010 increase by $114 million, to $502 million, because
of the lower cost of good sold. (This assumes that the write-down has no effect on
forecasted revenues on which forecasts for other years are based: it is often the
case the an inventory write-down means that the firm will have more trouble
selling its inventory.)
(b) The valuation based on the revised pro forma is:
Forward earnings, 2010
Total present value of AEG for 2011-2012
(26.64 – 9.92 = 16.72)
5
Continuing value (CV), 2012 =
= 100.00
1.10 − 1.05
Present value of CV =
100.0
1.210
502.00
16.72
82.64
601.36
Capitalization rate
Value of the equity =
0.10
601.36
0.10
Value per share on 1,380 million shares
6,013.6
4.36
The valuation is the same at that in Exercise 6.3.
(c) As the additional earnings of $114 million in 2010 will incur a tax of $39.9
million, they will be lower by that amount, that is $462.1 million. However, the
lower earnings provide a lower base for calculating AEG for 2011, so AEG in
2011 is higher than that in the pro forma in (a). The net effect is to leave the
valuation unchanged. (This assumes forecasts for other years are already after
tax.)
E6.17. Is a Normal Forward P/E Ratio Appropriate? Maytag Corporation
a. Actual traded forward P/E = $28.80/$2.94 = 9.80.
The firm was trading below a normal P/E, so the market was forecasting negative abnormal earnings
growth after 2003.
b.
A five-year pro forma with a 3.1% eps growth rate after 2004 and forecasted dps that maintains
the payout ratio in 2003:
2003
2004
2005
2006
Eps
2.94
3.03
3.12
3.22
3.32
Dps
0.72
0.74
0.76
0.79
0.81
Dps reinvested at 10%
0.072
0.074
0.076
0.079
Cum-dividend earnings
3.102
3.194
3.296
3.399
Normal earnings at 10%
3.234
3.333
3.432
3.542
Abnormal earnings growth
2007
-0.132 -0.139 -0.136 -0.143
An AEG valuation based on just these five years of forecasts is:
= $25.07
So, even if abnormal earnings growth were expected to recover to zero after 2007, the current
price of $28.80 is too high.
CHAPTER SEVEN
Viewing the Business Through the Financial Statements
Exercises
Drill Exercises
E7.1. Applying the Cash Conservation Equation (Easy)
a.
Apply the cash conservation:
? = $94 million
b.
Net dividend (d) = $162 + 53 = $215
Debt financing flows (F) = -$86
Now apply the cash conservation equation:
= $129 million
E7.2. Applying the Treasurer’s Rule
a.
The treasurer’s rule:
C – I – i – d = Cash applied to debt trading
$2,348 – 23 – (14 + 54) = $2,365 million
After paying interest and receiving $40 million (14 – 54) from the negative net dividend, there was
$2,365 of cash left over from the free cash flow. The treasurer used it to buy debt, either by buying
back the firm’s own debt or investing in debt assets.
b.
From the treasurer’s rule,
C – I – i = d + cash from trading in debt
-$1,857 – 32 = d + cash from trading in debt
= ($1,050 + stock repurchases – share issues) + cash from trading
in debt
(The dividend is $1.25 per share × 840 million shares = $1,050 million)
The cash shortfall after paying the dividend is $1,857 + 32 + 1,050 = $2,939
million. The treasurer meets this shortfall by selling debt – either issuing the
firm’s own debt or selling debt assets (financial assets) that the firm holds – or
by issuing shares.
E7.3. Balance Sheet and Income Statement Relations
Net financial assets = -$1,459 million
That is, the firm has net financial obligation (negative NFA)
Net operating assets = $2,056 million
Operating income (after tax) = $155 million
E7.4. Using Accounting Relations
The reformulated balance sheet:
Net Financial Obligations and Equity
Net Operating Assets
2009
Operating assets 205.3
Operating liabilities
189.9
40.6
2008
Financial liabilities
120.4
34.2 Financial assets 45.7
NFO
CSE
155.7
NOA
164.7
(a) Dividends
= Net income − ∆CSE
2009
2008
120.4
42.0
74.7
90.0
164.7
(Clean-surplus equation)
= 1.9
(These are net dividends)
(b) C − I
= OI − ∆NOA
= 21.7 − 9.0
= 12.7
(c) RNOAt
= OIt /½ (NOAt + NOAt-1)
= 21.7/160.2
= 13.55%
(d) NBC
= Net interest/½ (NFOt + NFOt-1)
= 7.1/76.55
= 9.27%
E7.5. Using Accounting Relations
(a)
Income Statement:
Start with the income statement where the answers are more obvious:
A = $9,162
B = 8,312
C=
94
78.4
77.3
155.7
(Comprehensive income = operating revenues – operating expenses – net financial
expenses)
Balance sheet:
D = 4,457
E = 34,262
F = 34,262
G = 7,194
H = 18,544
Before going to the cash flow statement, reformulate the balance sheet into net
operating assets (NOA) and net financial obligations (NFO):
Jun-09 Dec
Operating assets
Operating liabilities
Net operating assets
28,631
7,194
21,437
Jun-09 Dec
30,024
8,747
Financial obligations
Financial assets
Net financial obligations
7,424
4,457
2,967
6,971
4,238
2,733
Common equity
18,470
21,437
18,544
21,277
21,277
Cash Flow Statement:
Free cash flow:
J = 690
[C - I = OI - ∆NOA]
Cash investment:
I = (106)
(a liquidation)
[I = C - (C - I)]
Total financing flows:
M = 690
[C - I = d + F]
Net dividends:
K = 865
[Net dividends = Earnings - ∆CSE]
Payments on net debt:
L = (175)
[F = d + F - d]
(more net debt issued)
(b)
Operating accruals can be calculated in two ways:
1.
Operating accruals
=
266
2.
Operating accruals
=
266
=
234
(c)
∆NFO
(d)
The net dividend of $865 was generated as follows:
Operating income
less ∆NOA
Free cash flow
less net financial expenses
plus increase in net debt
850
160
690
59
631
234
865
E7.6. Inferences Using Accounting Relations
(a)
This firm has no financial assets or financial obligations so CSE = NOA and total
earnings = OI. Also the dividend equals free cash flow (C - I = d).
Price
CSE (apply P/B ratio to price)
Free cash flow
Dividend (d = C - I)
Price + dividend
Return (246.4 – 224)
Rate of return
2009
2008
224
140
238
119
8.4
8.4
246.4
22.4
10%
(b)
There are three ways of getting the earnings:
1.
Earnings
=
(12.6)
2.
OI
=
(12.6)
(Earnings
=
OI as there are no financial items)
Earnings
=
(12.6)
3.
(a loss)
Applications
E7.7. Applying the Treasurer’s Rule: Microsoft Corporation
a.
The treasurer would run through the following calculation to find the cash surplus or
deficit:
Cash flow from operations
Cash investment
Free cash flow
Interest receipts
$702 million
Taxes
253
Cash available to shareholders
Net payout to shareholders:
Stock repurchase
Dividends
Share issued
$
23.4 billion
3.2
20.2
0.449
20.649
40.0 billion
4.7
42.200
(2.5)
Cash surplus
(21.551)
As the surplus is actually a cash shortfall, the treasurer must sell debt. He or she does so
by selling part of the $23.7 billion in financial assets on hand.
b.
In the treasurer’s plan, $4.2 billion would be added to cash investments:
Cash flow from operations
Cash investment (3.2 + 4.2)
Free cash flow
Interest receipts
$702 million
Taxes
253
Cash available to shareholders
Net payout to shareholders:
Stock repurchase
Dividends
Share issued
Cash surplus
$
23.4 billion
7.4
16.0
0.449
16.449
40.0 billion
4.7
(2.5)
42.200
(25.751)
Now the treasurer must liquidate more of the $23.7 billion in financial assets on hand.
c.
With almost all of its financial assets of $23.7 billion distributed, under these scenarios,
Microsoft might need cash for further stock repurchases, dividends, or investments in
operations.
E7.8. Accounting Relations for Kimberly-Clark Corporation
a. Reformulate the balance sheet:
Operating assets
Operating liabilities
Net operating assets (NOA)
Financial obligations
Financial assets
$6,496.4
382.7
Common equity
2007
2008
$18,057.0
6,011.8
12,045.2
$16,796.2
5,927.2
10,869.0
(i)
6,113.7
$4,395.4
270.8 4,124.6
(ii)
$ 5,931.5
$ 6,744.4
(iii)
b. Free cash flow = Operating income – Change in net operating assets
= $2,740.1 – (12,045.2 – 10,869.0)
= $1,563.9
a. NOA (end) = NOA (beginning) + Operating income – Free cash flow
= $12,045.2
CSE (end) = CSE (beginning) + Comprehensive income – Net payout
Comprehensive income = Operating income – Net financial expense
= $2,593.0
$5,931.5 = 6,744.4 + 2593.0 – Net payout
Thus, net payout = $3,405.9
CHAPTER EIGHT
The Analysis of the Statement of Shareholders’ Equity
Exercises
Drill Exercises
E8.1. Some Basic Calculations
a.
= $205 million
b.
= -$149 million
(There was a net payment into the firm from shareholders.)
Comprehensive Earnings =
$62 million
This applies the stocks and flow equation underlying the reformulated equity statement. See equation
2.4 in Chapter 2.
c.
The difference of $25 million is other comprehensive income (dirty-surplus
income) reported in the equity statement.
E8.2.
Calculating ROCE from the Statement of Shareholders’ Equity
. Comprehensive Earnings
=
25.3
This applies the stocks and flow equation underlying the reformulated equity statement. See equation 2.4 in
Chapter 2. The net dividend is negative, that is share issues are in excess on cash paid out in dividends and
share repurchases.
ROCE
=
14.47%
[Beginning CSE is used in the denominator because the share issue was at the end of the year. If the share
issue was half way through the year, use average CSE in the denominator]
E8.3. A Simple Reformulation of the Equity Statement
Beginning balance (1,206 – 200)
Net transactions with shareholders:
$1,006
Share issues
Dividends
$45
(94)
Comprehensive income to common:
Net income
Currency translation loss
Unrealized gain on debt securities
Preferred dividends
(49)
$241
(11)
24
(15)
239
Ending balance (1396 – 200)
$1,196
Preferred stock has been subtracted from beginning and ending balances (to make it a statement of common
shareholders’ equity).
E8.4. Using Accounting Relations that Govern the Equity Statement
a.
Balance, December 31, 2008 = $4,500 - 2,100 = $2,400 million
Balance, December 31, 2009 = $5,580 – 2,100 = $3,480 million
These numbers supply the missing balances in the statement. Given these
balances, the only missing item is net income. This must be $1,083 million.
b.
The reformulated statement is as follows:
Balance, December 31, 2008
Net transactions with shareholders:
Issue of common stock
Common dividend
$2,400
$155
(132)
Comprehensive income:
Net income
Unrealized gain on securities
Translation loss
Preferred dividends
23
$1,083
13
(30)
(9)
$1,057
Balance, December 31, 2009
$3,480
Comprehensive income is $1,057 million.
E8.5. Calculating the Loss to Shareholders from the Exercise of Stock Options
Market price of shares issued in exercise
Exercise price
Loss on exercise before tax
Tax benefit
(at 36%)
Loss after tax
305 × $35
305 × $20
$10,675
6,100
$ 4,575
1,647
$ 2,928
E8.6. Reformulating an Equity Statement with Employee Stock Options
Before the reformulation, calculate the loss on exercise of stock options:
12
= 34
0.35
Tax Benefit (35%)
12
Loss on exercise =
Compensation, after tax
22
The loss is obtained from the tax benefit, reported in the equity statement. The 34 (rounded) is the amount
that draws a tax benefit at a 35% tax rate: Method 1 in the text. The after-tax loss, 22, goes into
comprehensive income.
The reformulation:
Balance, end of 2008
1,430
Net transactions with shareholders:
Share issues from options (810 + 34)
Stock repurchases
Dividends
Comprehensive income:
Net income
Unrealized gain on debt investments
Loss on exercise of employee options
844
(720)
(180)
(56)
468
50
(22)
496
Balance, end of 2009
1,870
Applications
E8.7. A Simple Reformulation: J.C. Penney Company
This reformulation is pretty straightforward. The main issue is taking out the preferred stock to convert the
statement to a statement of common shareholders’ equity: Take out preferred stock from beginning and
ending balances and omit preferred stock transactions (other than the preferred dividend)
Balance, January 29, 2000 ($7,228 – 446)
Transactions with shareholders:
Common stock issued
Common dividends
(249 – 24)
Comprehensive income (to common):
Net income
Unrealized change in investments
Currency translation loss
Other comprehensive income
Preferred dividends
$6,782
$ 28
(225)
(197)
(705)
2
( 14)
16
(24)
Balance, January 27, 2001 ($6,259 – 399)
(725)
$5,860
E8.8. Reformulation of an Equity Statement and Accounting for the Exercise of
Stock Options: Starbucks Corporation
a.
Reformulated Statement of Shareholders’ Equity
(in millions)
Balance, October 1, 2006
Net payout to shareholders:
Stock repurchase
Sale of common stock
$ 2,228.5
1,012.8
(46.8)
Issue of shares for employee stock option
Comprehensive Income:
Net income from income statement
Unrealized loss on financial assets
Currency translation gains
Balance, September 30, 2007
(225.2)
(740.8)
672.6
(20.4)
37.7
689.9
$2,177.6
Note: The closing balance excludes $106.4 million for “Stock-based compensation
expense” which is a liability rather than equity. (It is added to operating liabilities in the
reformulated balance sheet).
b.
Tax benefit from exercise of options in equity statement = $95.276 million
Tax rate = 38.4%
Loss from exercise, before tax (Method 1 in the text)
95.276
0.384
Tax benefit
Loss from exercise of options, after tax
$248.115
95.276
$152.839
C.
Market price per share
Weighted average exercise price
In-the-money amount
7.97
Number of options expected to be exercised
63,681,867
Option overhang (7.97 x 63,681.9 million)
Tax benefit (at 38.4%)
Option overhang after tax (a liability)
28.57
20.60
$507,544
194,897
$312,647
This is a floor estimate; it is only the in-the-money value of the options (it excludes
option value).
Note that the appropriate options number is the number that are expected to be
exercised. As options cannot be exercised until they vest (after a service period), the
appropriate number is the number expected to vest (some employees are expected to
leave before vesting). Here the number of options actually exercisable at the end of
2007 is 40,438,082. With a lower exercise price of $14.65, one calculates an option
overhang of $562.898 which could be recognized as the overhang.
E8.9. Calculating Comprehensive Income to Shareholders: Intel Corporation
Net income
Unrealized loss on securities
Loss on conversion of notes
10,535
(3,596)
(350-207)
(143)
Comprehensive income
6,796
The loss on conversion of subordinated notes is the difference between the market price of the common
shares and the exercise price at conversion. This is a loss from issuing shares at less than market price.
Intel also incurred a loss from the exercise of stock options by employees. Method 1 determines the loss on
exercise of stock options:
Loss on shares issued to employees calculated from the reported tax benefit:
Loss before tax
Tax
Loss after tax
=
887
0.38
2,334
887
1,447
This loss is a real loss to shareholders than might be included in comprehensive income. However, with
FASB Statement No. 123R and IFRS No. 2, grant date accounting brings some of the cost (but not all) into
income, so adding the loss at exercise could be double counting to some extent. As it is, however, the
reported income understates the loss.
E8.10. Loss on the Conversion of Preferred Common Stock: Microsoft Corporation
In 1999, Microsoft’s shares traded at an average price of $88.
With 14.901 million common shares issued -- 1.1273 shares for every one of the 12.5 million preferred
shares -- common stock worth $1,240 million was issued. As the carrying value of the preferred stock was
$990 million, the loss in conversion was $260 million:
Market value of common shares issued: 14.901 × $88
Carrying value of the preferred stock
Loss on conversion
= $1,240
980
$ 260
E8.11. Conversion of Stock Warrants: Warren Buffett and Goldman Sachs
The loss to shareholders is the difference between the market price of the shares and the
issue price:
Market price of shares issued on exercise of warrants:
43.5 million x $150
$6,525.0 million
43.5 million x $115
$5,002.5
43.5 million x $(150-115)
$1,522.5 million
Exercise price:
Loss:
The loss is not tax deductible.
E8.12. Reformulation of an Equity Statement: Dell Computer Corporation
a.
Loss on stock option exercise
=
260
0.35
=
743
Tax effect
260
483
b.
Reformulated Equity Statement:
Balance, February 1, 2002
Net transaction with shareholders:
Share issue, at market value (418 + 483)
901
Share repurchase, at market value
(1,400)
(2,290 – 890)
Comprehensive income:
CI reported
Loss on share repurchase
(890)
4,694
(499)
2,051
Balance, January 31, 2003
1,161
5,356
The loss on the stock repurchase occurred because shares were repurchased at $45.80 when the shares
traded at $28. The $45.80 repurchase price is the total amount paid, $2,290 million, divided by 50 million
shares repurchased. The repurchase at such a high price was a result of a share repurchase agreement that
gave the counter party the right to sell shares to Dell at $28. See Box 8.4 in the chapter. The loss is
calculated as follows:
Market value of shares repurchased $ 28 x 50 million shares = 1,400
Amount paid on repurchase
Lost on repurchase
2,290
890
The loss on exercise of options has not been included in comprehensive income because
of the potential double counting problem.
E8.13. Ratio Analysis for the Equity Statement: Nike and Reebok
Follow the ratio analysis in the chapter. Work from the reformulated equity statement in Exhibit 8.1. The
following summary starts with the profitability ratio (ROCE).
Profitability:
ROCE
=
25.9%
(Average CSE is used in the denominator. In ROCE calculated on beginning ROCE = 27.1%. As
earnings are earned over the whole year, we usually use average book value for the year in the
calculation.)
Payout:
Dividend payout
=
412.8
1,931.8
=
=
1,660.8
1,931.8
Total payout
Dividends-to-book value =
=
86.0%
412.8
= 5.2%
7,457.8 + 412.8
Retention ratio
Total payout-to-book value
21.4%
=
=
1,931.8 − 412.8
= 78.6%
1,931.8
1,660.8
= 18.2%
7,457.8 + 1,660.8
Growth:
Net investment rate
=
(1,252.8)
= -17.6%
7,118.3
Growth rate in CSE
=
679.0
7,118.3
= 9.5%
Nike added book value from business activities by over 25% of book value, as indicated by the ROCE.
Nike disinvested with cash dividends and share repurchases paid to shareholders in excess of share issues.
E8.14. Losses from Put Options: Household International
This exercise illustrates the trouble that a firm can get into with put contracts on its own shares, and how
GAAP failed to signal the trouble. (GAAP has since been modified: see the Postscript at the end of the
exercise.)
How share repurchase agreements work
Share repurchase agreements – and similar instruments like put options and put warrants --- are agreements
to purchase stock at a prespecified price, with settlement in cash or a net share transaction for equivalent
value. The agreements are written with private investors or banks who pay a premium for the option right.
Firms write put contracts – in this case forward share purchase agreements – presumably because they
think their shares are undervalued; they do not expect the option to be exercised. Or, if a share repurchase
program is in place, they may be hedging against increases in the repurchase price. But there may be more
sinister motives, as we will see.
GAAP accounting
When a firm is issuing stock for an average of $21.72 per share and using the cash to repurchase
stock at $53.88, one can easily see that it is losing value and endangering its liquidity and credit status. But
GAAP at that time treated the transactions as if they were plain vanilla share issues and repurchases at
market price, with no recognition of the losses. Further, in the case where settlement can be in shares, as
here, no liability is recorded when these contracts are entered into; rather the proceeds from the option
premium paid by the counterparties are treated as part of equity. So the firm treats a liability for current
shareholders to potentially give up value (and equity) as part of their equity. (A liability is recorded at the
amount of the premium if settlement is required in cash, that is, if the firm is required to repurchase shares
for cash rather than settling up in shares.)
If the option is not exercised (because the market price of the shares is above the strike price), the
firm pockets the premium paid for option and thus makes a gain for shareholders. GAAP does not report a
gain, however; rather the amount of the premium remains as part of issued capital, or is transferred to
equity if it had been carried as a liability. With Household International’s agreements, the counterparty is
required to deliver value, in the form of shares, for the difference between exercise price and market price,
augmenting the gain. If the option is exercised against the firm (because the market price is less than the
strike price), the share repurchase is recorded but no loss is recognized. But there is indeed a loss because
the firm repurchases shares at more than the market price.
a. Exercise of options. During the current quarter, Household International repurchased 2.1 million shares
at $55.68 under the agreements. The share issue (yielding $400 million from 18.7 million shares) was at
$21.39 per share. Taking this $21.39 as the market price at the time of the repurchase, the loss per share
(gross of the premium received for the contracts) was $34.29 per share (55.68 –21.39), for a total of
$72.009 million. See Box 8.4. In journal entry form, the appropriate accounting is (in millions of dollars):
Loss on stock repurchase
Common Stock
Dr. 72.009
Cr.
72.009
The $72.009 million credit to equity is the value of the stock net issued to settle. If settlement were in cash,
shares would be repurchased at market value (2.1 x $21.39 = $44.919 million), with the difference between
the share value and cash paid (2.1 x $55.68 = 116.928) recorded as the loss.
b. Options overhang. In addition, a liability exists at September 2002 for outstanding agreements. One
could apply option pricing methods to measure this liability, although this would be complex here because
of the varying triggers, the limits on shares to be delivered under the contracts, and the feature that the firm
receives shares if the stock price goes above the forward price. One can get a feel for the magnitude,
however, by comparing the weighted-average strike price for the 4.9 million options outstanding to the
closing market price at September 30, 2003:
Market price
4.9 x $28.31
Exercise price 4.9 x $52.99
Liability
$138,719
259,651
$120,932
