SOLUTIONS TO PRACTICE QUESTIONS
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
(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 Jun-09 Dec
Operating assets 28,631 30,024 Financial obligations 7,424 6,971Operating liabilities 7,194 8,747 Financial assets 4,457 4,238
Net financial obligations 2,967 2,733
Common equity 18,470 18,544Net operating assets 21,437 21,277 21,437 21,277
Cash Flow Statement:
Free cash flow: J = 690 [C - I = OI - NOA]
Cash investment: I = (106) [I = C - (C - I)] (a liquidation)
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 = Operating income Cash from operations
= 850 584
= 266
2. Operating accruals = NOA Investment
= 160 (-106)
= 266
(c) NFO = NFE (C - I) + d
= 59 690 + 865
= 234
(d) The net dividend of $865 was generated as follows:
Operating income 850 less NOA 160 Free cash flow 690 less net financial expenses 59 631 plus increase in net debt 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).
2009 2008
Price 224 238 CSE (apply P/B ratio to price) 140 119 Free cash flow 8.4 Dividend (d = C - I) 8.4 Price + dividend 246.4 Return (246.4 224) 22.4 Rate of return 10%
(b)
There are three ways of getting the earnings:
1. Earnings = Stock return - premium
= 22.4 (119 - 84)
= (12.6) (a loss)
2. OI = C - I + NOA
= 8.4 + (119 140)
= (12.6)
(Earnings = OI as there are no financial items)
3. Earnings = CSE + dividend
= -21 + 8.4
= (12.6)
E8.9. Calculating Comprehensive Income to Shareholders: Intel Corporation
Net income 10,535
Unrealized loss on securities (3,596)
Loss on conversion of notes (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 887 = 2,334
0.38
Tax 887
Loss after tax 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, Microsofts 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 = $1,240
Carrying value of the preferred stock 980
Loss on conversion $ 260
E8.12. Reformulation of an Equity Statement: Dell Computer Corporation
a.
Loss on stock option exercise = 260 = 743
0.35
Tax effect 260
483
b.
Reformulated Equity Statement:
Balance, February 1, 2002 4,694
Net transaction with shareholders:
Share issue, at market value (418 + 483) 901
Share repurchase, at market value (1,400) (499)
(2,290 890)
Comprehensive income:
CI reported 2,051
Loss on share repurchase (890) 1,161
Balance, January 31, 2003 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 2,290
Lost on repurchase 890
The loss on exercise of options has not been included in comprehensive income because of the potential double counting problem.
E9.4 Reformulation of a Balance Sheet and Income Statement
Balance sheet:
Operating cash $ 23
Accounts receivable 1,827
Inventory 2,876
PPE 3,567
Operating assets 8,293
Operating liabilities:
Accounts payable $1,245
Accrued expenses 1,549
Deferred taxes 712 3,506
Net operating assets 4,787
Net financial obligations:
Cash equivalents $( 435)
Long-term debt 3,678
Preferred stock 432 3,675
Common shareholders equity $1,112
Income statement:
Revenue $7,493
Operating expenses 6,321
Operating income before tax 1,172
Tax expense:
Tax reported $295
Tax on interest expense 80 375
Operating income after tax 797
Net financial expense:
Interest expense 221
Tax benefit at 36% 80
141
Preferred dividends 26 167
Net income to common $630
E9.6. Testing Relationships in Reformulated Income Statements
The solution has to be worked in the following order:
A = Operating revenues operating expenses
= 5,523 4,550
= 973
E = Interest expense after tax/ (1 tax rate)
= 42/0.65
= 64.6
F = E 42
= 22.6
D = 610 + 42
= 652
C = F
= 22.6
B = 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%
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.
E10.10. Free Cash Flow for Kimberly-Clark Corporation
a.
