Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
Peter Breugel, The
PageElder,
1
”The Blind Leading the Blind”of(1568)
52
Questions about Widget, Inc –
• Should we buy? Is business
solid? Any problems?
• How much should we pay?
What’s company’s value?
• Given problems, any
protections we should get?
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
Page 2
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Module IV – Corporate Finance
Chapter 9
Numeracy for Corporate Lawyers
Bar
exam
Corporate
practice
Law
profession
Citizen of
world
Corporations:
A Contemporary Approach
• Financial accounting
– Fundamental formula
– Accounting statements: Balance
sheet, income statement, cash flow
statement
– Accounting statement analysis
Workshop 1
• Business valuation
–
–
–
–
Future vs. present value
Accounting value vs. market value
Income vs. cash flow
Discounted cash flow
Workshop 2
Chapter 9
Numeracy for Corporate Lawyers
Page 3
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Accounting basics
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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“Cookie jar” business
You go into business, buying
and selling items from your
cookie jar. To keep track of
your money-making efforts
you keep accounts.
Fundamental equation:
Assets = Liabilities + Equity
Accounting entries
–
–
–
–
ID accounting event
Value event
Record event
Disclose event
Financial statements
– Balance sheet
– Income statement
– Cash flow statement
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Accounting entries
Assets = Liabilities + Equity
Put $12 in cookie jar
$12
$0
$12
Borrow $10 from Mom (put in IOU)
$22
$10
$12
Buy two felt-tip pens for $2 each
$22
$10
$12
Buy $5 scissors on credit
$27
$15
$12
Sell one of the felt-tip pens for $3
$28
$15
$13
Repay the $5 scissors debt
$23
$10
$13
Pay $2 rent for using the jar
$21
$10
$11
Take our $5 to go to movies
$16
$10
$6
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Where do financial statements come from?
Balance sheet
(assets = liabilities + equity)
Assets = Liabilities + Equity
Put $12 in cookie jar
$12
$0
$12
Borrow $10 from Mom (put in IOU)
$22
$10
$12
Buy two $2 felt-tip pens
$22
$10
$12
Buy $5 scissors on credit
$27
$15
$12
Sell one of the felt-tip pens for $3
$28
$15
$13
Repay the $5 scissors debt
$23
$10
$13
Pay $2 rent for using the jar
$21
$10
$11
Take our $5 to go to movies
$16
$10
$6
Income statement
(sales – expenses = net
income)
Cash flow statement
(cash at beginning – cash out
+ cash in = cash balance)
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Balance sheet
(assets = liabilities + equity)
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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What if market
price of scissors
goes up? or down?
Assets
Cash
Pens
Scissors
Balance sheet
(at end of Day 1)
What if you don’t
show the IOU to
Mom?
Total assets
Liabilities
$9
IOU (Mom)
$2
Credit (scissors)
$5
Total liabilities
Equity
Mine
Total equity
$16
?? Total Liabilities + Equity
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
$10
$0
$10
$6
$6
$16
??
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Income statement
(sales – expenses = net income)
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Income statement
(Day 1)
Net sales
What if you treat
jar as “asset”
not “expense”?
$3
Operating expenses
Cost of goods sold
$2
Rent (jar)
$2
Selling/adm expenses
$0
Total operating expenses
$4
Operating income
($1)
Interest expense (Mom/scissors)
$0
Income taxes
$0
Net income
($1)
Dividends paid
Corporations:
A Contemporary Approach
$5
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Numeracy for Corporate Lawyers
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Statement of cash flows
(cash at beginning – cash out + cash in =
cash balance)
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A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Is the “cookie jar”
business healthy?
sustainable?
Cash flow statement
(Day 1)
Operating activities
Net income
Decrease (increase) inventories
Total operating activities
Investing activities
--
Financing activities
Increase (decrease) short-term debt
Increase (decrease) long-term debt
Investment by owner
Distribution to owner
Total financing activities
Increase (decrease) cash position
Corporations:
A Contemporary Approach
($1)
($7)
($8)
Chapter 9
Numeracy for Corporate Lawyers
$0
$10
$12
($5)
$17
$9
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Corporations:
A Contemporary Approach
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Balance sheet - terms
Corporations:
A Contemporary Approach
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Numeracy for Corporate Lawyers
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How is “inventory”
valued? Avg cost /
FIFO / LIFO?