(Losses are not tax deductible, so there is no tax benefit to net out here.) This valuation of the liability
excludes the further option value and does not build in the effects of restrictions in the agreements. The
footnote does give some further information on the value of the liability because it indicates that 4.2 million
shares will have to be issued to settle outstanding contracts at the current market price of the shares. At
$28.31 per share, this is $118.902 million. But there are scenarios under the agreements, depending on the
price of the shares, where more shares would have to issued, up to a maximum of 29.8 million shares.
Share repurchase agreements and put options have a sharp barb for shareholders. When the share
price goes down, they of course lose. But if, in addition, the firm has these agreements, the shareholder gets
hit twice; the loss is levered. Yet GAAP (at that time) did not account for the loss.
The counterparties here were banks. So you could see the premium received as a loan from the
bank to be paid back in stock, with the expected interest being any difference between market and strike
price. However, this “loan” was not recorded as such, but rather as equity, so enhancing capital ratios and
improving book leverage. Effectively, the transactions took loans off balance sheet. Put it down as another
structured finance deal to move debt off the balance sheet.
c.
Here is how Floyd Norris described it in an article in The New York Times, November 8, 2002,
page C1:
Here's how it worked. Household, following the strategy recommended by Wall Street, decided in 1999
that it would embark on a big share-buyback program. It figured the stock was cheap. There was, however,
a limitation on how many shares Household could buy. It had promised investors that it would maintain
certain capital ratios, which required that it limit leverage. If it spent all that money, capital ratios would
fall too low.
It could have just waited to buy back the stock until it could afford to do so, but Household
had a better idea. It signed contracts with banks in which it promised to buy the shares within a year, for the
market price when it signed the contract plus a little interest to cover the cost of the bank's buying the stock
immediately. In reality, that amounted to a loan from the bank. But that is not the way that Household
accounted for it. It structured the contracts so that it had a right to pay off the loan by issuing new stock,
even though that was not what it intended to do. By doing that, it was able to pretend that the shares it had
agreed to buy were still outstanding, and to keep its capital ratios up. All that was in accord with some
easily abused accounting rules.
Postscript: In early 2003 the FASB began deliberations on dealing with the accounting issues posed by
forward purchase agreements, put warrants, and put options. As a result, FASB Statement No. 150 was
issued, requiring a liability to be recognized.
CHAPTER NINE
The Analysis of the Balance Sheet and Income Statement
Exercises
Drill Exercises
E9.1. Basic Calculations
a.
Reformulated balance sheet
Operating assets
$547
Financial obligations
$190
Operating liabilities
132
Net operating assets
$415
Financial assets
145
Net financial obligations
45
Common shareholders’ equity 370
$415
Operating liabilities = $322 – 190 = $132 million.
b.
Reformulated income statement
Revenue
Cost of goods sold
Gross margin
Operating expenses
Operating income
Net financing expense:
Interest expense
Interest income
Earnings
$4,356
3,487
869
428
441
56
$132
76
$ 365
E9.2 Tax Allocation
= $909 million
(This is the bottom-up method on Box 9.2)
E9.3 Tax Allocation: Top-Down and Bottom-Up Methods
Top-down method:
Revenue
Cost of goods sold
Operating expenses
Operating income before tax
Tax expense:
Tax reported
Tax on interest expense
Operating income after tax
Net interest:
Interest expense
Tax benefit at 37%
Earnings
$6,450
3,870
2,580
1,843
737
$181
50
231
506
135
50
85
421
Bottom-down method:
Earnings
Net interest:
Interest expense
Tax benefit at 37%
Operating income after tax
$421
135
50
85
$506
E9.4 Reformulation of a Balance Sheet and Income Statement
Balance sheet:
Operating cash
Accounts receivable
$
23
1,827
Inventory
PPE
Operating assets
Operating liabilities:
Accounts payable
Accrued expenses
Deferred taxes
Net operating assets
Net financial obligations:
Cash equivalents
Long-term debt
Preferred stock
Common shareholders’ equity
2,876
3,567
8,293
$1,245
1,549
712
$( 435)
3,678
432
3,506
4,787
3,675
$1,112
Income statement:
Revenue
Operating expenses
Operating income before tax
Tax expense:
Tax reported
Tax on interest expense
Operating income after tax
Net financial expense:
Interest expense
Tax benefit at 36%
$7,493
6,321
1,172
$295
80
375
797
221
80
141
26
Preferred dividends
Net income to common
167
$630
E9.5. Reformulation of a Balance Sheet, Income Statement, and Statement of Shareholders’ Equity
a.
Reformulated balance sheet
Operating cash
Accounts receivable
Inventory
PPE
Operating assets
Operating liabilities:
Accounts payable
Accrued expenses
Net operating assets
Net financial obligations:
Short-term investments
Long-term debt
Common shareholders’ equity
$
60
940
910
2,840
4,750
$1,200
390
$( 550)
1,840
1,590
3,160
1,290
$1,870
Reformulated equity statement:
Balance, end of 2008
Net transactions with shareholders:
$1,430
Share issues
Share repurchases
Common dividend
Comprehensive income:
Net income
Unrealized gain on debt investments
Balance, end of 2009
b.
$ 822
(720)
(180)
(
78)
$ 468
50
518
$1,870
Reformulated statement of comprehensive income
Revenue
Operating expenses, including taxes
Operating income after tax
$3,726
3,204
522
Net financing expense:
Interest expense
$ 98
Interest income
15
Net interest
83
Tax at 35%
29
Net interest after tax
54
Unrealized gain on debt investments 50
4
Comprehensive income
$ 518
After calculating the net financial expense, the bottom-up method is used to get operating income after
tax. That is, net interest expense is calculated first (= $4 million). Then, as comprehensive income is
$518 million, operating income must be 518 + 4 = 522. The number for operating expense (3,204) is
then a plug to get back to the $3,726 million revenue number. Bottom up.
E9.6. Testing Relationships in Reformulated Income Statements
The solution has to be worked in the following order:
A
E
F
D
=
Operating revenues – operating expenses
=
5,523 – 4,550
=
973
=
Interest expense after tax/ (1 – tax rate)
=
42/0.65
=
64.6
=
E – 42
=
22.6
=
610 + 42
=
652
C
B
=
F
=
22.6
=
A–C–D
=
973 – 22.6 – 652
=
298.4
Effective tax rate on operating income
=
Tax on operating income/ Operating income before tax
=
(B + C)/A
=
33.0%
Applications
E9.7. Price of “Cash” and Price of the Operations: Realnetworks, Inc.
a.
Price/book = 564.5/876 = 0.64
b.
NOA
= 422 million
c.
Price of operations = 564.5 – 454
= 110.5 million
E9.8. Analysis of an Income Statement: Pepsico Inc.
a. The reformulation:
Net Sales
Operating expenses
Operating income from sales (after
(before
tax)
tax)
Tax reported
Tax benefit of debt
Tax on
onnon-core
other operating
items income
Operating income from sales (after tax)
Other operating income
Gain on asset sales
Restructuring charge
Tax on other operating income(37%)
income, 36.1
Operating income (after tax)
Net financial expense:
Interest expense
Interst income
Tax on net interest
interest (37%)
(36.1%)
Net Income
20,367
17,484
2,883
1,606
88
(367)
1,083
65
1,018
367
363
118
245
88
1,327
1,556
651
2,207
157
2,050
c.
Effective tax rate on operating from sales =
1,327
= 46.0%
2,883
You might ask why the tax rate is so high: Pepsico had a special 10.6 percent extra tax charge on its
bottling operations in 1999.
E9.9. Financial Statement reformulation for Starbucks Corporation
a.
Reformulated Statement of Shareholders’ Equity
(In millions)
Balance, September 30, 2007
$2,177.6
Note: The closing balance excludes $106.4 million for “Stock-based compensation
expense” which is a liability rather than equity. (It is added to operating liabilities in the
reformulated balance sheet).
b.
Reformulated Comprehensive Income Statement, 2007
(in millions)
Net revenues
$ 9,411.5
Cost of sales and occupancy costs
3,999.1
Store opening expenses
3,215.9
Other operating expenses
294.1
Depreciation and amortization
467.2
General and administrative expenses
489.2
Operating income from sales (before tax)
946.0
Tax reported
$ 383.7
Tax benefit of net interest
5.6
Tax on other operating income
(6.6)
382.7
563.3
Operating income from sales (after tax)
Other operating income, before-tax item
Gain on asset sales
Other operating charges
Tax at (38.4%)
Operating income, after tax-items
Income from equity investees
26.0
(8.9)
17.1
6.6
10.5
108.0
Currency translation gains
37.7
719.5
Operating income (after tax)
Net financing expenses
Interest expense
Interest income
Net interest expense
Realized gain on financial assets
Tax (at 38.4%)
Unrealized loss on financial assets
156.2
38.2
(19.7)
18.5
(3.8)
14.7
5.6
9.1
20.4
29.5
689.9
Comprehensive income
Note: Interest income and interest expense are given in the notes to the financial
statements in the exercise. That note also identifies the other operating income here.
Reformulated Balance Sheets
(in millions)
2007
2006
Operating Assets
Cash and cash equivalents
Short-term investments—trading securities
Accounts receivable, net
Inventories
Prepaid expenses and other current assets
Deferred income taxes, net
Equity and other investments
Property, plant and equipment, net
Other assets
Other intangible assets
Goodwill
40.0
73.6
287.9
691.7
148.8
129.5
258.8
2,890.4
219.4
42.0
215.6
40.0
53.5
224.3
636.2
126.9
88.8
219.1
2,287.9
186.9
37.9
161.5
Total operating assets
4,997.7
4,063.0
390.8
332.3
74.6
92.5
257.4
296.9
340.9
288.9
54.9
94.0
224.2
231.9
Operating liabilities
Accounts payable
Accrued compensation and related costs
Accrued occupancy costs
Accrued taxes
Other accrued expenses
Deferred revenue
Other long-term liabilities
Total operating liabilities
460.5
1,905.0
262.9
1,497.7
Net operating assets
3,092.7
2,565.3
Net financial obligations
Short-term borrowing
Current maturities of long-term debt
Long-term debt
Cash equivalents (281.3-40.0 in 2008)
Short-term investments (available for sale)
Long-term investments (available for sale)
Net financial obligations
710.2
0.8
550.1
(241.3)
(83.8)
(21.0)
915.0
700.0
0.8
2.0
(272.6)
(87.5)
(5.8)
336.9
Common shareholders’ equity
2,177.6
2,228.5
Notes:
1. Short-term investment (trading securities) is operating assets connected to
employees.
2. Stock-based compensation, excluded from the equity statement, has been
added to other liabilities.
c.
ROCE = 689.9 / 2,228.5 = 30.96%
RNOA = 719.5 / 2,565.3 = 28.05%
NBC = 29.5 / 336.9 = 8.76%
E9.10. Reformulation and Effective Tax Rates: Home Depot, Inc.
First establish the firm’s marginal tax rate. This is the statutory rate (federal plus state) at which interest
income is taxed (or interest expense gets a tax saving). The footnote gives the effective rate (36.8% for
2005), which is the effective rate from the income statement (2,911/7,912 = 36.8%). But this is not the
marginal rate for it includes tax credits and foreign tax benefits, amongst other things. The marginal rate is
the statutory rate, federal and state combined (with the state rate recognizing that state taxes are deductible
in federal tax returns).
The federal statutory rate is 35%, but the state rate is not given. (Many firms do report it.) Home
Depot operates in many states; without more information, the statutory rate is somewhat of a guess. Home
Depot reports a ratio of state-to-federal taxes of 215/2,769 = 7.79% for 2005. Applied to the federal rate of
35%, this implies a state rate of 2.72%, or a total rate of 37.72%.
In the reformulation below, this 37.72% rate is used for the tax allocation. The top-down approach
proceeds as follows:
Reformulated Income Statement, January 30, 2005
($ millions)
Net sales
Cost of sales
Gross profit
Selling and store operating costs
General and administrative
Operating income before tax
Tax as reported
Tax benefit of net debt
Operating income after tax
73,094
48,664
24,430
15,105
1,399
16,504
7,926
2,911
5
Interest expense
Interest income
Net interest expense
Tax on net interest (37.72%)
2,916
5,010
70
56
14
5
9
Net income
5,001
Effective tax rate on operating income =
2,916
= 36.79%
7,926
This effective rate is almost the same as the reported rate because the net interest is almost zero.
The bottom-up approach proceeds as follows (in millions of dollars):
Net income
5,001
Interest expense
Interest income
Net interest expense
Tax on net interest (37.72%)
70
56
14
5
Operating income after tax
9
5,010
CHAPTER TEN
The Analysis of the Cash Flow Statement
Drill Exercises
E10.1. Classification of Cash Flows
A cash flow that affects cash flow from operation also affects free cash flow.
Cash from operations
FCF
Financing Flows
a.
b.
c.
d.
e.
f.
g.
Yes
No
No
Yes
No
No
Yes
Yes
No
Yes
Yes
No
No
Yes
No
No
No
No
Yes
Yes
No
Interest payments affect the GAAP number for cash from operations, but not the real
number. Purchases of short-term investments affect the GAAP measure of cash
investment, but not the real investment in operations nor free cash flow.
E10.2 Calculating Free Cash Flow from the Balance Sheet and Income Statement
First reformulate the balance sheet:
2009
3160
1290
1870
NOA
NFO
CSE
2008
2900
1470
1430
Method 1:
Free cash
Method 2:
= 240
= 376 – (1,870 – 1,430) = -64
So,
= 240
E10.3. Analyzing Cash Flows
a)
As there is no debt or financial assets,
= $150,000
OR
As there is no change in shareholders’ equity and no financial
income or expenses,
= $150,000
So,
= $150,000
(There is no change in net operating assets because there is no
change in
shareholders’ equity and no net financial obligations.)
b)
The increase in cash comes from operations, the sale of land (and
dividends decreased the cash):
Cash from operations
Sale of land
Dividends
Change in cash
= $135,000
$400,000
$535,000
150,000
$385,000
c) No change. The investment in the short-term deposit is a financing
activity, not an
investment in operations, so free cash flow is not affected. It’s a
disposition of
cash from operations, not generation of free cash flow.
E10.4. Free Cash Flow for a Pure Equity Firm
So free cash flow is -$26.1 million
Another solution
Earnings
= $25.3 million
= -26.1 million
E10.5 Free Cash Flow for a Net Debtor
By Method 2 in Box 10.1,
C - I = NFE – ∆NFO + d
∆NFO = 37.4 – 54.3 = -16.9 (net debt declined)
d = 8.3 – 34.3 = -26.1
(negative net payout)
So, C – I = 4 – (-16.9) + (-26.1)
= -5.2
(free cash flow was negative)
OR, using Method 1,
C-I
= OI - ∆NOA
= 29.3 - 34.5
= -5.2
Where
OI
= Comprehensive income (25.3) + NFE (4.0) = 29.3
∆NOA = ∆CSE - ∆NFO
= 51.4 - 16.9 = 34.5
Comprehensive income is plugged from the equity statement.
E10.6. Applying Cash Flow Relations
(a)
= - $40 million
(The firm reduced its investment in net operating assets.)
(b)
= - $69 million
Or, as ∆NOA is made up of investment and operating accruals,
= - $69 million
(c)
C - I = NFE - DNFs + d
So, with a negative net dividend of $13 million
∆NFO = - $400 million
(The firm reduced its NFO by $400 million by applying free cash flow and
the net dividend to reducing net debt).
E10.7. Applying Cash Flow Relations
(a)
Use the free cash flow generation equation: C - I = OI - ∆NOA
As there was no net financial income or expense, operating income (OI)
equals the comprehensive income of $100 million. The net operating
assets for 2009 and 2008 are as follows:
Operating assets
Operating liabilities
NOA
C-I
(b)
2009
2008
640
20
620
590
30
560
= $ 40 million
Use the free cash flow disposition equation: C - I = ∆NFA - NFI +d
The net dividend (d)
= - $60 million (a net capital contribution)
The net financial assets for 2009 and 2008 are as follows:
Financial assets
Financial liabilities
NFA
C-I
2009
2008
250
170
80
110
130
(20)
= $40 million
The firm invested the $40 million of free cash flow in financial assets. In
addition, it raised a net $60 million from shareholders which it also
invested in financial assets.
(c)
Net financial income or expense can be zero if financial income and
financial expense exactly offset each other. This firm moved from a net
debtor to a net creditor position in 2009 such that the weighted-average net
financial income was zero.
Applications
E10.8. Free Cash Flow and Financing Activities: General Electric Company
a. General Electric, while generating large cash flow from operations, has had a
huge investment program as it acquired new businesses, leaving it with negative
free cash flow.
b. Given that cash from operations from the businesses in place continues at, or
grows from the 2004 level, free cash flow will increase and will become positive
(probably by big amounts). Rather than borrowing or issuing shares to finance a
free cash flow deficit, GE will have cash to pay out. It can either,
1. But down its debt
2. Invest the cash flow in financial assets
3. Pay out dividends or buy back its stock.
The firm would not invest in financial assets for too long, but rather buy back debt
or pay out to shareholders. Indeed, in 2005, the firm announced a large stock
repurchase program.
E10.9. Method 1 Calculation of Free Cash Flow for General Mills, Inc,
By Method 1,
Free cash flow
= $1,351 million
E10.10. Free Cash Flow for Kimberly-Clark Corporation
a.
Reformulate the balance sheet:
Operating assets
Operating liabilities
Net operating assets (NOA)
Financial obligations
Financial assets
Common equity (CSE)
2007
2008
$18,057.0
6,011.8
12,045.2
$16,796.2
5,927.2
10,869.0
6,113.7
$4,395.4
270.8 4,124.6
$ 5,931.5
$ 6,744.4
$6,496.4
382.7
By Method 1,
Free cash flow
= 1,563.9
By Method 2,
Free cash flow
= 1,563.9
Net payout to shareholders (d) = 3,405.9
b.
Cash flow from operations reported
Net interest payments
Tax on net interest payments
Cash flow from operation
142.4
52.1
$2,429.0 million
Cash investment reported
Liquidation of short-term investments
898.0
56.0
90.3
2,519.3
954.0
$1,565.3 million
Free cash flow
E10.11. Extracting Information from the Cash Flow Statement with a
Reformulation: Microsoft Corporation
a. Cash dividends are read off the financing sections of the cash flow statement:
$33,498 million. A large dividend indeed! This dividend would also be reported
in the statement of shareholders’ equity.
Net dividend
= 33,672 million
As Microsoft has no debt, the net dividend is equal to the total of financing
activities.
b. Cash flow for operations reported
Interest received
Tax on interest (at 37.5%)
Cash from operations
$3,619 million
$378
142
236
$3,383
(Note: there is no interest paid.)
c. Cash generated from investments, reported
(Positive number means cash has been generated, not used)
Net sales of short-term investments
Cash generated from investing in operations
That is, $177 million was invested in operations.
d. Free cash flow = $3,383 – 177 = $3,206
$23,414
23,591
$ (177)
e. The actual cash invested in operations for 2003 (after adjusting for net investment
in interest-bearing securities) was $172, almost the same as 2004. Both year’s
numbers are affected by the net investment in interest-bearing securities.
f. The net investment in financial assets is the net investment in short-term
investments (in part d above) plus the change in cash and cash equivalents. (As
$60 million of working cash is the same at the beginning and end of the period,
the change in cash and cash equivalents (a negative $6,639 million) is all
investment in financial assets).
Investment in financial assets = -$23,591 - $6,639
= -$30,230 million
That is, Microsoft liquidated $30,230 of financial assets (to pay the large
dividend).
The Reformulated Cash Flow Statement (in millions of dollars)
Cash flow for operations reported
Interest received
Tax on interest (at 37.5%)
Cash from operations
Cash generated from investments, reported
Net sales of short-term investments
Cash generated from investing in operations
$3,619 million
$378
142
$23,414
23,591
Free cash flow
(177)
$3,206
Cash in financing activities:
Net dividend
Sale of financial assets
Interest in financial assets, after tax
CHAPTER ELEVEN
The Analysis of Profitability
Drill Exercises
E11.1 Leveraging Equations
(a)
236
$3,383
By the stocks and flows equation for equity
Net dividends = (93) (i.e. net capital contribution)
$33,672
(30,230)
( 236)
$ 3,206
(This answer assumes no dirty-surplus accounting)
NOA
NFO
CSE
2007
1,900
1,000
900
2008
2,400
1,200
1,200
Average
2,150
1,100
1,050
ROCE = 207/1,050 = 19.71%
Operating income (OI
= 279.6
RNOA = OI/ave. NOA = 279.6/2,150 = 13.0%
ROCE = [PM ×ATO] + [FLEV × (RNOA − NBC)]
PM
= OI/Sales = 279.6/2,100 = 0.1331 (or 13.31%)
ATO = Sales/ave. NOA = 2,100/2,150 = 0.9767
FLEV = Ave. NFO/ave. CSE = 1,100/1,050 = 1.0476
NBC = Net interest expense/ave. NFO = (110 × 0.66)/1,100 = 6.6%
So,
19.71% = (0.1331 × 0.9767) + [1.0476 × (13.0% - 6.6%)]
(b)
2008
2,700
(300)
2,400
2007
2,000
(100)
1,900
Operating assets
Operating liabilities
NOA
Implicit interest on operating liabilities (OL) = 9
Return on operating assets (ROOA)
= 12.28%
Operating liability leverage
= 0.093
So,
13.0% = 12.28% + [0.093 × (12.28% - 4.5%)]
(c)
This is the case of a net creditor firm (net financial assets).
Net dividends
= (361)
Average
2,350
(200)
2,150
ROCE
= 339/3,050 = 11.11%
Operating income
= 279.6 (as before)
RNOA
= 279.6/2,150 = 13.0% (as before)
Return on net financial assets (RNFA) = 6.6%
FLEV = -900/3,050 = -0.295
PM and ATO are as before.
So,
11.11% = (0.1331 × 0.9767) – [0.295 × (13.0% - 6.6%)]
E11.2 First-level Analysis of Financial Statements
(a)
First reformulate the financial statements:
Reformulated Balance Sheets
2008
1,395
NOA
NFO
CSE
2007
1,325
300
1,095
Average
1,360
300
1,025
300
1,060
Reformulated Income Statement, 2008
Sales
Operating Expenses
Tax reported
Tax on NFE
OI
Net interest
Tax on interest at 33%
NFE
Comprehensive Income
3,295
3,048
247
61
9
70
177
27
9
18
159
CSE2008 = CSE2007 + Earnings2008 – Net Dividends2008
1,095 = 1,025 + 159 - 89
Stock repurchase = 89
(b)
ROCE =
159
= 15.0%
1,060
RNOA =
177
= 13.0%
1,360
FLEV =
300
= 0.283
1,060
SPREAD = RNOA – NBC
NFE
18 