Reformulate the balance sheet:
2007 2008
Operating assets $18,057.0 $16,796.2 Operating liabilities 6,011.8 5,927.2 Net operating assets (NOA) 12,045.2 10,869.0
Financial obligations $6,496.4 $4,395.4 Financial assets 382.7 6,113.7 270.8 4,124.6
Common equity (CSE) $ 5,931.5 $ 6,744.4 By Method 1,
Free cash flow = Operating income Change in net operating assets = $2,740.1 (12,045.2 10,869.0) = 1,563.9
By Method 2,
Free cash flow = Net financial expense NFO + d
= 147.1 (6,113.7 4,124.6) + 3,405.9
= 1,563.9
Net payout to shareholders (d) = Comprehensive income CSE
= (2,740.1 147.1) (-812.9)
= 3,405.9
b.
Cash flow from operations reported $2,429.0 million
Net interest payments 142.4
Tax on net interest payments 52.1 90.3
Cash flow from operation 2,519.3
Cash investment reported 898.0
Liquidation of short-term investments 56.0 954.0
Free cash flow $1,565.3 million
E11.5 Profit Margins, Asset Turnovers, and Return on Net Operating Assets: A What-If Question
The effect would be (almost) zero.
Existing RNOA = PM ATO
= 3.8% 2.9
= 11.02%
RNOA from new product line is
RNOA = 4.8% 2.3
= 11.04%
E11.7. Analysis of Profitability: The Coca-Cola Company
Average balance sheet amounts are as follows:
2007 2006 Average
Net operating assets $26,858 $18,952 $22,905
Net financial obligations 5,114 2,032 3,573
Common shareholders equity $21,744 $16,920 $19,332
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%
E12.3. Analyzing the Growth in Shareholders Equity
Change in CSE = 583
Change in sales = 5,719
Change in 1/ATO = 1/2.4 1/2.5 = 0.4167 0.4 = 0.0167
Change in NFO = 1,984
Following Box 12.10,
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 Due to Due to
Sales NOA Borrowing
E12.7. Core Income and Core Profitability for The Coca Cola Company
Average balance sheet amounts are as follows:
2007 2008 Average
Net operating assets $26,858 $18,952 $22,905
Net financial obligations 5,114 2,032 3,573
Common shareholders equity $21,744 $16,920 $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 Cokes 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%
E13.14. Enterprise Multiples for IBM Corporation
Here are the totals for IBMs 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 = 141,290/28,470 = 4.96
Unlevered (enterprise) P/B = 160,909/48,089 = 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 = $102/$8.73 = 11.68
To get the unlevered P/E, first calculate forward OI:
Earnings forecast for 2008: $8.73 1,385.2 shares $12,092.8 Net financial expense for 2008: $19,619 3.3% 647.4 Forward operating income $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.
a. Free cash flow = OI NOA = 1,901 (12,847 12,297)
= 1,351
b. ReOI (2008) = 1,901 (0.058 12,297) = 1,188
c. 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
d. (This question is not in all printings of the book) Trailing P/E =
EdP +
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
649,1752250,20 +
= = 12.74
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? Its 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?
E13.18. 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
Forecasted RNOA = 1,294/4,632
(using beginning-of-year NOA)
$5.08
261.1 million
$1,326.4 million
32.4
$1,294.0 million
27.94%
(b) [ ] million8.6% - 27.94% ReOI Forecasted 6.895632,4 ==
Value =
1.04-1.086895.6
5,644 +
= $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 =
+ g
AOIGOIFF
211
1+ NFA
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 = 4,632 1.04
= 4,817.3
OI2007 = 4,817.3 0.2794
= 1,345.9
FCF2006 = OI2006 - NOA2006
= 1,294.0 185.3
= 1,108.7
AOIG2007 = OI2007 + FCF2006 reinvested (1.086 OI1997)
= 1,345.9 + (0.086 1,108.7) (1.086 1,294)
= $35.95 million
Method 2 (much simpler!): AOIG is growth in residual operating income from the previous
year
AOIG2007 = ReOL2006 0.04
= 895.6 0.04
= 35.82 (allow for rounding error)
Accordingly, the valuation is:
Value of equity =
+04.1086.1
82.35294,1086.01
+ 1,012
= $25,113 million or $96.18per share
(d) Value of operations = Value of equity - NFA
= 25,113 1,012
= $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
+=
11
01
1
0
1
0 1NBCOI
VELEV
OIV
EarnV NOANOAE
= 18.63 - [0.0244 (18.83 1/0.032]
= 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.