= 13.0% - 6.0% = 7.0%  NBC =
=
NFO 300 

C–I
= OI - ∆NOA
= 177 – 70
= 107
(b)
The ROCE of 15% is above a typical cost of capital of 10% - 12%. So
one might expect the shares to trade above book value. But, to trade at
three times book value, the market has to see ROCE to be increasing in the
future or investment to be growing substantially.
E11.3. Reformulation and Analysis of Financial Statements
c. Reformulated balance sheet
2009
Operating cash
Accounts receivable
Inventory
PPE
Operating assets
Operating liabilities:
Accounts payable
Accrued expenses
Net operating assets
2008
$ 60
940
910
2,840
4,750
$1,200
390
1,590
3,160
50
790
840
2,710
4,390
1,040
450
1,490
2,900
Net financial obligations:
Short-term investments
Long-term debt
Common shareholders’ equity
$( 550)
1,840 1,290
$1,870
( 500)
1,970
Reformulated equity statement (to identify comprehensive income):
Balance, end of 2008
$1,430
Net transactions with shareholders:
Share issues
$ 822
Share repurchases
(720)
Common dividend
(180)
( 78)
Comprehensive income:
Net income
Unrealized gain on debt investments
Balance, end of 2009
$ 468
50
518
$1,870
Reformulated statement of comprehensive income
Revenue
Operating expenses, including taxes
Operating income after tax
$3,726
3,204
522
Net financing expense:
Interest expense
$ 98
Interest income
15
Net interest
83
Tax at 35%
29
Net interest after tax
54
Unrealized gain on debt investments 50
4
Comprehensive income
$ 518
After calculating the net financial expense, the bottom-up method is used to get
operating income after tax.
Free cash flow
= 262
d. Ratio analysis
Profit Margin (PM) = 522/3,726 = 14.01%
Asset turnover (ATO) = 3,726/2,900 = 1.285
RNOA
= 522/2,900 = 18%
e. Individual asset turnovers
Operating cash turnover = 3,726/5 = 74.52
Accounts receivable turnover = 3,726/790 = 4.72
1,470
1,430
Inventory turnover = 3,726/840 = 4.44
PPE turnover = 3,726/2,710 = 1.37
Accounts payable turnover = 3,726/1,040 = 3.58
Accrued expenses turnover = 3,726/450 = 8.28
1/individual turnover aggregate to 1/ATO:
1/ATO = 1/1.285 = 0.778 = 0.013 + 0.212 + 0.225 + 0.730 – 0.279 – 0.121
(allow for rounding error)
f. ROCE = 518/1,430 = 36.22%
Financial leverage (FLEV) = 1,470/1,430 = 1.028
Net borrowing cost (NBC) = 4/1,470 = 0.272%
ROCE = 36.22% = 18.0% + [1.028 × (18.0% - 0.272%)]
g. NBC = 4/1,470 = 0.272% (as in part e)
If RNOA = 6% and FLEV = 0.8,
ROCE = 6.0% + [0.8 × (6.0% - 0.0.272%]
= 10.58%
Note: it is more likely that NBC will be at the core borrowing rate (that excludes
The unrealized gain of debt investments): Core NBC = 54/1,470 = 3.67%.
Chapter 12 identifies core borrowing costs.
h. Implicit cost of operating liabilities = 1,490 × 0.03 = 44.7
522 + 44.7
= 12.91%
Return on operating assets (ROOA) =
4,390
Operating liability leverage (OLLEV) = 1,490/2,900 = 0.514
RNOA = 18.0% = 12.91% + [0.514 × (12.91% - 3.0%)]
E11.4 Relationship Between Rates of Return and Leverage
(a)
ROCE = RNOA + [FLEV × (RNOA – NBC)]
13.4% = 11.2% + [FLEV × (11.2% - 4.5%)]
FLEV = 0.328
(b)
RNOA = ROOA + (OLLEV × OLSPREAD)
11.2% = 8.5%
OLLEV = 0.6
+ [OLLEV × (8.5% - 4.0%)]
(c)
First calculate NFO and CSE using the financial leverage ratio (
applied to the net operating assets of $405 million.
So
NFO
CSE
FLEV
=
NOA
= CSE + NFO
NFO
CSE
= 1 + FLEV
= 1.328
As NOA
= $405 million
Then CSE
=
$405 million
1.328
= $305 million
and NFO
= $100 million
Now distinguish operating and financing assets and liabilities
NFO
)
CSE
So
OL
=
NOA
0.6
OLLEV
=
OL
= 0.6 × $405 million
= $243 million
OA
= NOA + OL
= 405 + 243
= $648 million
Financial assets
= total assets – operating assets
= 715 – 648
= $67 million
Financial liabilities
= NFO + financial assets
= 100 + 67
= $167 million
Reformulated Balance Sheet
Operating assets
Operating liabilities
648
243
Financial liabilities
Financial assets
Common equity
405
167
67
100
305
405
E11.5 Profit Margins, Asset Turnovers, and Return on Net Operating Assets: A
What-If
Question
The effect would be (almost) zero.
Existing RNOA
= 11.02%
RNOA from new product line is
RNOA
Applications
= 11.04%
E11.6. Profitability Measures for Kimberly-Clark Corporation
The exercise is best worked by setting up the reformulations balance sheet:
Operating assets
Operating liabilities
Net operating assets (NOA)
Financial obligations
Financial assets
$6,496.4
382.7
Common equity (CSE)
2007
2008
$18,057.0
6,011.8
12,045.2
$16,796.2
5,927.2
10,869.0
a (1)
6,113.7
$4,395.4
270.8 4,124.6
a (2)
$ 5,931.5
$ 6,744.4
a (3)
a.
The answers to question (a) are indicated beside the reformulated statement.
b.
Comprehensive income = 2,740.1 – 147.1 = 2,593 million
ROCE = 2,593/6,744.4 = 38.45%
RNOA – 2,740.1/10,869.0 = 25.21%
FLEV = NFO/CSE = 4,124.6/6,744.4 = 0.612
NBC = 147.1/4,124.6 = 3.57%
c.
The financial leveraging equation is:
ROCE = RNOA + [FLEV × (RNOA – NBC)]
= 25.21% + [0.612 × (25.21% - 3.57%)]
= 38.45%
d.
On sales of $18,266 million for 2007,
PM = 2,740.1/18,266
15.00%
×
×
= 25.2%
E11.7. Analysis of Profitability: The Coca-Cola Company
Average balance sheet amounts are as follows:
ATO = 18,266/10,869
1.68
2007
Net operating assets
$22,905
Net financial obligations
3,573
Common shareholders’ equity
$19,332
$26,858
2006
Average
$18,952
5,114
2,032
$21,744
$16,920
a.
RNOA = 6,121/22,905 = 26.72%
NBC = 140/3,573 = 3.95%
b.
FLEV = 3,573/19,332 = 0.185
c.
ROCE = RNOA + [FLEV × (RNOA – NBC)]
= 26.72% + [0.185 × (26.72% - 3.95%)]
= 30.93 % = 5,981/19,332
d.
PM = 6,121/28,857 = 21.21%
ATO = 28,857/22,905 = 1.26
RNOA = 21.21% × 1.26 = 26.72%
e.
Gross margin ratio = 18,451/28,857 = 63.94%
Operating profit margin from sales = 5,453/28,857 =18.90%
Operating profit margin = 6,121/28,857 = 21.21%
E11.8. A What-If Question: Grocery Retailers
Net operating assets for $120 million in sales and an ATO of 6.0 are $20 million.
An increase in sales of $15 million and an increase in inventory of $2 million
would
increase the ATO to
120 + 25
= 6.59.
20 + 2
With a profit margin of 1.5%, the RNOA would be:
RNOA
= 9.89%
The current RNOA is:
RNOA
= 9.6%
So the membership program would increase RNOA slightly.
E11.9. Financial Statement Reformulation and Profitability Analysis for Starbucks
Corporation
a.
To prepare a reformulated income statement, first identify comprehensive income in the
equity statement. If you worked Exercise E9.9, you would have done this and produced
the statement below. If not, you just need to calculate the comprehensive income of
$689.9 million in the statement here.
Reformulated Statement of Shareholders’ Equity
(in millions)
Balance, October 1, 2006
2,228.5
Net payout to shareholders:
Stock repurchase
Sale of common stock
Issue of shares for employee stock options
Comprehensive Income:
Net income from income statement
Unrealized loss on financial assets
Currency translation gains
689.9
$
1,012.8
(46.8)
(225.2)
(740.8)
672.6
(20.4)
37.7
Balance, September 30, 2007
$2,177.6
Note: The closing balance excludes $106.4 million for “Stock-based compensation
expense” which is a liability rather than equity. (It is added to operating liabilities in the
reformulated balance sheet).
With comprehensive income identified, reformulate the (comprehensive) income
statement that totals to comprehensive income:
Reformulated Comprehensive Income Statement, 2007
(in millions)
Net revenues
$ 9,411.5
Cost of sales and occupancy costs
3,999.1
Store opening expenses
3,215.9
Other operating expenses
294.1
Depreciation and amortization
467.2
General and administrative expenses
489.2
Operating income from sales (before tax)
946.0
Tax reported
$ 383.7
Tax benefit of net interest
5.6
Tax on other operating income
(6.6)
382.7
563.3
Operating income from sales (after tax)
Other operating income, before-tax item
Gain on asset sales
Other operating charges
Tax at (38.4%)
Operating income, after tax-items
Income from equity investees
Currency translation gains
26.0
(8.9)
17.1
6.6
10.5
108.0
37.7
719.5
Operating income (after tax)
Net financing expenses
Interest expense
Interest income
Net interest expense
Realized gain on financial assets
Tax (at 38.4%)
156.2
38.2
(19.7)
18.5
(3.8)
14.7
5.6
9.1
Unrealized loss on financial assets
20.4
29.5
689.9
Comprehensive income
Note: Interest income and interest expense are given in the notes to the financial
statements in the Exercise 9.9. That note also identifies the other operating income
here.
The reformulated balance sheet is as follows:
Reformulated Balance Sheets
(in millions)
2007
2006
Operating Assets
Cash and cash equivalents
Short-term investments—trading securities
Accounts receivable, net
Inventories
Prepaid expenses and other current assets
Deferred income taxes, net
Equity and other investments
Property, plant and equipment, net
Other assets
Other intangible assets
Goodwill
40.0
73.6
287.9
691.7
148.8
129.5
258.8
2,890.4
219.4
42.0
215.6
40.0
53.5
224.3
636.2
126.9
88.8
219.1
2,287.9
186.9
37.9
161.5
Total operating assets
4,997.7
4,063.0
Operating liabilities
Accounts payable
Accrued compensation and related costs
Accrued occupancy costs
Accrued taxes
Other accrued expenses
Deferred revenue
Other long-term liabilities
Total operating liabilities
390.8
332.3
74.6
92.5
257.4
296.9
460.5
1,905.0
340.9
288.9
54.9
94.0
224.2
231.9
262.9
1,497.7
Net operating assets
3,092.7
2,565.3
710.2
0.8
700.0
0.8
Net financial obligations
Short-term borrowing
Current maturities of long-term debt
Long-term debt
Cash equivalents (281.3-40.0 in 2008)
Short-term investments (available for sale)
Long-term investments (available for sale)
Net financial obligations
Common shareholders’ equity
550.1
(241.3)
(83.8)
(21.0)
915.0
2.0
(272.6)
(87.5)
(5.8)
336.9
2,177.6
2,228.5
Notes:
3. Short-term investment (trading securities) is operating assets connected to
employees.
4. Stock-based compensation, excluded from the equity statement, has been
added to other liabilities.
b.
ROCE = 689.9 / 2,228.5 = 30.96%
RNOA = 719.5 / 2,565.3 = 28.05%
NBC = 29.5 / 336.9 = 8.76%
c.
ROCE = 28.05% + [0.151 x (28.05% - 8.76%)]
= 30.96%
d.
Operating profit margin = 719.5/9,411.5 = 7.64%
Operating profit margin from sales = 563.3/9,411.5 = 5.99%
ATO = 9,411.5/2,565.3 = 3.67
e.
OLLEV = 1,497.7/2,565.3 = 0.584
f.
Implicit interest on operating liabilities = 0.036 × 1,497.7 = 53.92
719.5 + 53.92
= 19.04%
ROOA =
4,063.0
RNOA = ROOA + OLLEV× (ROOA – 3.6%)
= 19.04% + 0.584 × (19.04% - 3.6%)
= 28.05%
E11.10. Operating Profitability Analysis: Home Depot, Inc.
a. Reformulation
If you have worked Exercise 9.10 in Chapter 9, you will have calculated the tax rate to
use in the income statement reformulation for 2005. This is the statutory rate (federal plus
state) at which interest income is taxed (or interest expense gets a tax saving). The
footnote gives the effective rate (36.8% for 2005), which is the effective rate from the
income statement (2,911/7,912 = 36.8%). But this is not the marginal rate for it includes
tax credits and foreign tax benefits, amongst other things. The marginal rate is the
statutory rate, federal and state combined (with the state rate recognizing that state taxes
are deductible in federal tax returns).
The federal statutory rate is 35%, but the state rate is not given. (Many firms do
report it.) Home Depot operates in many states; without more information, the statutory
rate is somewhat of a guess. Home Depot reports a ratio of state-to-federal taxes of
215/2,769 = 7.79% for 2005. Applied to the federal rate of 35%, this implies a state rate
of 2.72%, or a total rate for 2005 of 37.72%.
Following the same procedure for 2004, the ratio of state-to-federal taxes for 2004
is 217/2,395 = 9.06% and the implied state tax rate = 9.06% × 35% = 3.17%, giving a
total of 38.17%.
In the reformulation below, these rates are used for the tax allocation. Of course, given
the small net interest, the precise calculation does not matter.
Reformulated Income Statements, 2005 and 2004
($ millions)
2005
Net sales
Cost of sales
Gross profit
Selling and store operating costs
General and administrative
Operating income from sales, before tax
Tax as reported
Tax benefit of net debt
Operating income from sales, after tax
Other operating income – currency translation gains
Operating income
Interest expense
Interest income
Net interest expense
Tax on net interest
Comprehensive income
2004
73,094
48,664
24,430
15,105
1,399
2,911
5
70
56
14
5
16,504
7,926
2,916
5,010
137
5,147
64,816
44,236
20,580
12,588
1,146
2,539
1
9
5,138
Note: Currency translations gains are after tax (as are all items in other comprehensive
income)
62
59
3
1
13,734
6,846
2,540
4,306
172
4,478
2
4,476
Reformulated Balance Sheets, 2003-2005
2005
2004
2003
50
1,499
10,076
450
22,726
1,394
228
36,423
50
1,097
9,076
303
20,063
833
129
31,551
50
1,072
8,338
254
17,168
575
244
27,701
5,766
1,055
412
1,546
161
1,578
1,309
763
12,590
5,159
801
419
1,281
175
1,210
967
653
10,665
4,560
809
307
998
227
1,127
362
491
8,881
23,833
20,886
18,820
(456)
(1,659)
(369)
11
2,148
(325)
(1,053)
(1,749)
(84)
509
856
(1521)
(2,138)
(65)
(107)
7
1,321
(982)
Common equity
24,158
22,407
19,802
Averages:
Operating assets
Operating liabilities
Net operating assets
Net financial obligations
33,987
11,628
22,359
(923)
29,626
9,773
19,853
(1,252)
Common equity
23,282
21,105
Operating assets:
Operating cash
Receivable
Inventories
Other current assets
PPE (net)
Goodwill
Other assets
Operating liabilities:
Accounts payable
Accrued salaries
Sales tax payable
Deferred revenue
Income tax payable
Other accrued taxes
Deferred income tax
Other liabilities
Net operating assets
Net financial obligations:
Cash equivalents
Short-term investments
Notes receivable
Current debt
Long-term debt
b. Analysis of Operating Profitability
Second Level
ROCE
RNOA
PM
ATO
PM×ATO
2005
2004
22.07%
23.02%
7.04%
3.269
23.02%
21.21%
22.56%
6.91%
3.265
22.56%
Income statement ratios:
Profit Margin drivers (%)
Gross margin
Selling expense ratio
G&A Expense Ratio
Operating Sales PM before tax
Tax expense ratio
Sales PM
Other item PM
33.42
(20.67)
(1.91)
31.75
(19.42)
(1.77)
10.84
(3.99)
6.85
0.19
10.56
(3.92)
6.64
0.27
7.04
6.91
Note that the income statement ratios aggregate to the PM.
Turnover ratios (using average balance sheet amounts)
2005
Asset turnover drivers
Accounts receivable turnover
Inventory turnover
PPE turnover
Other asset turnover
Operating asset turnover
Accounts payable turnover
Other liability turnover
Note that the sum of individual
ATO
56.31
7.63
3.42
42.53
2.15
-13.38
-11.86
3.27
2004
1/ATO
0.018
0.131
0.293
0.024
0.465
(0.075)
(0.084)
0.306
ATO
59.77
7.44
3.48
53.17
2.19
-13.34
-13.19
3.26
1
1
equals
for all operating assets and liabilities.
ATO
ATO
1
is the amount of the asset or liability that is put in place to support sales.
ATO
1/ATO
0.017
0.134
0.287
0.019
0.457
(0.075)
(0.076)
0.306
CHAPTER TWELVE
The Analysis of Growth and Sustainable Earnings
Drill Exercises
E12.1 Analyzing a Change in Core Operating Profitability
∆Core RNOA = -1.47% = (-0.4% x 2.5) + (-0.1 x 4.7%)
=
-1.0%
- 0.47%
↓
↓
[Due to ∆PM] [Due to ∆ATO]
E12.2. Analyzing a Change in Return on Common Equity
ROCE for 2009: 15.2% = 11.28 + [0.4678 x (11.28 – 2.9)]
ROCE for 2008: 13.3% = 12.75 + [0.0577 x (12.75 – 3.2)]
∆ROCE
1.9%
∆RNOA
∆ROCE due to financing
-1.47%
3.37%
This change due to financing is due to a change in leverage and a change in SPREAD:
∆FLEV
0.4101
∆SPREAD
-1.17%
The explanation of the change in ROCE due to change in operating profitability
(∆RNOA) is given in Exercise E12.1. Using a similar scheme, the explanation of the
change due to financing is
∆ROCE due to financing = 3.37% = (-1.17% x 0.0577) + (0.4101 x 8.38%)
=
-0.07%
+ 3.44%
↓
↓
[Due to change in spread] [Due to change in leverage]
E12.3. Analyzing the Growth in Shareholders’ Equity
Change in CSE = 583 = (5,719 x 0.4) + (0.0167 x 16,754) – 1,984
= 2287.6 + 279.8 – 1,984.0
↓
Due to
Sales
↓
↓
Due to Due to
NOA Borrowing
E12.4. Calculating Core Profit Margin
The reformulated statement that distinguishes core and unusual items is as follows (in
millions of dollars):
Sales
Core operating expenses
Core operating income before tax
Tax as reported
Tax benefit of net debt
Tax on operations
Tax allocated to unusual items:
Core operatimg inome after tax
Unusual items
Start-up costs
Merger charge
Gain on asset disposals
667.3
580.1
(73.4 +13.8)
87.2
18.3
(0.39 × 20.5)
8.0
26.3
5.4
31.7
55.5
(4.3)
(13.4)
3.9
(13.8)
Tax effect (0.39)
5.4
(8.4)
Translation gain
8.9
Comprehensive operating income
0.5
56.0
Note:
1. The currency translation gain is transitory; it does not affect core
income.
2. Translation gains, like all items reported in other comprehensive
income are after-tax.
3. The gain on disposal of plant may attract a higher tax rate than 39% due
to depreciation recapture.
Core operating income (after tax)
= 55.5
Core profit margin
=
Core operating income (after tax)
Sales
= 8.32%
E12.5. Explaining a Change in Profitability
Reformulate balance sheets and income statements:
Balance Sheets
2009
C ash
A/R
Inventory
PP E
Accr. Liab.
A/P
D ef. T axes
NOA
100
900
2,000
8,200
(600)
(900)
(490)
S/T investm ents
Bank loan
Bonds payable
Preferred stock
9,210
C SE
Leverage (N FO /C SE )
Average leverage
2008
NFO
NOA
100
1,000
1,900
9,000
(500)
(1,000)
(500)
2007
N FO
(300)
(300)
4,300
1,000
5,000
4,210
9,210
4,300
1,000
5,000
5,000
10,000
10,000
1.188
1.086
Income Statements
1.000
0.853
NOA
120
1,250
1,850
10,500
(550)
(1,100)
(600)
11,470
N FO
(330)
3,210
1,000
1,000
4,880
6,590
11,470
.741
2009
Sales
CGS
S&A
Core OI b/4 tax
Tax on OI
Core OI after tax
Restructuring charge
Tax Benefit
Operating income
Net Financial expenses
Net interest expenses
Tax Benefit
Gain on retirement (after tax)
Preferred divs.
NI available for common
22,000
13,000
8,000
190
65
406
(138)
268
0
268
80
Tax on Core OI (2009) = 134 + 138 + 65 = 337
Tax on Core OI (2008) = 675 + 137
= 812
Net borrowing cost (NBC): Net fin. exp/average NFO
2009: 348/5,000 = 6.96%
2008: 248/4,940 = 5.02%
Return on net operating assets (RNOA): OI/average NOA
2009: 538/9,605
= 5.60%
2008: 1,838/10,735 = 17.12%
Core profit margin (PM): Core OI/Sales
2009: 663/22,000 = 3.01%
2008: 1,838/24,000 = 7.66%
2008
21,000
1,000
337
663
24,000
13,100
8,250
21,350
2,650
812
1,838
(125)
538
(348)
190
405
(137)
268
100
168
80
(248)
1,590
Asset turnover (ATO):
Sales/average NOA
2009: 22,000/9,605 = 2.290
2008: 24,000/10,735 = 2.236
Unusual items to net operating assets: UI/average NOA
2009: -125/9,605
2008:
Spread:
= -1.30%
=0
RNOA - NBC
2009: -1.36%
2008: 12.10%
Explaining ∆ROCE:
ROCE (2009) = CI avail for common/Average CSE = 190/4,605 = 4.13%
ROCE (2008)
= 1,590/5,795 = 27.44%
∆ROCE (2009)
= -23.31%
As ROCE = RNOA + [FLEV × (RNOA - NBC)], this change in ROCE is
determined by:
∆RNOA = -11.52%
∆FLEV = 1.086 – 0.853 = 0.233
∆NBC = 1.94%
Explaining the ∆ RONA component:
∆ RNOA
= [∆ core profit margin × turnover (2008)] + [∆ turnover × core
profit margin (2009)] + ∆ unusual items/NOA
= [-0.0465 × 2.290] + [0.054 × 0.0766] - 0.0130
= -0.1152
In words, the decrease in ROCE is explained by an decrease in profit margin (despite a small increase in
asset turnover) that was levered up by an decrease in the spread over net borrowing costs, the effect of
which was further increase by an increase in leverage. In addition there were unusual changes in 2009 that
reduced operating profitability.
E12.6. Analysis of Growth in Common Equity for a Firm with Constant Asset
Turnover
The ingredients:
2,009
4,560
301
0
902
3
Average CSE
Growth in average CSE
Growth in average NFO
Growth in sales
Asset turnover (Sales/Average NOA)
2,008
4,259
3
As asset turnover is constant and average net financial obligations did not change from
2004 to 2006, the growth in CSE is explained solely by the growth in sales:
Growth in CSE = Growth in sales ×
1
ATO
= 301
Applications
E12.7. Core Income and Core Profitability for The Coca Cola Company
Average balance sheet amounts are as follows:
Net operating assets
Net financial obligations
Common shareholders’ equity
2007
2008
Average
$26,858
5,114
$21,744
$18,952
2,032
$16,920
$22,905
3,573
$19,332
As no unusual items are reported in the income statement, all income reported is core income. So,
Core income from sales (after tax) = $5,453 million
Core operating income
= $6,121 million
One might be tempted to treat equity income from bottling subsidiaries as non-core income. However, this
is part of Coke’s business of selling beverages (they just do this business through bottling firms). The
equity income is not income from top-line sales, however; rather it is income from sales in the subsidiaries
that is reported here on a net basis (after expenses).
Here are the measures requested:
a. Core profit margin from sales = 5,453/28,857 =18.90%
b. Core profit margin = 6,121/28,857 = 21.21%
c. Core RNOA = 6,121/22,905 = 26.72%
E12.8. Identification of Core Operating Profit Margins for Starbucks
To reformulate the income statement to identify core income, first separate net financial income from
operating income, then separate core operating income from unusual items, then separate core operating
income from sales from other core income.
Reformulated Comprehensive Income Statement Identifying Core Operating Income,
2007
(in millions)
Net revenues
$ 9,411.5
Cost of sales and occupancy costs
3,999.1
Store opening expenses
3,215.9
Other operating expenses
294.1
Depreciation and amortization
467.2
General and administrative expenses
489.2
Operating income from sales (before tax)
946.0
Tax reported
$ 383.7
Tax benefit of net interest
5.6
Tax on other operating income
(6.6)
382.7
Core OI from sales (after tax)
Equity income from investees (after tax)
Core operating income
Unusual items, before-tax item
Gain on asset sales
Other operating charges
Tax at (38.4%)
563.3
108.0
671.3
26.0
(8.9)
17.1
6.6
10.5
Operating income, after tax-items
Currency translation gains
37.7
Operating income (after tax)
719.5
Net financing expenses
Interest expense
Interest income
Net interest expense
Realized gain on financial assets
Tax (at 38.4%)
38.2
(19.7)
18.5
(3.8)
14.7
5.6
9.1
20.4
Unrealized loss on financial assets
29.5
689.9
Comprehensive income
The question only asked for calculations of operating income, but the financing part of the statement is also
prepared to calculate the tax benefit ($5.6 million) from financing activities to allocate to the operating
activities. (You need only get to the $5.6 million number.) Note that taxes have also been allocated between
(taxable) unusual items and core operating income. The reformulated statement brings in the currency gains
and losses from the equity statement (which is an unusual item). Unusual items also include items in “net
interest and other income” that are detailed in the footnote. (Realized gains on available-for-sale
investments are gains on financial asset s, often called “investments as in the footnote.)
a.
Core operating income from sales = $563.3 million
b.
Other core income = $108.0 million (this is income from sales in subsidiaries but it is a net figure,
that is, sales minus expenses)
c.
Core operating profit margin from sales = $563.3 million/$,=9,411.5 million = 5.99%.
d.
Unusual items = $48.2 million
E12.9. Analysis of Changes in Operating Profitability: Home Depot, Inc.
First reformulate the statements, then carry out an analysis of profitability, followed up with an analysis of
the changes in profitability.
1.
The reformulated statements:
Reformulated Income Statements, 2005 and 2004
($ millions)
2005
Net sales
Cost of sales
Gross profit
Selling and store operating costs
General and administrative
Operating income from sales, before tax
Tax as reported
2004
73,094
48,664
24,430
15,105
1,399
2,911
16,504
7,926
64,816
44,236
20,580
12,588
1,146
2,539
13,734
6,846
Tax benefit of net debt
Operating income from sales, after tax
Unusual operating income – currency gains
Operating income
Interest expense
Interest income
Net interest expense
Tax on net interest
Comprehensive income
5
70
56
14
5
2,916
5,010
137
5,147
9
1
62
59
3
1
5,138
Note: Currency translations gains are after tax (as are all items in other comprehensive
income). The tax rates for the allocation of taxes were calculated as follows (from the
solution for Exercise 9.10 in Chapter 10):
The tax rate for the tax allocation is the marginal tax rate. The footnote gives the effective
rate (36.8% for 2005), which is the effective rate from the income statement (2,911/7,912
= 36.8%). But this is not the marginal rate for it includes tax credits and foreign tax
benefits, amongst other things. The marginal rate is the statutory rate, federal and state
combined (with the state rate recognizing that state taxes are deductible in federal tax
returns). The statutory tax rates are given in the Exercise.
2,540
4,306
172
4,478
2
4,476
Reformulated Balance Sheets, 2003-2005
2005
2004
2003
50
1,499
10,076
450
22,726
1,394
228
36,423
50
1,097
9,076
303
20,063
833
129
31,551
50
1,072
8,338
254
17,168
575
244
27,701
5,766
1,055
412
1,546
161
1,578
1,309
763
12,590
5,159
801
419
1,281
175
1,210
967
653
10,665
4,560
809
307
998
227
1,127
362
491
8,881
23,833
20,886
18,820
(456)
(1,659)
(369)
11
2,148
(325)
(1,053)
(1,749)
(84)
509
856
(1521)
(2,138)
(65)
(107)
7
1,321
(982)
Common equity
24,158
22,407
19,802
Averages:
Operating assets
Operating liabilities
Net operating assets
Net financial obligations
33,987
11,628
22,359
(923)
29,626
9,773
19,853
(1,252)
Common equity
23,282
21,105
Operating assets:
Operating cash
Receivable
Inventories
Other current assets
PPE (net)
Goodwill
Other assets
Operating liabilities:
Accounts payable
Accrued salaries
Sales tax payable
Deferred revenue
Income tax payable
Other accrued taxes
Deferred income tax
Other liabilities
Net operating assets
Net financial obligations:
Cash equivalents
Short-term investments
Notes receivable
Current debt
Long-term debt
2. The operating profitability analysis (as in the solution to Exercise E 11.8 in Chapter 11,
modified to distinguish core profitability):
ROCE
RNOA
PM
ATO
PM XATO
Core RNOA
UI/NOA
Income statement ratios:
Gross margin ratio
Selling expense ratio
G&A expense ratio
Operating PM before tax
Tax expense
nseratio
ratio
Core PM from sales
Unusual operating income to sales
Operating PM
2005
2004
22.07%
23.02%
7.04%
3.269
23.02%
22.41%
0.61%
21.21%
22.56%
6.91%
3.265
22.56%
21.69%
0.87%
33.42%
(20.67)
(1.91)
10.84
(3.99)
6.85%
0.19
7.04%
31.75%
(19.42)
(1.77)
10.56
(3.92)
6.64%
0.27
6.91%
Note that the income statement ratios agregate to the PM.
Currency gains are unusual items (UI), outside core operating income.
Turnover ratios (using average balance sheet amounts)
2005
Asset turnover drivers
Accounts receivable turnover
Inventory turnover
PPE turnover
Other asset turnover
Operating asset turnover
Accounts payable turnover
Other liability turnover
Note that the sum of individual
ATO
56.31
7.63
3.42
42.53
2.15
-13.38
-11.86
3.27
2004
1/ATO
0.018
0.131
0.293
0.024
0.465
(0.075)
(0.084)
0.306
ATO
59.77
7.44
3.48
53.17
2.19
-13.34
-13.19
3.26
1
1
equals
for all operating assets and liabilities.
ATO
ATO
1
is the amount of the asset or liability that is put in place to support sales.
ATO
1/ATO
0.017
0.134
0.287
0.019
0.457
(0.075)
(0.076)
0.306
3. Analysis of Changes in Profitability
∆RNOA = ∆Core RNOA + ∆(UI/NOA)
= 0.46%
The increase in RNOA of 0.46% in 2005 was due to an increase in core profitability of
0.72% and a drop in the profitability effect of currency changes of 0.26%.
∆Core RNOA = (∆Core PM x ATO2004) + (∆ATO x Core PM2005)
= (0.21% x 3.269) + (0.004 x 6.85%)
= 0.69% + 0.03%
= 0.72%
(allow for rounding error)
The increase in core profitability of 0.72% was due to an increase in core profit margin of
0.69% and a 0.03% effect from the increase in ATO.
The reasons for the increase in core PM and ATO can be discovered by comparing the
changes in expense ratios and individual ATOs above.
E12.10. Explaining Changes in Income: US Airways
First prepare the reformulated income statements to distinguish core operating
income from sales, other core income, unusual items and net financial expenses:
Core operating revenues
1998
8,688
1997
8,514
Core operating expenses
Personnel costs
Aviation fuel
Commissions
Aircraft rent
Other rent and landing fees
Aircraft maintenance
Other selling expenses
Depreciation and amortization
Other
3,101
623
519
440
417
448
342
318
1,466
3,179
805
595
475
420
451
346
401
1,258
Total operating expenses
7,674
7,930
Core operating income before tax
Tax as reported
1,014
584
1
Tax benefit of debt (38%)
Tax on unusual items
Core operating income from sales
Other core income: equity income in affiliates
Core operating income
Unusual items
Other income
Gain on sale of interests in affiliates
2
Less tax (38%)
364
(353)
43
1
56
(73)
(4)
0
(4)
1
Operating income
1
Tax effect (38%)
Preferred dividends
3
Net income, adjusted
(370)
954
30
984
13
180
193
(3)
(73)
604
Net financial expenses
Net interest
Notes: 1.
2.
408
606
1
607
1,104
112
148
43
69
6
56
92
64
75
529
120
156
948
Marginal tax rate is assumed to be 38%.
Gains on sale of securities may be taxed at a lower capital gains tax rate.
3.
Net income and net interest are before capitalized interest. ($3million in
1998 and $13 million in 1997).
Explaining increase in before-tax operating income from $584 million to $1,014
million; standardizing for the increase in sales:
(a)
1998
1997
35.7
7.2
6.0
5.1
4.8
5.2
3.9
3.7
16.9
88.5
11.7
100.2
37.3
9.5
7.0
5.6
4.9
5.3
4.1
4.7
14.8
93.2
6.9
100.1
As a percentage of sales:
Personnel costs
Fuel
Commissions
Aircraft rent
Other rent and landing fees
Aircraft maintenance
Other selling expenses
Depreciation and amortization
Other expenses
Total core operating expenses
Core PM before tax
Operating expenses as a percentage of sales declined in 1998;
the largest declines were in personnel costs, commissions and depreciation and amortization. But "other
expenses" (for which there is limited information) increased. Note that operating income, as reported, does
not include all components of operating income. Gains on sale of shares in operating affiliates are also
operating income. But reported operating income does identify core income (before tax).
While core operating income increased before tax, it decreased after tax. The after-tax decrease
was due to negative taxes in 1997 (see below). One could classify the negative taxes in 1997 as an unusual
item.
(b)
The decline in net income (on an increase in before-tax operating income) can be explained as
follows:
1. Transitory effect of negative taxes in 1997
2. Transitory gain on sale of shares of affiliates in 1997
3. Change in interest capitalization
4. Decrease in "other income"
5. Change in net financial expenses: a decrease in both after-tax net interest and
preferred dividends.
(c)
The negative taxes with positive income seems strange. This could be due to
either:
1. Tax credits in 1997 from features of operations that are given credits; this is
unlikely for an airline.
2. Changes in deferred taxes.
The second reason was indeed the case. US Airways had accumulated tax
benefits from operating losses in the year prior to 1997. In 1997 it determined
that it was "more likely than not" that it would be able to utilize these tax
benefits in the future. So it reduced its previous valuation allowance on
deferred tax assets substantially.
The calculation of 1997 tax expense, relative to 1996, was as follows (in
thousands):
1997
1996
Current provision:
Federal
State
Total current provision
$ 100,879
7,680
108,559
$ 6,423
3,000
9,423
Deferred provision:
Federal
State
Total deferred provision
(406,571)
(54,651)
(461,222)
2,686
2,686
Provision (credit) for income taxes
$(352,663)
$12,109
You see that taxes were assessed but the change in the deferred tax provision
yielded negative taxes.
The accounting for the deferred tax asset in the exercise shows the change
in the valuation allowance. The change of $642 million should be treated as a
transitory item.
Accordingly, the tax on core operating income would be
calculated as follows:
Tax on core operating income before unusual component
(370)
Change in valuation allowance
642
Core tax on operating income
272
(d)
1998 income is more indicative of future income:
1. It is the more recent income year.
2. It has fewer transitory items.
E12.11. Analysis of Effects of Operating Leverage: US Airways
(a)
The fixed and variable operating cost breakdown is:
Variable cost (VC)
Fixed cost (FC)
$3,636 million
4,038
$7,674 million
One measure of operating leverage is
FC = 1.11
VC
Another measure is
OLEV =
4.98
(b)
% change in core operating income =
4.98%
That is, operating income will increase 4.98% for an increase in sales by 1%.
This can be proofed:
1% increase in sales
Variable cost (at 41.9%)
Contribution Margin
$86.88 million
36.40
50.48
Additional contribution as a % of operating income =
50.48
= 4.98%
1,014
(c)
Breakeven occurs at the point where sales = fixed costs + variable costs, or where
contribution margin equals fixed costs. As fixed costs are $4,038 million, that point is
Breakeven = 4,038/0.581 = $6,950 million of sales
where 0.581 is the contribution margin ratio (contribution margin/sales).
CHAPTER THIRTEEN
The Value of Operations and the Evaluation of Enterprise Price-to-Book
Ratios and Price-Earnings Ratios
Drill Exercises
E13.1. Residual Earnings and Residual Operating Income
Using beginning of period balance sheet amounts,
Residual earnings (RE) = 900 – (0.12 × 5,000) = $300 million
Residual operating income (ReOI) = 1,400 – (0.11 × 10,000) = $300
Residual financing expense (ReNFE) = 500 – (0.10 × 5,000) = 0
E13.2. Calculating Residual Operating Income and its Drivers
2006
2007
2008
2009
Operating income (OI)
187.00
200.09
214.10
229.08
Net operating assets (NOA)
1,214.45
1,299.46
1,390.42
1,487.75
RNOA (%)
16.48
16.48
16.48
Residual operating income (ReOI)
77.48
82.90
88.71
Growth rate for NOA
7.0%
7.0%
7.0%
E13.3. Calculating Abnormal Operating Income Growth
The long-hand method:
Operating income (OI)
Net operating assets (NOA)
Free cash flow (C-I = OI - ∆ NOA)
Income from reinvested free cash flow (at 10.1%)
Cum-dividend OI
Normal OI
Abnormal OI Growth (AOIG)
2006
2007
2008
2009
187.00
1,214.45
107.55
200.09
1299.46
115.08
10.86
210.95
205.89
5.06
214.10
1,390.42
123.31
11.62
225.72
220.30
5.42
229.08
1,487.75
131.76
12.45
241.53
235.72
5.81
The short hand method: AOIG = ∆ReOI, so just calculate the changes in ReOI from the
ReOI calculated in Exercise E13.2.
2007
2008
2009
Residual operating income (ReOI)
77.48
Abnormal operating income growth (AOIG)
(As there is no ReOI for 2006, the ∆ReOI cannot be calculated for 2007)
82.90
88.71
5.42
5.81
E13.4. Residual Operating Income and Abnormal Operating Income Growth
2009
2,700 - (0.10 × 20,000)
= 700
Residual operating income
(ReOI)
Abnormal operating income growth
(AOIG = ∆ReOI)
2008
2,300 – (0.10 × 18,500)
= 450
250
E13.5. Cost of Capital Calculations
By CAPM,
Equity cost of capital = 4.3% + [1.3 × 5.0%] = 10.8%
Debt cost of capital = 7.5% × (1- 0.36)
= 4.8%
Equity cost of capital
Cost of capital for debt
(after tax)
10.8%
4.8%
Market value of equity
Net financial obligations
Market value of operations
$2,361 million ($40.70 x 58 million)
1,750
4,111
 2,361
  1,750

Cost of capital for operations (WACC) = 
× 10.8%  + 
× 4.8%  = 8.25%
 4,111
  4,111`

E13.6. Calculating the Required Return for Equity
= 11.47%
E13.7. Residual Operating Income Valuation
This carries Exercise E13.2 over to valuation.
2005A
2006E
2007E
2008E
2009E
1,135
187.00
1,214.45
200.09
1,299.46
214.10
1,390.42
229.08
1,487.75
RNOA (%)
16.48
16.48
16.48
16.48
Residual operating income (ReOI)
Discount rate (1.101t )
72.37
1.101
77.48
1.212
82.90
1.335
88.71
1.469
Operating income (OI)
Net operating assets (NOA)
PV of ReOI
65.73
Total PV of ReOI
63.91
62.12
60.37
253
Continuing value (CV)
PV of CV
3061.93
2,084
Value of NOA
3,472
Book value of NFO
720
Value of equity
2,752
The continuing value calculation:
CV =
PV of CV =
88.71 × 1.07
= 3,061.93
1.101 − 1.07
3,061.93
= 2,084.36
1.469
As ReOI is growing at 7% from 2007 to 2009, this is extrapolated into the future as the long-term growth
rate.
(Allow for rounding errors)
Residual operating income (ReOI) is OIt – (ρF – 1)NOAt-1. So, for 2006, ReOI = 187.00 – (0.101 x 1,135) = 72.37
E13.8. Abnormal Operating Income Growth Valuation
This extends Exercises E13.2 and E13.3 to valuation.
2005A
2006E
2007E
2008E
2009E
187.00
200.09
214.10
229.08
1,214.45
1,299.46
1,487.75
RNOA (%)
16.48
16.48
1,390.4of
CV2
16.48
Residual operating income (ReOI)
72.37
77.48
82.90
88.71
5.06
5.42
5.81
Operating income (OI)
Net operating assets (NOA)
1,135
Abnormal operating income growth (AOIG)
In this calculation, AOIG is just the change in ReOI. One can also calculate AOIG
as follows, and proceed from there to the valuation:
Operating income (OI)
Net operating assets (NOA)
2005A
2006E
2007E
2008E
2009E
1,135
187.00
1,214.45
200.09
1299.46
214.10
1,390.42
229.08
1,487.75
16.48
Free cash flow (C-I = OI - ∆ NOA)
Income from reinvested free cash flow (at 10.1%)
Cum-dividend OI
Normal OI
Abnormal OI Growth (AOIG)
Discount rate
PV of AOIG
Total PV of AOIG
Continuing value
PV of continuing value
Forward OI for 1997
Capitalization rate
Value of operations
Book value of NFO
Value of equity
107.55
115.08
10.86
210.95
205.89
5.06
1.101
4.60
123.31
11.62
225.72
220.30
5.42
1.212
4.46
131.76
12.45
241.53
235.72
5.81
1.335
4.35
13.41
200.54
150.22
87.00
350.63
0.101
3,472
720
2,752
↵
The continuing value calculation:
CV =
5.81×1.07
= 200.54
1.101 − 1.07
Present value of CV:
PV of CV =
200.54
= 150.22
1.335
As AOIG is growing at 7% from 2007 to 2009, this is extrapolated into the future as the
long-term growth rate. Note that ReOI is also growing at 7%: if ReOI grows at 7%, then
AOIG must also grow at 7%.
The calculations above are as follows:
Income from reinvested free cash flow is prior year’s free cash flow earning at the
required return of 10.1%. So, for 2007, income from reinvested free cash flow is
0.101 x 107.55 = 10.86.
Cum -dividend OI is operating income plus income from reinvesting free cash flow. So,
for 2007, cum-dividend OI is 200.09 + 10.86 = 210.95.
Normal OI is prior years operating income growing at the required return. So, for 2007,
normal OI is 187.00 x 1.101 = 205.89.
Abnormal OI growth (AOIG) is cum-dividend OI minus normal OI. So, for 2007,
AOIG is 210.95 – 205.89 = 5.06. AOIG is also given by OIt-1 × (Gt - ρF). So, for 2007,
AOIG is (1.1281 – 1.101) × 187.00 = 5.06.
But AOIG is also always equal to the change on ReOI.
E13.9 Growth, the Cost of Capital, and the Normal P/E Ratio
(a)
The repurchase was at fair value (value received was equal to value
surrendered). So there is no effect on value. More technically, the value
of the equity is driven by the value of the operations and the value of the
operations did not change. The total dollar value of the equity changed,
but not the per-share value.
(b)
The $10.00 million is operating income (from operations) with no debt
service. The net financial expense increased to $2.50 million due to the
new debt, reducing earnings (to the equity) to $7.5 million.
(c)
Although forecasted earnings decreased to $7.5 million, shares
outstanding dropped from 10 million to 5 million, increasing eps: stock
repurchases increase eps (providing leverage is favorable).
(d)
The required return for the equity is given by the following calculation:
Required Equity Return = Required Return for Operations
+ (Market Leverage × Required Return Spread)
where
Market Leverage
=
Value of Net Debt
Value of Equity
Required Return Spread
= Required Return for Operations After- tax Cost of Debt
So, after the stock repurchase,
 $ 50million

Required return for equity = 10% + 
× (10% − 5% ) = 15%
 $50million

(e)
The expected ROCE for Year 1 is 15%, an increase over the 10% before
the repurchase. As the required return was 15%, the expected residual
earnings is zero – as must be the case for the equity is worth its book
value.
(f)
The case with leverage:
The equity must be worth its book value (as expected residual operating
income for years after Year 1 is zero), and expected Year 1 book value, is
$57.50 million, or $11.50 per share.
The case with no leverage:
Again, the value of the equity must be worth its book value, $110.0
million, or $11.00 per share.
The leverage case gives a higher expected price per share (target
price) at the end of Year 1, so it looks as if leverage has added value. But,
the expected price must be higher in the leverage case to yield a higher
expected return to compensate for the higher risk of not getting the
expected price. Equity value is always expected to grow at the required
equity return (before dividends). In the leverage case, Year 0 per-share
value is $10.00 and the required return is 15%, giving an expected Year 1
value of 11.50 ($10.00 x 1.15). In the no leverage case, Year 0 per-share
value is also $10.00, but the required return is only 10%, giving an
expected Year 1 value of $11.00 ($10.00 x 1.10). In both cases, the present
value of the expected Year 1 price is $10.00, discounting with the
(leverage) risk adjusted discount rate.
Note that the value of the equity in the leverage case is expected to
grow at 14.6% in Year 2 because that is the required return for equity at
the beginning of Year 2: financial leverage has changed over Year 1,
changing the required return. Note that the ROCE for Year 2 is 14.6%
also, giving expected residual earnings of zero for Year 2. Do you see
how accounting data and required returns fit together?
(g)
For the leverage case:
The eps in Year 1 is expected to be $1.50 and the price-per-share is
expected to be $11.50. So the P/E is 7.67. This P/E is appropriate for a
normal P/E. The required equity return is 15%. (after the stock
repurchase) and so the normal P/E is
1.15
= 7.67.
0.15
For the no-leverage case:
Eps in Year 1 are expected to be $1.00 and the price $11.00. So the P/E is
expected to be 11.0. This is a normal P/E for a required return of 10%.
Why are the two P/Es different? Well, they are both normal P/Es, so
earnings growth is expected at a rate equal to the required return. But the
required equity return is different, and P/E ratios are based on both
expected growth and the required return.
E13.10 Levered and Unlevered P/B and P/E
Value of the equity = $233 × 2.9 = $675.7
Value of the operations = $675.7 + 236 = $911.7
(a)
Levered P/E
= 675.7/56 = 12.07
(b)
Enterprise P/B = 911.7/469 = 1.94
(no dividends)
Enterprise P/E = (VNOA + FCF)/ OI
What was the free cash flow? Free cash flow is equal to
C – I = NFE - ∆NFO + dividends = 14
Thus, Enterprise P/E = 13.22
You might prove that the levered and unlevered multiples reconcile according to
equations 13.10, 13.11, and 13.12 in the text. (The net borrowing cost (NBC) = 5.93%).
E13.11. Levered and Unlevered P/E Ratios
First value the firm from forecasted residual operating income or abnormal operating
income growth:
2009A
2010E
2011E
2012E
Residual o per at ing income
Ab normal operating i nco me growth
PV o f ReO I(1 8/0.0 9)
N et operati ng assets
V al ue o f operati ons
N et financial obligat ions
V al ue o f equity
18
18
0
18
0
Fo recast ed free cash flow :
O I- N O A
135
135
1 35
Fo recast ed div idend :
d= Earnings - CSE
120
120
1 20
(a) Fo recasted valu e of oper atio ns
Forecasted valu e of equi ty
1,50 0
1,20 0
1,50 0
1,20 0
1,500
1,200
(b) Levered P/E ratio
U nlevered P/ E rati o
11.0 0
12.1 1
11.0 0
12.1 1
11.00
12.11
200
1300
1500
300
1200
The forecasted residual operating income is expected to be a perpetuity of $18
million, and net operating assets are expected to be $1,300 always. So the value of the
 18 
operations is expected to be 1,300 + 
 =1,500 in all years. The "cum-dividend"
 0.09 
value of the operations in 2010 is expected to be 1,500 + free cash flow = 1,500 + 135 =
1,635. So the "cum-dividend" value is growing at the required return of 9% (and so on
for subsequent years).
The value of the operations can also be calculated using the abnormal earnings
growth method. As residual earnings are not forecasted to grow, abnormal operating
income growth (AOIG) is forecasted to be zero. Accordingly, the value of the operations
in calculated by capitalizing forward operating income:
V NOA = 135/0.09 = 1,500
and so for all years.
The value of the equity is (with similar reasoning) expected to remain at $1,200.
The cum-dividend equity value in 2010 is expected to be 1,200 + 120 = $1,320
The levered and unlevered trailing P/E ratios are calculated using these cumdividend (dividend-adjusted) values:
Unlevered Trailing P/E = 12.11
This P/E is a normal for a cost of capital for operations of 9%:
1.09
= 12.11 .
0.09
The unlevered forward P/E is:
Unlevered Forward P/E = 11.11
This is normal for a cost of capital of 9%:
1
= 11.11. Normal unlevered P/E’s are
0.09
appropriate because residual operating income is forecasted to be constant and abnormal
operating income growth is zero.
Now to the levered P/E:
Trailing Levered P/E = 11.0
This is a normal P/E for a cost of capital of 10%.
Forward Levered P/E = 10
This is a normal P/E for a cost of capital of 10%.
(c)
As earnings are expected to be constant (at $1,000 million), residual
earnings (on equity) must also be constant. So the levered P/E is a normal
P/E. For a normal P/E of 11.0, the equity cost of capital is 10%.
You can prove this with the calculation:
Required equity return =
Applications
 300

9% + 
× (9% − 5% ) = 10%
1,200

E13.12. The Quality of Carrying Values for Equity Investments: SunTrust Bank
Sun Trust Banks acquired the Coke shares many years earlier. The historical cost of
$110 million is a poor indicator of their value. The current market value of $1,077
million is a better quality number. But beware: was the market value an efficient price,
or was Coke undervalued or overvalued in the market? Would we accept the market
value of Coke’s shares during the bubble of 1997-2000 as fair value? Coke was a hot
stock then whose market price subsequently declined.
E13.13. Using Market Values in the Balance Sheet: Penzoil
The investment in Chevron is an operating asset and the income from the investment is operating income. But the income
reported from the investment is in the form of dividends and unrealized gains and losses, neither of which is very informative
about the value of the Chevron shares. The fair value is, however.
So, to value PennzEnergy, include the Chevron shares in net operating
assets at market value and apply the residual operating income model to the rest
of the operations. Calculate residual operating income by excluding Chevron
dividends and unrealzed gains from operating income and exclude the Chevron
investments from the NOA to be charged at the cost of capital:
Value of PennzEnergy’s operations
= Net operating assets + Present value of residual earnings from
operations other than the Chevron investment.
The ReOI adjusted for the Chevron investment is:
Operating income before Chevron dividends and unrealized gains
- [cost of capital for operations x (NOA – Fair Value of Chevron investments)]
This applies the principle that forecasting is not required for assets at fair value on the balance sheet.
Note: This evaluation does assume that the fair (market) value of Chevron’s shares is an “efficient”
one.
E13.14.
Enterprise Multiples for IBM Corporation
Here are the totals for IBM’s balance sheet, first with book values and then with market values:
Book Value
Market Value
Net operating assets (NOA)
48,089
160,909
Net financial obligation (NFO)
19,619
19,619
Common equity (CSE)
28,470
1,385.2 × $102 =
141,290
The amounts for NOA and the market value of NOA are obtained by adding NFO back to CSE. The book
value of NFO is considered to be the market value.
a.
Levered P/B = 4.96
Unlevered (enterprise) P/B = 3.35
Leverage explains the difference according to the formula,
Levered P/B = Unlevered P/B + FLEV × [Unlevered P/B – 1.0]
4.96 = 3.35 + (0.689 × 2.35)
b.
Forward levered P/E = 11.68
To get the unlevered P/E, first calculate forward OI:
Earnings forecast for 2008: $8.73 × 1,385.2 shares
Net financial expense for 2008: $19,619 × 3.3%
Forward operating income
$12,092.8
647.4
$12,740.2
Forward unlevered (enterprise) P/E = $160,909/$12,740 = 12.63
E13.15. Residual Operating Income and Enterprise Multiples: General Mills, Inc.
Free cash flow
a. ReOI (2008)
= 1,351
= 1,188
b. Market value of equity = $60 × 337.5 shares = 20,250
Net financial obligations
6,458
Minority interest ($242 × 3.26)
789
Enterprise market value
27,497
(Minority interest is valued at book value multiplied by the P.B ratio for common
equity).
Enterprise P/B = 27,497/12,847 = 2.14
c. (This question is not in all printings of the book)
Trailing P/E =
P+d
E
The trailing P/E is usually calculated on a per-share basis, with dividends being
dividends per share. Per-share amounts are not giving in the Exhibits, but one can
calculate a P/E on a total dollar basis, with the dividend being the net dividend.
The net dividend = Comprehensive income – ∆CSE = 752. So the trailing P/E is
=
20,250 + 752
= 12.74
1,649
On the required return: The WACC number calculated in Box 13.2 uses a number of
inputs that give one pause (see Box 13.3):
- market values are used for the weighting, but it is market value that
valuation tries to challenge. One is building the speculation in price into
the calculation.
- Market risk premiums used to get the equity required return (5% here) are
just a guess. More speculation.
- Betas are estimated with error.
Does 5.4% seem a lit low? It’s only 1.4% above the risk-free rate (of 4% in Box 13.2).
This is a low beta firm, but surely less risky high-grade bonds would yield more?
E13.16. Calculating Residual Operating Income: Dell Computer
NOA, beginning of year = 13,230 – 20,439 = -7,209 (NOA are negative)
ReOI = OI – (0.12 x NOA)
= 3,483
Because Dell’s NOA were negative, its ReOI is greater than is operating income.
Dell generated value in operations from
(1)
Operating income of $1,325 million (sales less operating expenses in
trading with customers)
(2)
A negative investment in NOA: shareholders earned 12% on operating
debt in excess of operating assets. (Operating creditors financed operating
assets and more). Dell used other people’s money. See Chapter 9 for
coverage of Dell.
Further analysis of the drivers of residual operating income would involve analysis of
profit margins and asset turnovers.
E13.17. Residual Operating Income Valuation: Nike, Inc., 2004
Here are the totals for Nike’s balance sheet at the end of 2004, first with book values and then with market
values:
Book Value
Market Value
Net operating assets (NOA)
4,551
19,444
Net financial assets (NFA)
289
289
Common equity (CSE)
4,840
263.1 × $75
=
19,733
The amount for the market value of NOA is obtained by subtracting NFA from the market value of CSE.
The book value of NFO is considered to be the market value.
a.
Levered P/B = 4.08
Unlevered (enterprise) P/B = 4.27
b. ReOI = 588.6
c. RNOA = 22.19%
d. OI for 2005 = NOA at the end of 2004 × Forecasted RNOA
= 1,010
ReOI for 2005
d.
= 618.6
If ReOI is expected to be constant for 2005 onwards, the value is
E
V2004
= CSE 2004 +
E
V2004
= 4,840 +
Re OI 2005
ρF − g
618.6
= $18,287.8 or $69.51 per share
1.086 − 1.04
E13.18. Valuation of Operations: Nike, Inc., 2005
(a)
Analysts’ eps forecast
Shares outstanding
Analysts’ earnings forecast
Forecast of net financial income
1,012 × 0.032
Forecast operating income
$5.08
261.1 million
$1,326.4 million
Forecasted RNOA = 1,294/4,632
(using beginning-of-year NOA)
27.94%
32.4
$1,294.0 million
(b) Forecasted ReOI = [27.94% - 8.6% ] × 4,632 = 895 .6 million
Value
= $25,114 million, or $96.18 per share
(c) If ReOI is to grow at 4%, then abnormal operating income growth will also grow at
at 4%, and the formula for calculating the value of the equity will be
Value of equity =
AOIG2 
1 
+ NFA
OI 1 +
ρF −1 
ρ F − g 
where g is the forecasted growth rate of 4%.
First calculate AOIG two years ahead (2007). There are two methods for doing this.
Method 1: Difference between cum-FCF OI for 2007 minus normal OI for 2007
Forecast of OI for 2007 = NOA2006 × RNOA2007
NOA2006 = 4,817.3
OI2007 = 1,345.9
FCF2006 = 1,108.7
AOIG2007 = $35.95 million
Method 2 (much simpler!): AOIG is growth in residual operating income from the
previous year
AOIG2007 = 35.82 (allow for rounding error)
Accordingly, the valuation is:
Value of equity = $25,113 million or $96.18per share
(d)
Value of operations = $24,101 million
(e) ReOI is driven by RNOA and growth in net operating assets. So, if RNOA is
forecasted to be constant, net operating assets must be forecasted to grow at 4% per year.
(f) Forward enterprise P/E = $24,101/$1,294 = 18.63
Forward levered P/E = $25,113/$1,326.4 = 18.93
(ELEV1 = NFE/Earnings = -32.4/1,326.4 = -0.0244
(g) Stock repurchases change financial leverage; in this case, Nike liquidated its financial
assets to pay for the stock repurchase. Operating income will not be affected because
NOA are not affected by stock repurchase. With fewer shares outstanding, eps will
increase, as the denominator effect (fewer shares) overwhelms the number effect (loss in
interest income on the financial assets). The only exception is the case where financing
leverage is unfavorable (RNOA less than RNFA). Also, the expected eps growth rate
will increase. But, if the share repurchase is at fair market value, price will not change.
See Boxes 13.5 and 13.6.
E13.19 Stock Repurchases: Expedia, Inc.
a. EPS and the EPS growth rate are likely to increase. See Box 13.5.
b. Risk increases for shareholders. See the reversed WACC formula in equation
13.8: the required return for operations does not change, but the increase in
leverage increases the required return for equity.
c. If repurchases are made at fair value, they cannot add to the per-share value.
However, if the firm pays less than fair value (buying the shares cheaply), it will
add value for shareholders (who did not sell their shares). See Box 13.6. A P/E of
26 looks high; if Expedia is overpaying, then it is losing value for shareholders.
d. No. Management can increase EPS with a stock repurchase but not add value for
shareholders, yet get a bonus.
CHAPTER FOURTEEN
Anchoring on the Financial Statements:
Simple Forecasting and Simple Valuation
Drill Exercises
E14.1. An SF2 Forecast and a Simple Valuation
a. ReOI2010 = $35.7 million
Therefore,
OI2010 = $161.4 million
b. With ReOI2010 forecasted to be a constant, an SF2 valuation applies:
= $1,614 million
Forward (enterprise) P/E
= 10.0
Constant ReOI (and an SF2 valuation) implies a normal P/E ratio for a 10% required
return)
E14.2. An SF3 Forecast and a Simple Valuation
a. Core RNOA2009 = 990/9,400 = 10.53%. This is the SF3 forecast of RNOA for
2010.
SF3 forecast of OI for 2010 = $1,019.5 million
b. Growth rate for NOA in 2009 = 9,682/9400 = 1.03 (3%)
ReOI2010 = 1,019.5 – (0.09 × 9,682) = 148.12
An SF3 valuation applies the NOA growth rate from the financial statements:
= $10,153.7 million
Enterprise value = 12,140.7
Enterprise P/B = 12,140.7/9,682 = 1.25
E14.3. Two-Stage Growth Valuation
Free cash flow for 2010
= 334
Reinvested FCF for 2008 =334 × 0.09 = 30.06
OI for 2011
= 868.00
Cum-dividend OI for 2011
898.06
Cum-div OI growth rate for 2011 = 898.06/782 = 1.1484 (14.84%)
a.
= $18,837.5 million
Value of equity = Enterprise value – NFO = $18,081.5 million
b. Forward enterprise P/ = 24.09
(This is equal to the term that multiplies the forward earnings of 782 in Part b)
E14.4. Reverse Engineering
Reverse engineer the SF3 formula:
P NOA = NOA ×
RNOA1 − ( g − 1)
ρF − g
The solution for the expected return is ρ = 1.1287 (12.87%)
The following formula gives the solution for the expected return:

NOA 
 NOA
 
Expected return =  NOA × Forecasted RNOA + 1 − NOA  × ( g − 1)
P
P
 


(equation 14.8)
= 12.87%
(Note: this is the expected return for investing in the firm, not the (levered( return for
investing in the stock)
E14.5. Reverse Engineering with Two-stage Growth Rates
a. Free cash flow for 2010
= 334
Reinvested FCF for 2008 =334 × 0.09 = 30.06
OI for 2011
= 868.00
Cum-dividend OI for 2011
898.06
Cum-div OI growth rate for 2011 = 898.06/782 = 1.1484 (14.84%)
b. Use the two stage growth valuation formula:
V0NOA = OI 1 ×
1  G2 − Glong 


ρ F − 1  ρ F − Glong 
Set VNOA equal to the current enterprise price, 756 + ($52 × 450) = $24,156 million:
24,156 = 782 ×
1  1.1484 − g 
0.09  1.09 − g 
Thus, g = 1.057, a growth rate of 5.7%
The market is forecasting a 5.7% growth rate while you are forecasting a growth rate
of 4%. The stock looks expensive to you.
(The solution can also be obtained by plugging in your forecasts and comparing the
intrinsic value they imply with the market price.)
E14.6. Simple Valuation with Sales Growth Rates
If RNOA is constant and ATO is also constant, the growth rate for ReOI is given by the
sales growth rate. So,
 RNOA − ( g − 1) 
V0NOA = NOA × 

ρF − g


Hence, the enterprise P/B ratio =
0.155 − 1.05
1.095 − 1.05
= 2.33
E.14.7 Simple Forecasting and Valuation
(a)
Residual operating income (ReOI) is
91.4 = (12% - required return) × 4,572
So required return = 10%
(b)
Value of equity = $4,243 million
(c)
Required return for equity
= 11.17%
So the comprehensive earnings forecast for 2008 is
Operating income
548.6
(4,572 × 12%)
Net financial expense
74.6
(1,243 × 6%)
Comprehensive
474.0
The residual earnings forecast is
RE
= 474.0 - (0.1117 × 3,329) = 102.2
Applications
E14.8. Simple Valuation for General Mills, Inc.
a. An SF2 valuation forecasts ReOI for 2009 as the same as Core ReOI for 2008.
ReOI2008 = 1,560 – (0.08 × 12,297) = 576.2
One can also forecast the ReOI for 2009 by forecasting OI for 2009 as an SF2
forecast:
OI2009
= 1,604
ReoI2009 = 576.2
The SF2 valuation:
E
V2008
= 6,216 +
576.2
0.08
= $13,418.5 million or $39.76 per share
b. The SF3 forecast of OI for 2009 in NOA at the end of 2008 earning at the core
RNOA rate:
Core RNOA2008 = 1,560/12,297 = 12.69%
OI2009 = 12,847 × 0.1269 = 1,630.3
ReOI2009 = 1,630.3 – (0.08 × 12,847) = 602.5
ReOI2009 can also be calculated by growing ReOI2008 by the NOA growth rate
for 2008:
NOA growth rate for 2008 = 12,847/12,297 = 4.47%
ReOI2009 = 576.2 × 1.0447 = 602.5 (allow for rounding error)
The SF3 valuation applies the NOA growth rate in 2008 as ReOI growth:
E
V2008
= 6,216 +
602.5
1.08 − 1.0447
= $23,285 million or $68.99 per share
The SF3 valuation can also be calculated by applying the enterprise P/B multiplier
to NOA, as in model 14.3a:
 Core RNOA − ( g − 1) 
V0NOA = NOA × 

ρF − g


 0.1269 − 0.0447 
V0NOA = 12,847 × 

 1.08 − 1.0447 
= 12,847 × 2.329
= 29,916
NFO
VE
6,631
(NOA – CSE)
23,285 or $68.99 per share
E14.9. Simple Valuation for Coca-Cola Company
a.
2005
2004
2003
2002
Core PM (CoreOI/Sales)
21.40%
22.40%
21.30%
22.10%
ATO (Sales/NOA)*
1.395
1.382
1.397
Core RNOA (PM × ATO)
29.85%
30.96%
29.76%
Sales growth rate
6.26%
4.24%
6.61%
Average sales growth rate
5.70%
* On beginning-of-year NOA
b.
c.
Enterprise value is given by the SF3 multiplier formula:
 Core RNOA − ( g − 1) 
V0NOA = NOA × 

ρF − g


NOA = $16,945 + 1,010 = $17,955
Set Core RNOA = 29.85% (as in 2005; one can also use average of 30.19% for 2003-05)
Set growth (g) = average sales growth rate
= 5.70%
(this is NOA growth rate with constant ATO)
 0.2985 − 0.057 
V0NOA = 17,955 × 

 1.10 − 1.057 
= $100,840 million
NFO
VE
1,010
$ 99,830 or 42.14 per share on 2,369 million shares
E14.10. Reverse Engineering for Starbucks Corporation
a.
(1) Core operating PM = 671 / 9,412 = 7.13 %
(2) Core RNOA = 671/ 2,565 = 26.16 %
(3) ATO = 9,412/2,565 = 3.669
(4) NOA growth rate = 3,093/2,565 – 1 = 20.58%
Operating income, 2008
= NOA2007 x Core RNOA2007
= 809.4
b.
ReoI2008 = (0.2616 – 0.09) x 3,093
= 530.8
(One can also get the number by forecasting OI2008 = NOA2007 × 0.2616)
c.
Market price of equity = $20 x 738.3 million shares = 14,766
The reverse engineering problem:
14,766 = 2,178 +
530.8
1.09 − g
g = 1.048 (a growth rate of 4.8 %)
d,
Now reverse engineer the SF3 model for the expected return: Solve for ρ:
 RNOA − ( g − 1) 
P0NOA = NOA × 

ρF − g


The formula is:

NOA 
 NOA
 
Expected return =  NOA × Forecasted RNOA + 1 − NOA  × ( g − 1)
P
P
 


Enterprise price = Equity price + NFO = 15,681
Enterprise book/price = 0.197
(eq. 14.8)
Expected return = [0.197 × 26.16%] + [0.803 × 3.5%]
= 7.96%
E14.11. A Simple Valuation and Reverse Engineering: IBM
a. OI2005
= $7,915.6 million
ReOI2005
= $2,736.8 million
 0.188 − 0.088 
E
b. V2004
= 42,104 × 
 - 12,357
 1.123 − 1.088 
= 120,298 -12,357.0
= $107,941 million or $65.59 per share on 1,645.6 million shares
Forward enterprise P/E = 120,298/7,915.6 = 15.20
Enterprise P/B ratio = 120,298/42,104 = 2.86 (the amount in the square brackets
above)
a. Set VE = $95 × 1,645.6 million shares = $156,332 million:
$156,332 = 42,104 ×
0.188 − 0.088
- 12,357
ρ − 1.088
The solution for ρ, the expected return, is 1.1130 (an 11.3% return)
This expected return is less than the required return, so the stock is expensive.
Note that the expected return is solved with the following formula (equation 14.8)
E14.12. A Simple Valuation with Short-term and Long-term Growth Rates:
Cisco Systems
Pro forma Cisco as follows:
2003
2004
Eps
0.54
0.61
Dps
Reinvested dividends
0.00
0.00
Cum-dividend earnings
0.61
Cum-div growth rate (G2)
Long-term growth (Glong)
12.96%
4.0%
Applying the two-stage growth formula:
NOA
V2002
= OI 1 ×
1  G2 − Glong 


ρ F − 1  ρ F − Glong 
= $10.75 per share
(The forward P/E is 19.9). This valuation is less than the market price of $15. The
market is pricing Cisco at a forward P/E of 15/0.54 = 27.8. So the market implicitly is
seeing long-term growth in excess of 4% (if the required return is 9%) if one takes
analysts forecasts for 2003 and 2004 as sound estimates.
E14.13. Comparing Simple Forecasts with Analysts’ Forecasts: Home Depot Inc.
A summary of the reformulated balance sheets is given in the exercise, but the
income statement has to be reformulated to identify core operating income:
Reformulated Income Statements, Fiscal Year Ended January 30, 2003 –
2005 ($ millions)
2005
Net sales
Cost of sales
Gross profit
Selling and store operating costs
General and administrative
Core operating income before tax
Tax as reported
Tax benefit of net debt
Core operating income after tax
Interest expense
2004
2003
73,094
48,664
24,430
15,105
1,399
2,911
5
70
16,504
7,926
2,916
5,010
64,816
44,236
20,580
12,588
1,146
2,539
1
62
13,734
6,846
2,540
4,306
58,247
40,139
18,108
11,276
1,002
2,208
(16)
37
12,278
5,830
2,192
3,638
Interest income
Net interest expense
Tax on net interest (37.7%)
56
14
5
Net income
(9)
5,001
59
3
1
(2)
4,304
79
(42)
16
26
3,664
Calculate Core RNOA, NOA growth and return on net financial assets (RNFA) from the
financial statements:
Core RNOA2005 = 5,010/22,356 = 22.41% (using average NOA)
NOA Growth2005 = 323,833/20,886 = 1.1411 (a 14.11% growth rate)
RNFA2005 = 9/923 = 0.98%
(The RNFA looks a bit low; there was a considerable change in NFA over the prior and
the average of beginning and ending balances is a crude average. But financial income is
a very small component of net earnings.)
Here are the forecast of OI for 2006 and 2007 based on the financial statements:
2006
OI for 2006: NOA2005 × Core RNOA2005
23,833 × 0.2241
2007
$5,341
OI for 2007: NOA2006 × Core NOA2005
27,196 × 0.2241
$6,095
Net interest income for 2006: NFA2005 × RNFA2005
325 × 0.0098
3
0
Net income forecast
$5,344
$6,095
EPS (on 2,185 million shares)
$2.45
$2.79
Analysts’ Forecasts
2.59
2.93
Note:
NOA2006 = NOA2005 × NOA Growth2005 = 23833 x 1.1411 = 27,196
The net interest income for 2007 is set to zero
One could also calculated Core RNOA and NOA based on averages over 2003-2005.
The forecasts from the financial statements are a little below those for the analysts. Either
analysts have more information (outside the financial statements) or are being too
optimistic. It is always good to check an analyst’s against what you get from the financial
statements and ask: Why are they different?
Postscript:
One can also forecast from the financial statements by applying the 2005 sales growth
rate of 12.77% and converting forecasted sales into operating income at the 2005 core
PM of 6.85%. So,
2006
Sales, 2006: $73,094 ×1.1277
2007
$82,428
Sales, 2007: $82,429 × 1.1277
$92,954
Core PM, 2005
0.0685
0.0685
Operating income
$5,646
$6,367
Net interest income
3
0
Net income
$5,649
$6,367
EPS
$2.59
$2.91
These forecast s almost precisely the same as the analysts’ forecasts.
E14.14. Valuation Grid and Reverse Engineering for Home Depot Inc.
a.
First calculate the market price of the operations, for it is this number we are
challenging.
Market price of equity: $42 x 2,185 million shares =
Net financial assets
PNOA
$91,770 million
325
$92,095 million
Now, with Core RNOA = 22.41%, reverse engineer to the growth rate from this market
valuation using the formula:
 Core RNOA − ( g − 1) 
V0NOA = NOA0 × 

ρF − g


Students have to choose a required return for the operations. The solution here uses 9%.
1.2241 − g 
NOA
V2005
= 92,095 = 23,833 × 

 1.09 − g 
Solving, g = 1.043 or a = 4.3% growth rate (approx), a little higher than the GDP growth
rate.
Note: the following version of the formula can also be reversed engineered:
V0NOA = NOA0 +
CoreRNOA1 − ( ρ F − 1) NOA0
ρF − g
b. Now reverse the simple valuation model for the expected return:
 1.2241 − 1.04 
NOA
= 92,095 = 23,833 × 
V2005

 ρ − 1.04 
The solution for the expected return is 8.745%. The formula (equation 14.8) is:

NOA 
 NOA
 
Expected return =  NOA × Forecasted RNOA + 1 − NOA  × ( g − 1)
P
P
 


c. Using a required return of 9%, model alternative scenarios and identify those
that are consistent with the current price. For example, an RNOA of 18% with an
NOA growth rate of 5% will justify the price for the operations (approximately):
 0.18 − 0.06 
NOA
= 23,833 × 
V2005
 = $95,332
 1.09 − 1.06 
Adding the NFA of $325 yield an equity value of $95,657 and a value per share of
$43.78.
Clearly, there a number of combinations of RNOA and g that will yield the current
market price. A full valuation grid gives these scenarios and the analyst can ask
whether these are reasonable scenarios with some probability. The following grid
gives enterprise value (in billions of dollars) for different combinations of growth in
sales and RNOA. Some cells are filled in, but the grid in easily completed.
Valuation Grid (per share)
RNOA
Growth in
NOA
14%
16%
18%
19%
20%
22%
23%
2%
4%
39.42
5%
35.60
6%
43.78
7%
Postscript:
A grid can also be prepared for the expected return under alternative forecasts of RNOA
and growth. If the analyst has a relatively firm idea of RNOA and growth, the expected
return from investing at the market price can be estimated as in Part b of the Exercise:

NOA 
 NOA
 
Expected return =  NOA × Forecasted RNOA + 1 − NOA  × ( g − 1)
P
P
 


The grid takes the following form:
Expected Return Grid
RNOA
Growth in
NOA
14%
16%
18%
19%
20%
22%
23%
2%
4%
5%
8.9%
6%
7%
The 8.9% expected return for a 20% RNOA forecast and a 5% NOA growth rate is
indicated here. Fill out the expected returns for other combinations.
CHAPTER FIFTEEN
Full-Information Forecasting, Valuation, and Business Strategy
Analysis
Drill Exercises
E15.1. A One-Stop Forecast of Residual Operating Income
a.
The one-stop formula is:
= 11.600
Proof:
OI = 1,276 ×0.05 = 63.8
NOA = 1,276/2.2 = 580
ReOI = 63.8 – (0.09 × 580) = 11.6
b.
0.09 

Re OI = 1,276 × 0.045 −
+0 + 0
2.2 

= 5.220
c.
The calculation in the square must be negative to yield negative ReOI. So a PM less than
4.0909% will yield negative ReOI.
E15.2. A Revised Valuation: PPE, Inc.
The revised pro forma:
Sales (growing at 6%)
Operating income (PM = 0.07)
NOA
ReOI (11.34% charge)
Growth rate for ReOI
Year 0
Year 1
Year 2
Year 3
124.9
9.80
74.42
132.39 140.34
9.27
9.82
73.86
78.29
0.894 0.942
5.4%
148.76
10.41
82.99
0.999
6.0%
OI = Sales x 0.07
NOA = Sales one year ahead/1.9
Sales, OI, NOA, and ReOI will grow at 6% after Year 3: constant ATO and PM.
a.
Value of Equity = 66.72 +
0.894
0.942
+
1.1134 (1.1134 − 1.06) × 1.1134
= 83.37 (or $0.83 per share)
b.
Extending the pro forma:
Sales (growing at 6%)
Operating income (PM = 0.07)
Net financial income (expense) (at 10%)
Earnings
Year 0
Year 1
Year 2
Year 3
124.9
9.80
132.39 140.34
9.27
9.82
(0.77) ( 0.20)
8.50
9.62
148.76
10.41
( 0.07)
10.34
NOA
NFA
74.42
( 7.70)
Free cash flow (OI – ∆NOA)
Dividends (40% of earnings)
Payment of debt
73.86
(2.04)
78.29
(0.70)
82.99
0.80
9.83
3.40
6.43
5.39
3.85
1.54
5.71
4.14
1.57
The NFA position each year is NFAt-1 + NFEt – (FCF – dividend).
E15.3. Forecasting Free Cash Flows and Residual Operating income, and Valuing a
Firm
(a)
2009
2010
2011
2012
2013
Free cash flow (C – I = d)
70
75
75
75
75
Investment (I)
Cash from operations (C)
80
150
89
164
94
169
95
170
95
170
As the firm is “pure equity’ (no debt), free cash flow (C - I) is equal to dividends.
Forecast operating income and residual operating income:
2009
2010
2011
2012
2013
∆NOA
C–I
OI
39
70
109
30
75
105
24
75
99
14
75
89
9
75
84
Beginning net operating assets
596
635
665
689
703
ReOI (0.12)
37
29
19
6
0
As the firm is a “pure equity” firm, net operating assets (NOA) equal common
shareholders’ equity (CSE) and operating income (OI) equals comprehensive income.
And comprehensive income equals ∆CSE + dividends. As an alternative calculation, OI
= C – I + ∆NOA (as above),
(b) Based on the forecasted ReOI, with zero ReOI forecasted after 2013,
Value = 596 +
37
1.12
+
29
1.12
2
+
19
1.12
3
+
6
1.12 4
= 669.5
(c)
Using DCF analysis, one is tempted by the following calculation:
Value =
70
 75 
+
 /1.12
1.12  0.12 
= 620.5
This is different from that value in part (b). The 75 in free cash flow after 2009 looks like a perpetuity, so has been capitalized as
such in this valuation. But free cash flow cannot be a perpetuity at 75. Forecasted NOA for the beginning of 2012 is 703 + 84 - 75 =
712. If the firm were to hold net operating assets at 712 and thus earn 85.44 in operating income (at an RNOA of 12 % to yield a zero
ReOI), free cash flow would be 76.44: C – I = OI – ∆NOA = 85.44 – (712 – 703) = 76.44. If the firm were to maintain a zero ReOI
after 2013 and still grow net operating assets, free cash would be lower, but would have to grow.
The point:
1.
Make sure you get to steady state before calculating a continuing value.
2.
DCF valuation often requires longer forecasting horizons.
E15.4. Analysis of Value Added
Pro forma and valuation under the status quo:
0
1
2
3
Sales
Operating income (PM = 7%)
857.0
60.0
882.7
61.8
909.2
63.6
936.5
65.6
(grows at 3%)
(grows at 3%)
Net operating assets
441
454.2
467.8
481.9
(grows at 3%)
PM
ATO
RNOA
7%
2.0
14%
7%
2.0
14%
7%
2.0
14%
7%
2.0
14%
ReOI
Value of operations under the status quo:
Value of NOA = 441 +
17.64
18.18
18.73
(grows at 3%)
17.64
1.10 − 1.03
= 693
Pro forma and valuation under the plan:
0
1
2
3
Sales
857.0
891.3
926.9
964.0
(grows at4%)
Operating income
(PM = 7%)
60.0
62.4
64.9
67.5
(grows at4%)
Net operating assets
(ATO = 1.67)
534.8
556.1
578.4
601.6
(grows at 4%)
PM
ATO
RNOA
7%
1.67
11.67%
7%
1.67
11.67%
7%
1.67
11.67%
7%
1.67
11.67%
8.93
9.29
9.66
ReOI
(grows at 4%)
Value of operations under
the plan:
Value of NOA
= 534.8 +
8.93
1.10 − 1.04
= 684
The plan (marginally) loses value. The additional growth (that generates additional profit
margin) is not sufficient to cover the required return on the additional investment in net operating
assets.
E15.5. Evaluating a Marketing Plan
(a)
This is an SF3 valuation:
Value of operations0 = NOA0 + Re OI1
ρF − g
Re OI = (15% − 11% ) × 498
1
= 19.92
For a profit margin (PM) of 7.5% and an RNOA of 15%, the ATO must be 2.0. With a constant ATO (implied by the constant
PM and RNOA), the growth in ReOI is given by the growth in sales. So,
Value of operations = $896 million
(b)
A reduction of the ATO to 1.9 would reduce forecasted profitability (RNOA) to
14.25%:
RNOA = PM × ATO
= 14.25%
Under the status quo, residual operating income is expected to be generated as follows:
NOA at
beginning
498.0
527.9
559.6
Year
1
2
3
↓
Sales
996.0
1,055.8
1,119.2
PM
7.5%
7.5%
7.5%
ATO
2.0
2.0
2.0
RNOA
15%
15%
15%
ReOI
19.92
21.12
22.38
ReOI
Growth
--6%
6%
Under the marketing plan, residual operating income is expected to be generated as
follows:
NOA of
beginning
Sales
PM
ATO
RNOA
ReOI
ReOI
Growth
1
498.0
996.0
7.5%
2.0
14.25%
19.92
----
2
3
↓
557.0
591.8
628.8
1,058.3
1,124.4
1,194.7
7.5%
7.5%
7.5%
1.9
1.9
1.9
14.25%
14.25%
14.25%
18.10
19.23
20.44
6.25%
6.25%
6.25%
Year
[The plan is implemented in year 1, to take effect in year 2.]
The valuation under the plan is

Re OI 2 
/1.11
1
.
11
− 1.0625 

Value of operations = NOA + Re OI1 + 
1.11
= $859 million
The plan reduces the value calculated in part (a). The additional investment in receivables loses value (when charged at the required
return) even though it generates more value from the additional operating income that comes from the additional sales growth.
E15.6. Forecasting and Valuation
(a) Forecast return on net operating assets (RNOA) for 2010.
= 17.5%
RNOA
(b) Forecast residual operating income for 2010. Use a required return for operations
of 9%.
ReOI 2010
= 268.6
(c) Value the shareholders’ equity at the end of the 2009 fiscal year using residual
income methods.
VE
= 10,823
(growth in ReOI is equal to growth in sales, 6%, because ATO is constant)
(d) Forecast abnormal growth in operating income for 2011.
Method 1:
AOIG = growth in ReOI
AOIG2011 = 268.6 x 0.06
= 16.12
Method 2:
The Pro forma:
2009
Operating income
Net Operating assests
FCF (OI - ∆NOA)
Reinvested FCF (at 9%)
3,160.00
2010
553.00
3,349.60
363.40
Normal OI (553 x 1.09)
AOIG
Note: OI and NOA both grow at 6% per year.
OI for 2007 = 3,160 x 0.175 = 553.
2011
586.18
32.71
618.89
602.77
16.12
(e) Value the shareholders’ equity at the end of 2009 using abnormal earnings growth
methods.
E
V2009
=
AOIG2011 
1 
- NFO
OI 2010 +
0.09 
ρ F - g 
1 
16.12 
553 +
- 1,290

0.09 
1.09 - 1.06 
= 10,825
[OI 2010 = 3,160 x 0.175 = 553]
=
(f) After reading the stock compensation footnote for this firm, you note that there
are employee stock options on 28 million shares outstanding at the end of 2009. A
modified Black-Scholes valuation of these options is $15 each. How does this
information change your valuation?
E
V2009
before option overhang
10,825
Option overhang :
Value of outstanding options
28 million × 15 = 420
Tax benefit (@35%) 147
273
Adjusted valuation
10,552
(g) Forecast (net) comprehensive income for 2010.
Forecast of operting income for 2010
Forecast of net financial expense
NFO x NBC = 1,290 x 0.056
Tax benefit (at 35%)
553
72
25
Compensation income
47
506
[NBC for 2010 is the same as for 2009: 83/1,470=5.6%]
E15.7. Valuing a Property-Casualty Insurer
a.
ReOI2009
= 254
b.
Value of equity = Value of investments + Value of underwriting business
= $6,901 million
(Investments are marked to market on the balance sheet)
E15.8. Integrity of Pro Formas
(a)
(1) Net financial expenses are growing even though net financial obligations remain constant.
(2)
Successive numbers for common equity are not reconciled by the stocks and
flows
equation: ∆CSE = Comprehensive income – Net dividends
(3)
Free cash flow does not obey the relation, C – I = OI – ∆NOA.
(4)
Successive net financial obligations do not obey the relation,
∆NFO = NFE – (C – I) + d.
In short, accounting discipline is lacking from the pro forma.
(b)
Sales are forecasted to grow at 6% per year. The forecasted asset turnovers are constant (at 2.0) and the RNOA is forecasted to
be a constant 20% (on beginning NOA). So residual operating income must be forecasted to grow at the sales growth rate of 6%.
E15.9. Comprehensive Analysis and Valuation
Part I
(a)
Loss from exercise of stock options = 12/0.35 = 34
Tax benefit
12
Compensation expense, after tax
22
(b)
Market price of shares repurchased 25
Amount paid for shares: 720/24 mill.
Loss per share
Number of shares
24 million
Total loss
30
5
120 million
(These losses are not tax deductible)
(c)
Comprehensive income statement
Sales
3,726
Operating expenses
OI before stock compensation
Stock compensation
(22)
Operating income
500
Interest expense
98
Interest income
(15)
83
Tax benefit 29
54
Unrealized gain on investments
124
Put option losses
120
Comprehensive income
(3,204)
522
(50)
376
(d)
2009
2008
Net operating assets 3,160 2,900
Net financial obligations
1,290 1,470
Common shareholders’ equity
1,870 1,430
Financial leverage (FLEV) = 1,290/1,870 = 0.690
Operating liability leverage (OLLEV) = 1,590/3,160 = 0.503
(Operating liabilities = 1,200 + 390 = 1,590)
(e)
FCF
= 240
Part II
(a)
RNOA
(b)
ReOI2010
(c)
VE =
= 17.5%
= 268.6
= 10,823
(Growth rate in ReOI is the sales growth rate because ATO is constant)
(d)Method 1:
OI2011
FCF2010, reinvested
Normal OI
AOIG
586.18
32.71
618.89
602.77
16.12
Method 2:
AOIG = growth in ReOI
AOIG2011 = 268.6 x 0.06
= 16.12
(OI and NOA both grow at 6%)
(e)
E
V2009
=
AOIG2011 
1 
− NFO
OI 2010 +
0.09 
ρ F − g 
=
1 
16.116 
553 +
− 1,290

0.09 
1.09 − 1.06 
= 10,823
(OI2010 = 3,160 x 0.175 = 553)
(f)
VE before option overhang
Option overhang:
Value of outstanding options
28 mill x 15
420
Tax benefit (35%)
147
Adjusted valuation
10,550
10,823
273
(g)
Forecast of operating income for 2010
Forecasts of net financial expense:
NFO x NBC = 1,290 x 0.056
Tax benefit (at 35%)
Forecast of comprehensive income
553
72
25
47
506
(The NBC used is the core net borrowing cost on net debt for 2002: 83/1470 = 0.056)
Applications
E5.10. Forecasting and Valuation for General Mills, Inc.
General Mills Pro Forma
Sales
Operating income
2008A
13,652
1,560
2009E
14,881
1,701
2010E
16,220
1,854
2011E
17,193
1,965
Net operating assets
Net financial obligations
Common equity
12,847
6,631
6,216
14,613
15,489
16,419
Core profit margin
ATO
11.43%
1.11
673.2
1.08
623.3
685.0
1.1664
587.3
725.9
1.2597
576.2
ReOI (8%)
Discount rate
PV of ReOI
Total PV of ReOI
Continuing value (CV)
PV of CV
NOA
Enterprise Value
Net financial obligations
Value of equity
2012E
18,225
2,083
769.5
1.3605
565.6
2,352.4
26,933
19,796.0
12,847.0
34,995.4
6,631.0
28,364.4
or $84.04 per share
[Forecasts of NOA are made by applying ATO to forecasted sales one year ahead]
E5.11. Pro Forma Analysis and Valuation: Nike, Inc.
Nike Pro Forma
Sales
Operating income
Net operating assets
Net financial assets
Common equity
ReOI (8.6%)
Discount rate
PV of ReOI
Total Pv of ReoI
Continuing value (CV)
PV of CV
Value of equity
2008A
18,627
2009E
20,490
1,844
2010E
22,334
1,898
2011E
24,120
1,930
5,806
1,991
7,797
6,569
6,891
7,169
1,344.7
1.086
1,238.2
1,333.1
1.1794
1,130.3
1,337.4
1.2808
1,044.2
1,319.5
1.3910
948.6
4,361
29,832
21,447
33,605
or $68.43 per share
E15.12. One-Step Residual Operating Income Calculation: Coca-Cola
a.
The one-step calculation of residual operating income is:
ReOI = $3,277.3 million
An alternative solution:
Core OI = ($24,088 × 0.20) + 102 = $4,919.6
NOA
= $24,088/1.32 = 18,248.5
ReOI
= $4,919.6 – (0.09 × 18,248.5) = 3,277.3 million
b.
0.09 

ReOI = $24,088 ×  0.20 −
 + 102
1.70 

= $3,644.4 million
E15.13. A Valuation from Operating Income Growth Forecasts: Nike
(a)
2012E
25,809
1,936
2005
2006
2007
2008
2009
783.6
854.7
676.0
608.6
663.4
71.1
-178.7
-67.4
54.8
1.086
1.179
1.281
65.47
-151.57
-52.62
2010
ReOI (8.6% charge)
696.6
Abnormal OI Growth (= ∆ReOI)
33.2
Discount rate
1.391
PV of AOIG
39.40
Total PV to 2009
33.17
CV
1.086 − 1.05
921.39
PV of CV
Operating income
Capitalize at required return
Enterprise value (1,842.31/0.086)
Net financial assets
Option overhang
Value of equity
-99.3
662.4
1,175.0
1,738.1
0.086
20,211
289
20,500
452
20,048
Note:
AOIG is equal to the change in residual operating income (ReOI) given in Box 15.3.
From 2010 onwards, ReOI is forecasted to grow at a 5% rate – and thus so is AOIG, for
AOIG is always the change in ReOI. So the continuing value uses a 5% growth rate.
(b)
The two-stage growth model (14.5) incorporates short-term and longterm growth rates, G2 and Glong:
NOA
V2004
= OI 1 ×
1  G2 − Glong 


ρ F − 1  ρ F − Glong 
Calculating G2:
Cum-FCF OI for 2006 = normal income + abnormal income growth
= 1,347.15
G2
= 1,347.15/1,175 = 1.1465 (14.65%)
Set Glong = 1.05, the long-term growth rate forecasted by the analyst,
NOA
V2004
= 1,175 ×
1 1.1465 − 1.05 
0.086  1.086 − 1.05 
= $36,628 million
The forward P/E is 31.17.
Why is this value greater than that in (a)? Because the two-stage growth model
implies a gradual decay in the growth rate from the 14.65 % in 2006 to the 5% in the
(very) long term. So, it does not pick up the slower AEG growth after 2006 that is
apparent in the full pro forma.
E15.14. Evaluating an Acquisition: PPE Inc.
The important point in this exercise is to calculate the effect of the proposed
acquisition on the per-share value of PPE. As shareholders of the acquired firm are to
share in the benefits of the merger, the division of the value added in the merger between
PPE’s shareholders and those of the acquired firm has to be calculated. The value added
will depend on the value of the merged firm. The division of the value will depend on
the relative shares in the value (which depend on the rate of exchange of shares in the
acquisition).
(a)
To solve the problem proceed as follows:
1.
Calculate the value of the equity of the merged firm at the end of Year 1.
2.
Calculate the per-share value of the equity of the merged firm at Year 1.
3.
Calculate the present value (at Year 0) of the per-share value of Year 1 plus
the present value of the Year 1 dividend.
4.
Compare the Year 0 per share value with that calculated without the
acquisition (from the pro forma in the text: $0.96).
Is per-share value added?
The following calculates the value of the merged firm at the end of the year 1 and the pershare value of the 220 shares in the new firm (steps 1 and 2):
Year
2
3
4
5
6
RNOA
7.16%
8.46%
9.92%
21.30%
21.31%
Residual operating
income (11%)
income (11%)
(4.90)
(3.10)
(1.27)
11.59
12.30
PV of ReOI to
Year 5
Year 5
1
1.63
Continuing value,
Year 5
246.0
PV of CV
162.05
Net operating
assets, Year 1
127.50
Value of NOA,
Year 1
Year 1
291.18
Value of NFO
5.71
Value of equity
285.47
Value per share
(220 shares)
1.298
12.30 

CV = 1.11 - 1.06 


Note that the ReOI is growing at 5% per year after Year 5.
(Calculations use a 11% required return for operations.)
The Year 0 per share value to PPE’s shareholders (step3) is
Value at Year 1
$1.298
Dividend at year 1
0.038
Year 1 pay off
1.336
PV at Year 0 (1.1134)
$1.200
[The discount rate for PPE pre-acquisition is used.]
The value of a PPE share without the acquisition is $0.96, so the proposed acquisition
adds value.
(b)
The revised pro forma, without amortization of goodwill, excludes the amortization
expense in the income statement and maintains goodwill in the balance sheet:
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Sales
Core expenses
131.15
120.86
189.00
168.87
200.34
179.00
212.36
189.74
225.10 238.61
201.13 213.19
Operating income
10.29
20.13
21.34
22.62
23.97
Net operating assets
127.50
Net financial obligations 5.71
Common equity
121.79
133.17
139.18
145.55
152.30 159.46
Income Statement
25.42
Balance Sheet
(c)
Calculate forecasts of residual operating income (ReOI) for the alternative pro forma and
value the operations from those forecasts.
Year 1
ReOI
ReOI growth rate
Year 2
Year 3
Year 4
Year 5
Year 6
6.105
6.691
9.60%
7.310
9.25%
7.960
8.89%
8.667
8.86%
The ReOI growth rate is declining each year, but is not in steady state. Sales and
operating income are growing at 6%, as in part (a), but the book values of NOA are not.
However, the book values will eventually converge to the 6% sales growth rate. You
need a computer: Input the pro forma into a spreadsheet and continue computations for
years after Year 6:
•
Grow operating income at 6% per year
•
Calculate the free cash flow each year from either pro forma: FCF = OI – ∆NOA.
(Free cash flow does not change with the changed accounting, of course, so will
be the same when calculated from either pro forma.) Appreciate that free cash
flow grows at a 6% rate. So, as FCF is $18.26 for Year 6, subsequent FCF can be
extrapolated at 6%.
•
Calculate NOA each year as NOAt = NOAt-1 + OIt - FCFt
•
Calculate ReOI and present value it
•
Add NOA at the end of Year 1 to get the value of operations at that point.
This Year 1 value is the same at that in part (a) (the accounting does not affect the
value!), the value at Year 0 is also the same.
CHAPTER SIXTEEN
Creating Accounting Value and Economic Value
Drill Exercises
E16.1. A Simple Demonstration of the Effect of Accounting Methods on Value
a.
Value of investment = Present value of cash expected cash flow
= 105.50
b.
Book value of investment = $100
Earnings, Year 1 = $115 - $100 = $15
ReOI1 = 15 – (0.09 × 100) = 6
Value of investment = $100 + Present value of expected ReOI = $105.50
c.
Book value of investment = $80
Earnings, Year 1
= $115 – 80
= $35
ReOI1 = 35 – (0.09 × 80) = 27.8
Value of investment = $80 + Present value of expected ReOI
= $105.50
E16.2. Valuation of a Project under Different Accounting Methods
a.
Year 0
Year 1
Year 2
1,540
1.09
1,412.8
1,540
1.1881
1,296.2
Year 0
Year 1
Year 2
2,200
1,540
1,100
440
1,100
1,540
1,100
440
0
Cash flows
Discount rate
PV of cash flows
Total PV of cash flows
2,709
b.
Revenue
Depreciation
Earnings
Book value
RNOA
40.0%
Residual earnings
Discount rate
PV of residual earning
Total PV
20.0%
242
1.09
222.0
509
341
1.1881
287.0
Value of project
2,709
c.
Revenue
Depreciation
Earnings
Book value
RNOA
71.1%
Residual earnings
Discount rate
PV of residual earning
Total PV
Value of project
Year 0
Year 1
Year 2
2,200
1,540
1,300
240
900
1,540
900
640
0
10.91%
42
1.09
38.5
559
1.1881
470.5
509
2,709
The value of the project does not change, but the accounting numbers do. The more
conservative depreciation in Year 1 decreases earnings, RNOA, and residual earnings in
that Year, but creates earnings, RNOA, and residual earnings in Year 2.
d.
Year 0
Revenue
Depreciation
Earnings
Book value
RNOA
105.33%
Residual earnings
Discount rate
PV of residual earning
Total PV
Value of project
1,500
Year 1
Year 2
1,540
750
790
750
1,540
750
790
0
52.67%
655
1.09
600.9
722.5
1.1881
608.1
1,209
2,709
The value is unchanged, but the conservative accounting (expensing advertising),
increases subsequent earnings, RNOA, and residual earnings.
e.
For capitalizing and expensing advertising in part b, P/B = 2,709/2,200 = 1.23
For expensing advertising on part d. P/B = 2,709/1,500 = 1.81
Conservative accounting increases P/B ratios.
E16.3. Valuation of a Going Concern Under Different Accounting Methods
Initial investment $2,200 million
Further investment of $2,200 million each year
Sales revenue 70 percent of the investment
Accounting depreciation: straight-line over those two years
Hurdle rate = 9%
a. Price-to-book ratio = 3.80
Foreward P/E = 19.01
Year 0
Sales
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
Operating expenses (depreciation)
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
From investments in Year 5
Operating income
Net Operating Asset (NOA)
From investments in Year 1
From investments in Year 2
From investments in Year 3
Year 1
Year 2
1540.0
1540.0
1540.0
1540.0
3080.0
1100.0
1100.0
1100.0
Year 3
1540.0
1540.0
3080.0
1100.0
1100.0
Year 4
1540.0
1540.0
3080.0
1100.0
1100.0
0.0
1100.0
2200.0
2200.0
2200.0
-
440.0
880.0
880.0
880.0
2200.0
1100.0
2200.0
1100.0
2200.0
1100.0
From investments in Year 4
From investments in Year 5
2200.0
Investment
Free cash flow
2200.0
3300.0
3300.0
3300.0
1100.0
2200.0
3300.0
2200.0
(2,200.0)
2200.0
(660.0)
2200.0
880.0
2200.0
880.0
2200.0
880.0
20.0
28.6
0.7
50.0
26.7
28.6
0.9
0.0
583.0
140.9
86.5
341.0
N/A
26.7
28.6
0.9
0.0
583.0
0.0
9.0
0.0
N/A
26.7
28.6
0.9
0.0
583.0
0.0
9.0
0.0
N/A
9777.8
6477.8
2.96
12.1
11.1
9%
9777.8
6477.8
2.96
12.1
11.1
9%
9777.8
6477.8
2.96
12.1
11.1
9%
RNOA (%)
Profit margin (%)
Asset turnover
Growth in NOA (%)
ReOI
Growth in ReOI (%)
Growth in cum-dividend OI (%)
AOIG (0.10)
Growth in AOIG (%)
242.0
N/A
Value of firm
Premium over book value
P/B
Trailing P/E
Forward P/E
Equity Return
8364.9
3.80
19.01
9777.8
6477.8
2.96
20.7
11.1
9%
b. 20 percent of the projected investment to be expensed each year.
Price-to-book ratio = 4.75
Foreward P/E = 38.02
Year 0
Sales
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
Operating expenses (depreciation)
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
From investments in Year 5
440.0
440.0
Year 1
Year 2
1540.0
1540.0
1540.0
1540.0
3080.0
880.0
440.0
880.0
880.0
440.0
1320.0
2200.0
Year 3
Year 4
1540.0
1540.0 1540.0
1540.0
3080.0 3080.0
880.0
880.0
440.0
880.0
880.0
440.0
2200.0 2200.0
Operating income
Net Operating Asset (NOA)
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
From investments in Year 5
Investment
Free cash flow
(440.0)
220.0
1760.0
880.0
1760.0
880.0
1760.0
880.0
880.0
1760.0
880.0
1760.0
2640.0
2640.0
2640.0
880.0
1760.0
2640.0
2200.0
(2,200.0)
2200.0
(660.0)
2200.0
880.0
2200.0
880.0
2200.0
880.0
12.5
14.3
0.9
50.0
61.6
N/A
33.3
28.6
1.2
0.0
642.4
942.9
273.0
580.8
N/A
33.3
28.6
1.2
0.0
642.4
0.0
9.0
0.0
N/A
33.3
28.6
1.2
0.0
642.4
0.0
9.0
0.0
N/A
9777.8
7137.8
3.70
41.4
11.1
9%
9777.8
7137.8
3.70
12.1
11.1
9%
9777.8
7137.8
3.70
12.1
11.1
9%
9777.8
7137.8
3.70
12.1
11.1
9%
Year 3
Year 4
RNOA (%)
Profit margin (%)
Asset turnover
Growth in NOA (%)
ReOI
Growth in ReOI (%)
Growth in cum-dividend OI (%)
AOIG (0.10)
Growth in AOIG (%)
Value of firm
Premium over book value
P/B
Trailing P/E
Forward P/E
Equity Return
880.0
8364.9
4.75
38.02
c. 5% investment growth rate; no immediate expense
Price-to-book ratio = 7.31
Foreword P/E = 36.53
Year 0
Sales
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
Operating expenses (depreciation)
From investments in Year 1
Year 1
Year 2
1540.0
1540.0
1617.0
1540.0
3157.0
1100.0
1100.0
1617.0
1697.9
3314.9
1697.9
1782.7
3480.6
From investments in Year 2
From investments in Year 3
From investments in Year 4
From investments in Year 5
1155.0
0.0
Operating income
Net Operating Asset (NOA)
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
From investments in Year 5
Investment
Free cash flow
2255.0
2367.8
2486.1
-
440.0
902.0
947.1
994.5
2200.0
1100.0
2310.0
1155.0
2425.5
1212.8
2546.8
2200.0
3410.0
3580.5
3759.5
1273.4
2674.1
3947.5
2200.0
(2,200.0)
2310.0
(770.0)
2425.5
731.5
2546.8
768.1
2674.1
806.5
20.0
28.6
0.7
55.0
242.0
N/A
26.5
28.6
0.9
5.0
595.1
145.9
89.3
353.1
N/A
26.5
28.6
0.9
5.0
624.9
5.0
12.3
29.8
-91.6
26.5
28.6
0.9
5.0
656.1
5.0
12.3
31.2
5.0
18287.5
14877.5
5.36
39.8
20.3
9%
19201.9
15621.4
5.36
22.1
20.3
9%
20162.0
16402.4
5.36
22.1
20.3
9%
21170.1
17222.6
5.36
22.1
20.3
9%
16071.1
7.31
36.53
c. 5% investment growth rate; 20% immediate expense
Price-to-book ratio = 9.13
Foreword P/E = 81.17
1212.8
1273.4
1100.0
RNOA (%)
Profit margin (%)
Asset turnover
Growth in NOA (%)
ReOI
Growth in ReOI (%)
Growth in cum-dividend OI (%)
AOIG (0.10)
Growth in AOIG (%)
Value of firm
Premium over book value
P/B
Trailing P/E
Forward P/E
Equity Return
1155.0
1212.8
Year 0
Sales
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
Operating expenses (depreciation)
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
From investments in Year 5
Operating income
Net Operating Asset (NOA)
From investments in Year 1
From investments in Year 2
From investments in Year 3
From investments in Year 4
From investments in Year 5
Investment
Free cash flow
440.0
Year 2
1540.0
1540.0
1617.0
1540.0
3157.0
880.0
462.0
880.0
924.0
485.1
Year 3
1617.0
1697.9
3314.9
924.0
970.2
509.4
Year 4
1697.9
1782.7
3480.6
440.0
1342.0
2289.1
2403.6
970.2
1018.7
534.8
2523.7
(440.0)
198.0
867.9
911.3
956.9
1760.0
880.0
1848.0
924.0
1940.4
970.2
2037.4
1760.0
2728.0
2864.4
3007.6
1018.7
2139.3
3158.0
2200.0
(2,200.0)
2310.0
(770.0)
2425.5
731.5
2546.8
768.1
2674.1
806.5
11.3
12.9
0.9
55.0
39.6
N/A
31.8
27.5
1.2
5.0
622.4
1471.7
303.3
582.8
N/A
31.8
27.5
1.2
5.0
653.5
5.0
12.6
31.1
-94.7
31.8
27.5
1.2
5.0
686.2
5.0
12.6
32.7
5.0
18287.5
15559.5
6.70
88.5
21.1
9%
19201.9
16337.5
6.70
23.0
21.1
9%
RNOA (%)
Profit margin (%)
Asset turnover
Growth in NOA (%)
ReOI
Growth in ReOI (%)
Growth in cum-dividend OI (%)
AOIG (0.10)
Growth in AOIG (%)
Value of firm
Premium over book value
P/B
Trailing P/E
Forward P/E
Equity Return
Year 1
16071.1
9.13
81.17
20162.0 21170.1
17154.3 18012.1
6.70
6.70
23.0
23.0
21.1
21.1
9%
9%
Applications
E16.4. Inventory Accounting, P/B, and P/E Ratios: Ford Motor Company
(a)
The LIFO reserve is the amount by which cumulative FIFO profits would have
been greater than LIFO profits. But that difference would attract taxes, so shareholders’
equity would be higher by the amount of the LIFO reserve, after tax. The LIFO reserve is
the amount by which inventories would be higher under FIFO than LIFO, but the extra
taxes payable would also be recognized, to net to the effect on shareholders’ equity.
1999 Shareholders’ Equity (FIFO) = $28.241 billion
1998 Shareholders’ Equity (FIFO) = $24.177 billion
(b)
FIFO Earnings
= $7.173 billion
(There was a liquidation of the LIFO reserve).
1999 ROCE (FIFO)
= 29.67%
(c)
= $64.13 billion
Market value of equity
P/B (LIFO)
= 2.33
P/B (FIFO)
= 2.27
P/B (LIFO) is higher than P/B (FIFO) because book value is lower with LIFO.
(d)
P/E (LIFO)
= 8.86
P/E (FIFO)
= 8.94
(Dividends are ignored in these calculations.)
P/E (LIFO) is lower than P/E (FIFO) because earnings are higher under LIFO due to the
inventory liquidation. Typically, however, LIFO P/E ratios are higher than FIFO P/E
ratios because, with inventory growth rather than liquidation, LIFO earnings are lower
than FIFO earnings.
E16.5.
The Accounting for Research and Development and Economic Profit Measures
(a)
2008
Sales
Operating expenses (80%)
OI before R&D
R&D expense
Operating income
Net operating assets
80
RNOA
ReOI (10%)
2009
2010
2011
2012
2013
2014
160
128
32
100
(68)
320
256
64
100
(36)
480
384
96
100
(4)
640
512
128
100
28
800
640
160
100
60
800
640
160
100
60
80
80
80
80
80
80
-85.0%
(76)
-45.0%
(44)
-5.0%
(12)
35.0%
20
75.0%
52
75.0%
52
32
20
12
64
40
24
96
60
36
128
80
48
160
100
60
160
100
60
260
320
360
380
380
380
6.6%
(6)
9.2%
(2)
11.25%
4
13.3%
12
15.8%
22
15.8%
22
(b)
OI before R&D
Amortization
Operating income
Net operating assets
RNOA
ReOI (10%)
180
(c)
The RNOA and ReOI are different because of the treatment of R&D
expenditures. Expensing initially gives lower RNOA and ReOI, but higher RNOA and
ReOI subsequently.
(d)
RNOA2015 with expensing = 75.0%
RNOA2015 with capitalizing = 15.8%
ReOI2015 with expensing = $52 million
ReOI2015 with capitalizing = $22 million
(The firm is in steady-state.)
The forecasts differ because of the relative conservative accounting: expensing yields
higher RNOA and ReOI.
(e)
With expensing:
V0NOA = 80 +
(76) + (44) + (12) + 20 +  52  / 1.10 4
1.10 1.10 2
1.10 3
1.10 4


 0.10 
= $334 million
With capitalization:
V0NOA = 180 +
(6) + (2) + (4) + 12 +  22  / 1.10 4
1.10 1.10 2
1.10 3
1.10 4


 0.10 
= $334 million
The valuations are the same:
forecasted.
the accounting does not matter once steady-state is
(f)
In both cases, the full valuation would not be captured because 2011 is prior to
steady-state.
E16.6. Depreciation Methods, Profitability, and Valuation
(a)
Pro forma with three-year estimated life
Revenues
Depreciation
Other Expenses (70%)
Operating Income
2009
-----
2010
250
200
175
(125)
2011
1,530
433
1,071
(26)
2012
3,540
700
2,478
362
2013
4,295
800
3,007
488
2014
4,305
900
3,014
391
2015
4,410
967
3,087
356
2016
4,500
1,000
3,150
350
2017
4,500
1,000
3,150
350
Net Operating Assets
Investment
RNOA
600
600
--
1,100
700
-20.8%
1,467
800
-2.4%
1,666
900
-24.7%
1,866
1,000
29.3%
1,967
1,000
21.0%
2,000
1,000
18.1%
2,000
1,000
17.5%
2,000
1,000
17.5%
2016
4,500
940
3,150
410
2,980
1,000
14.0%
2017
4,500
980
3,150
370
3,000
1,000
12.4%
2018
4,500
1,000
3,150
350
3,000
1,000
11.7%
2019
4,500
1,000
3,150
350
3,000
1,000
11.7%
Pro forma with five-year estimated life
Revenues
Depreciation
Other expenses (70%)
Operating income
Net operating assets
Investment
RNOA
2009
----600
600
--
2010
250
120
175
(45)
1,180
700
-7.5%
2011
1,530
260
1,071
199
1,720
800
16.9%
2012
3,540
420
2,478
642
2,200
900
37.3%
2013
4,295
600
3,007
688
2,600
1,000
31.3%
2014
4,305
800
3,014
491
2,800
1,000
18.9%
2015
4,410
880
3,087
443
2,920
1,000
15.8%
(b)
Depreciation over five years yields higher operating income in 2013: for the same
revenues and other expenses, depreciation expense is lower. And depreciation over five
years yields a higher RNOA in 2013 (31.3% compared with 29.3%). Even though net
operating assets are higher with five-year estimated lives, the numerator effect dominates
the denominator effect (prior to steady state). Note, however, that these RNOA are not a
good forecast of the relative RNOA once steady state is realized: steady-state RNOA
with three-year estimated lives is 17.5% compare to 11.7% with five-year estimated lives.
(c)
Three-year estimated life
2013
ReOI
PV of ReOI to 2015

 150
= 1,500 

 0.10
PV of continuing value 
Net operating assets
Value at 2013
2014
204
2015
159
2016
150
2017
150
2018
150
2019
150
2014
231
2015
163
2016
118
2017
72
2018
50
2019
50
317
1,240
1,866
3,423
Five-year estimated life
2013
ReOI (10%)
PV of ReOI to 2017
 50

= 500 
 0.10

PV of continuing value 
Net operating assets
Value at 2013
482
341
2,600
3,423
(d)
Good analysis would find that the RNOA in 2013 is not indicative of the long-run
RNOA for this firm (see part (b)). But maybe the market does not see this. If an
investment banker were pricing the IPO on the basis of multiples of earnings from
comparison firms, and did not adjust for depreciation methods, she might price the
earnings with five-year lives higher for the IPO. Would the market penetrate this illusion?
(e)
In 2018, profit is the same for both depreciation methods (and so, of course, is the
value of the firm). However, RNOA is higher with three-year life depreciation. Would
the market interpret this higher profitability (incorrectly) as requiring a higher price? If
the officers of the firm believed that the market could be "fooled," they might choose the
three-year method to get a higher price for the shares obtained from exercise of the
options. Shareholders beware!
E16.7.
The Quality of Free Cash Flow and Residual Operating Income: Coca-Cola
Company
(a)
Economic profit is similar to residual operating income (ReOI). To see the
difference between free cash flow and ReOI, see how they are calculated:
ReOIt = OIt – (cost of capital × NOAt - 1)
Free cash flowt = OI – ∆NOAt
So ReOI and free cash flow are the same if net operating assets grow at the cost of
capital. In 1995, the two methods were approximately the same and total capital grew at
approximately the 9% rate used to calculate economic profit.
The growth in the two measures are compared as follows:
Growth in ReOIt =
OI t − (cos t of capital × NOA t −1 )
OI t −1 − (cost of capital × NOA t − 2 )
Growth in free cash flowt =
OI t − ∆ΝΟΑt
ΟΙ t −1 − ∆ΝΟΑt −1
So the growth rates are the same if net operating assets grow at the cost of capital
consistently.
(b)
Both methods would work with Coke.
E16.8. Research and Development Expenditures and Valuation
The pro forma for the firm is as follows:
0
1
2
3
4
5
6
7
Sales
R&D
Other expenses (80%)
Operating income
1,000
350
800
(150)
1,500
350
1,200
(50)
2,000
350
1,600
50
2,500
350
2,000
150
3,000
350
2,400
250
3,500
350
2,800
350
3,675
368
2,940
367
3,859
386
3,087
386
Net operating assets
714
1,429
1,786
2,143
2,500
2,625
2,756
(121)
(110)
(93)
(77)
(29)
(22)
36
25
100
62
105
ReOI (10%)
PV of RE
Total PV to Yr. 5
(122)
2,100
105
Continuing value
1.10 − 1.05
PV of CV
Value of firm
1,304
1,896
110
(a)
Value of the firm is $1,896 million
(b)
Earnings for years 1 to 3 are of low quality because they don’t forecast long-run
earnings. The low quality is due to the expensing of R&D expenditures.
(c)
R&D-to-sales
1
2
3
4
5
6
7
23.3%
17.5%
14.0%
11.7%
10.0%
10.0%
10.0%
The ratio settles down to a steady-state of 10% from year 5 onwards. Prior to that the
ratio is higher, indicating that the sales from R&D have not yet been realized.
E16.9. The Quality of Forecasted Residual Operating Income and Free Cash Flow
(a)
The pro forma is as follows:
2009
Sales
Depreciation
Operating income
Net operating assets
400
RNOA
ReOI (10%)
2010
2011
2012
2013
2014
240
200
40
484
420
64
530
460
70
576
500
76
622
540
82
640
700
760
820
880
10%
0
10%
0
10%
0
10%
0
10%
0
2010
2011
2012
2013
2014
40
240
(200)
64
60
4
70
60
10
76
60
16
82
60
22
–
–
150%
60%
38%
Value of firm is book value = $400 (Zero ReOI is forecasted).
(b)
Free cash flow:
Operating income
∆NOA
Free cash flow
Growth in free cash flow
Free cash flow is low in years 2010 and 2012 but grows after that. However, the growth
rate in free cash flow is not constant, making the firm hard to value with a (constant growth)
continuing value. For discounted cash flow analysis, the forecast horizon has to be extended to a
point where the growth rate converges to its long-term rate. As free cash flow forecasting
requires a long forecast horizon, it can be said to be of low quality.
CHAPTER SEVENTEEN
The Analysis of the Quality of Financial Statements
Drill Exercises
E17.1. Following the Trail: Identifying Hard and Soft Components of Income
a. The “hard” part of the income in free cash flow = $234 million. The “soft” part of OI is
that which is due to change in net operating assets:
OI = Free Cash Flow + ∆NOA
So,
∆NOA
= $1,064 million.
Cash flow from operations
Operating accruals
= $921 million
= $377 million
E17.2. Income Shifting and Net Operating Assets
a. RNOA = 2,234/NOAt-1 = 9%
Therefore, NOAt-1 = $24,822.22 million
OI/24,822.22 = 12%
Therefore, OI = 2,978.67, so $744.67 has to be added to income.
b. To add $744.67 to OI for the current year, the CFO will have to add the same amount to
NOA: OI = Free cash flow + ∆NOA. This NOA will be the base for next year’s RNOA,
reducing that RNOA.
E17.3. Following the Trail to the Balance Sheet
a. Increase receivables (and thus increase sales) or increase inventories (and thus reduce
cost of goods sold)
b. Increase net accounting receivable (by reducing allowance for bad debt)
c. Increase net property, plant and equipment
d. Increase accrued expenses
e. Increase capitalized software costs
E17.4. Interpretation of Diagnostics
Bad debt expense/Sales: lower ratio suggests lower RNOA in the future
Warranty expense/Sales: higher ratio suggests higher RNOA on the future
Net sales/Accounts receivable: higher ratio suggests higher RNOA in the future
Inventory/Sales: higher ratio suggests lower RNOA in the future
Depreciation/ Cap. Ex.: lower ratio suggests lower RNOA in the future
Deferred revenue/Sales: higher ratio suggests higher RNOA is the future
Note: these are the effects on future RNOA holding all else constant. A lower depreciation/Cap.
Ex., for example, might mean that higher capital expenditures will produce a lot more revenues
that will increase RNOA in the future. Higher inventory to sales might mean the firm is investing
in inventory in anticipation of higher sales (and RNOA) rather than excess inventory that will
reduce cost of good sold and RNOA.
E17.5. Normalized Asset Turnover
Free cash flow
= -$157 million
Normalized operating income
= $136 million
This analysis indicates that operating income is of good quality: The net operating assets
increases as a percentage of sales at a normal level. Accordingly the ATO for the current year
(5,751/2,614 = 2.2) remained at the historical level.
E17.6. Change in Asset Turnover and Earnings Quality
a. PM = RNOA/ATO = 19.0%/1.9 = 10.0%
b. A decrease in the ATO says that NOA have increased at a higher rate than sales. This could
be due to the firm booking fewer expenses to increase the profit margin.
E17.7. Red Flags in the Cash Flow Statement
Red Flags:
1. Net income as a percentage of cash flow from operations has increased to 113.5%
of sales from 25.6% of sales: there is a higher accrual component to earnings.
2. Depreciation has decreased as a percentage of capital expenditures, even though
capital expenditures are growing: Will depreciation be higher in the future?
3. Accounts receivable have increased (by $33.3 million) even though sales have
declined: What is the quality of those receivables?
4. Deferred revenues have declined: Has sales be propped up by bleeding back
deferred revenues from the balance sheet?
5. The reverse restructuring charge increases income relative to cash flows. Is this
just a cash payment for a previous charge – there were none in 2008 – or is it a
bleed back of an earlier charge to income?
Applications
E17.8. The Quality of Revenues: Bausch & Lomb
A red flag on the quality of revenues is raised by comparing the percentage change in
sales with the percentage change in revenues. Days in accounts receivable also raises concerns.
Percentage change in sales
Percentage change in receivables
Days in account receivable
1991
1992
1993
11.1%
1.1%
49 days
12.4%
35.1%
59 days
9.5%
38.8%
75 days
Percentage change in receivables increased dramatically relative to the percentage change is
sales. Days in accounts receivable also increased significantly. The firm was booking sales (into
receivables) for which customers were not paying (to reduce receivables).
E17.9. The Quality of Gross Margins: Vitesse Semiconductor Corp.
Gross margin ratio
2003
2002
2001
53.21%
27.40%
47.50%
The charges increase cost of goods sold in the year that they are taken and so reduce gross
margins. However, the lower inventory amounts from the write-down become lower cost of
goods sold in subsequent years. Thus subsequent margins increase unless revenue is also
negatively affected. The higher gross margins in 2003 could be due to the write-downs in the
previous years.
E17.10. The SEC and Microsoft
(a)
The issue in question in the SEC’s investigation was the deferring of revenue in the
unearned revenue liability.
The claim was that Microsoft was “over reserving” with this
unearned revenue and might bleed the unearned revenue back into income as it wanted.
Unearned revenue did decrease by $110 million in the September 1999 quarter, so $110 million
of revenue in the income statement was not from “new sales” but from revenue in the past that
was not recognized in the income statement. Microsoft might reply that revenue is legitimately
deferred because sales contracts (to provide upgrades, for example) require further services to the
customer.
(b)
Microsoft reported a decline in cash from operations while its revenues and earnings
increased. This raises a question as to whether there are unjustified accruals. You see that
$1.363 billion of the total $5.344 billion in sales is from recognizing unearned revenue from
prior periods (and only $1.253 billion of current period’s revenue was deferred to the future).
Note also that other current liabilities decrease on an increase in sales, also raising a red flag.
And $156 million of income was from a sale of a business.
E17. 11. Spot the Red Flags in a Cash Flow Statement: EDS and Cerner
Corporation
Electronic Data Systems: Red Flags
1. Increasing income relative to cash flow from operations:
1999 21.8%
2000 73.3%
2001 79.2%
Accruals are an increasing component of net income.
2. Constant depreciation and amortization on increasing income: One expects depreciation
to grow with income unless the technology for producing income changes.
3. Continuing asset write-downs: Are their continuing problems; are write-downs
excessive?
4. What is the $340 million of “other” in 2001 that increases income relative to cash flow?
5. Receivable growth is high in 2001: Quality of receivables? Unbilled revenue?
6. Accounts payable and accrued liabilities drop in 2000 and 2001: Is the firm recognizing
fewer expenses? (Prepaid expenses go the other way, however, reducing income.)
7. Deferred revenue drops in 2001 and 2000: More revenue in the income statement is
coming from revenue deferred from the past rather than current sales.
Cerner Corporation: Red Flags
1. One-time gain of $4,308 thousand in 2002 increases income.
2. Write down of $127,616 thousand in 2001: Does that reduce expenses for 2002 via a
bleed back?
3. Deferred taxes are down in 2002 on increasing income: Inspect deferred tax footnote for
the reason.
4. Large increase in receivables in 2002: Quality of receivables?
5. Deferred revenues in both 2001 and 2002 have been reduced: More revenue in the
income statement is coming from revenue deferred from the past rather than current sales.
6. Accrued liabilities in 2002 have decreased, yielding lower expenses in the income
statement.
7. Cerner is capitalizing software development costs: Is the capitalization appropriate or
excessive?
8. The cash investment of (a negative) $26,798 thousand is affected by $90,119 sale of
securities (a financing activity). Without this item, cash investment is (a positive)
$63,321 and free cash flow is considerably lower than suggested by the cash flow
statement. Cerner is actually selling off securities to finance a negative free cash flow.
9. While income increased significantly in 2002, cash flow from operations dropped
significantly. The reason, of course, is the accrual items mentioned in points 1 – 7.
E17.12. Tracking Changes in Net Operating Assets and the Asset Turnover: Regina
Company
1984
1985
1986
1987
1988
Operating income before tax
4,456
9,826
14,878
21,904
Tax as reported
Tax benefit of interest
Tax on operating income
405
1,143
1,548
3,807
753
4,560
6,189
618
6,807
7,761
1,244
9,005
Operating income after tax
2,908
5,266
8,071
12,899
28,435
(365)
30,457
2,022
40,342
9,867
93,622
53,280
Free cash flow (=OI - ∆NOA )
3,273
3,244
(1,796)
(40,381)
ATO (on ending NOA
∆ATO
2.38
2.50
0.12
3.18
0.68
1.93
-1.25
Net operating assets
∆NOA
28,800
Note: NOA = Common equity + Long-term debt + Short-term borrowing + current portion of
term-debt – cash equivalents
Cash equivalents = Cash – $28 million
a.
Normalized operating income = FCF +
∆Sales
Normal ATO
Set normal ATO at average ATO for 1985–1987 = 2.69
52,889
2.69
= -$20,720 thousand
Normal OI for 1988 = − 40,381 +
This is well below reported operating income (after tax) of $12,899 thousand, calling into
question the quality of the reported income.
b.
Increase in ATO (as in 1987) implies income may be too low.
Decrease in ATO (as in 1988) implies income may be too high.
A decreasing ATO suggests too few expenses are booked to income (and too much cost
remains in the balance sheet). Further, there may be too much of sales in low quality
receivables.
c.
Other red flags:
1. Free cash flow is a large negative amount in 1988. Why?
2. Growth in NOA in 1988 is far greater that growth in sales (as the normalized OI
captures). Changes in individual ATO ratios are also high:
-
accounts receivables
inventory
3. Accounts payable and accrued liabilities declined in 1988 (inducing lower
expenses): Are fewer expenses being accrued to income?
E17.13. Quality Diagnostics: Gateway, Inc.
To start, note the red flags in the text for Chapter 17:
A Red Flag. In 2000, Gateway, the personal computer manufacturer decided to finance
computer sales to high-risk customers that outside financing companies were shunning. Its
consumer finance receivables, net of allowances for bad debts, increased from 3.3 percent
of sales to 7.3 percent of sales over the year. In the first quarter of 2001, the firm wrote off
$100 million of these receivables.
A Red Flag. Gateway, the computer manufacturer, had always operated on a high asset
turnover. In 1999, its ATO was 13.2 on sales of $8,965 million, and even higher in earlier
years. In 2000 sales increased by $636 million to $9,601 million, resulting in operating
income, after tax, of $231 million. Net operating assets, however, grew by $1,086 (more
than sales), resulting in a negative free cash flow of $855 million. The firm was investing
rapidly in new stores and inventory, providing consumer credit and increasing accruals, yet
sales growth was modest. Normalized operating income was -$855 + (636/13.2) = -$807
million, considerably less than reported operating income. In 2001, Gateway wrote off $876
million of net operating assets and reported an after-tax operating loss of $983 million.
From the information in the question, the following diagnostics can be calculated:
ATO
∆ATO
Decline in ATO is a red flag
Changes in individual ATOs:
Accounts receivable (no red flag)
Inventory (red flag: inventory build up)
PPE (red flag: lower sales from plant)
Financing receivables (red flag: fin. receivables build up)
2000
1999
5.43
-7.73
13.16
17.6
30.5
10.7
13.7
13.9
46.7
12.0
30.3
Warranties / Sales (no red flag)
Other accrued liabilities / sales (red flag)
Deferred revenue / sales (no red flag)
Allowance for uncollectibles / receivables (slight red
flag: lower allowance as a percentage of receivables)
1.98%
4.5%
1.8%
2.3%
2.1%
5.2%
1.9%
2.5%
The primary concern is in the build up of inventory and the increasing finance receivables. The
decline in accrued liabilities on rising sales also is a concern.
E17.14. A Financial Statement Restatement: Sunbeam
Sunbeam’s financial statement restatement involved a restatement of revenues (as
indicated in the question). Sunbeam had a practice of “bill and hold,” that is, billing customers
(and booking revenue) while they still held the goods and allowed customers to cancel orders.
The revenue restatements involved reversing the revenue from “bill and hold” billings.
The question asks you to focus on the accruals in the cash flow statement. Comparing
the original and restated statements, you will see the following:
1.
The accruals for restructuring charges and special charges totaling $283.7
million in 1996 were deemed to be excessive so were reduced.
Excessive restructuring accruals are bled back to future income statements
(so increasing profits), and you see in the original 1997 statement an income-increasing
reversal of a restructuring accrual of $43.4 million that is reduced in the restated
numbers.
2.
Deferred income taxes were reduced in the 1997 restatement. Deferred
income taxes are for accruals recognized in the income statement but not in the tax return, so these accruals
were reversed.
3.
The increase in receivables of $84.6 million in 1997 was reduced to $57.8
million because revenues had to be restated. 1996 receivables were also reduced.
4.
Inventories were restated upwards, reflecting the inventories that had been
deemed sold under the bill-and-hold policy but now are deemed not sold. This increase
in inventory reduces cost of goods sold and increases income. But inventories were
written down at the end of 1996, increasing 1997 income.
5.
Prepaid expenses and other net current assets and liabilities in 1996 were
revised downwards, reducing 1996 income.
6.
The “other” item was reduced in 1997, reducing 1997 income.
E17.15. Stock Market Reactions to Earnings Announcements: Eastman, Kodak, and Intel
(a)
(In millions of dollars)
Eastman Kodak
1998
1997
Sales
Net income
Net profit margin
Change in net profit margin
3,400
398
11.7%
5.6%
3,780
231
6.1%
6,700
1,600
23.9%
6,147
1,600
26.0%
Intel Corporation
Sales
Net income
Net profit margin
Eastman Kodak’s profit and profit margin increased on declining sales. The declining
sales in itself is bad news for the future, and increasing earnings on declining sales raise
questions as to the quality of the earnings. Were expenses reduced by manipulation? This is a
case of increasing margins with declining asset turnover, which raises a red flag.
Intel’s income is seen as high quality. Income did not increase on increasing sales. If
there were any manipulation, it would have to be recognizing mire expenses than necessary, so
reducing expenses to be recognized in the future. The market saw the sales increase as good
news and did not interpret the increase in expenses per dollar of sales as bad news.
(b)
The following red flags are raised in the cash flow statement:
1.
Earnings increased while cash flow from operations decreased. So, accruals
increased even though sales increased, and accruals can involve manipulation.
2.
Earnings in 1998 included a one-time gain on sale of a business of $107 million.
3.
Even though sales decreased over 1997, 1998 net accounts receivable increased
by $216 million. Are these good quality receivables? Have bad debt allowances
been reduced?
4.
There is inventory build-up in 1998 (by $334 million) on a decline in sales. Is the
firm having trouble moving its inventory?
5.
Operating liabilities decreased in 1998 by $553 million, compared to $285 million
in 1997. Is the firm reducing expenses by reducing accrued expenses and other
operating liabilities?