Balance sheet
Assets
Current assets
Cash
Accts receivable
Inventories
Prepaid expenses
(as of date)
What does it mean
to “write off” a
loss?
Liabilities
Current liabilities
Accounts payable
Notes payable
Accrued expenses payable
Long term liabilities
Fixed assets
Land
Buildings
Machinery
Office equipment
Less accumulated
depreciation
Owner’s equity
Common stock
Paid-in capital
Retained earnings
Intangible assets
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Balance sheet analysis
Liquidity analysis – can Widget
pay its current debts?
Check “current ratio”
Debt analysis – can Widget take
on new debt?
Check “debt-equity ratio”
Equity analysis – does Widget
have value to its owners?
Check “book value”
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Liquidity analysis
Balance sheet
Assets
Liabilities
Current assets
Current liabilities
Cash
Accts receivable
Inventories
Prepaid expenses
Accounts payable
Notes payable
Accrued expenses payable
Long term liabilities
Fixed assets
Land
Buildings
Machinery
Office equipment
Less accumulated
depreciation
Intangible assets
Corporations:
A Contemporary Approach
Owner’s equity
Current Ratio
Current Assets
divided by
Current Liabilities
Common stock
Paid-in capital
Retained earnings
FY 2 = 1.62
FY 1 = 1.29
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Numeracy for Corporate Lawyers
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Debt analysis
Balance Sheet
Assets
Liabilities
Current assets
Current liabilities
Cash
Accts receivable
Inventories
Debt/Equity Ratio
debt
PrepaidLong-term
expenses
divided by Equity
Accounts payable
Notes payable
Accrued expenses payable
Long term liabilities
Fixed assets
Land FY 2 = 1.32
FY 1 = 1.79
Buildings
Machinery
Office equipment
Less accumulated
depreciation
Owner’s equity
Common stock
Paid-in capital
Retained earnings
Intangible assets
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A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Equity analysis
Balance Sheet
Assets
Current assets
Cash
Accts receivable
Inventories
Prepaid expenses
Liabilities
Current liabilities
Accounts payable
Notes payable
Accrued expenses payable
Long term liabilities
Fixed assets
Book value
Land
Assets
Owner’s equity
Buildings
minus
Common stock
Liabilities
Machinery
Paid-in capital
Office equipment
Retained earnings
Less accumulatedFY 2 = $1,510,000
depreciation FY 1 = $1,120,000
Intangible assets
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Income statement - terms
Is Widget, Inc profitable?
•
•
•
•
Corporations:
A Contemporary Approach
Net income
EBITDA
Operating margin
Return on equity
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Numeracy for Corporate Lawyers
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Income statement analysis
Net sales
Operating expenses
Cost of goods sold
Depreciation
Selling and administrative expenses
Research and development
Operating income
Widget net income
(after expenses,
depreciation,
Interest, taxes)
FY 2: $390,000
FY 1: $254,000
FY 0: $226,000
Interest expense
Income before taxes
Income taxes
Special income
Net Income
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Income statement analysis
Net sales
Operating expenses
Cost of goods sold
Depreciation
Selling and administrative expenses
Research and development
Operating income
Interest expense
Widget EBITDA
(Earnings before Interest,
taxes, depreciation,
amortization)
FY 2: $1,170,000
FY 1: $1,005,000
FY 0: $923,000
Income before taxes
Income taxes
Special income
Net Income
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Income statement analysis
Net sales
Operating expenses
Cost of goods sold
Depreciation
Selling and administrative expenses
Research and development
Operating income
Widget
operating margin
(net sales minus
operating expenses,
divided by net sales)
FY 2 = 920/7500 = 12.3%
FY 1 = 765/7000 = 10.9%
FY 0 = 723/6800 = 10.6%
Interest expense
Income before taxes
Income taxes
Net Income
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Compare income statement / balance sheet
Widget
return on equity (ROI)
(net income divided by
stockholders' equity
as of prior year)
FY 2 = 390/1120 = 34.8%
FY1 = ??
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Cash flow analysis
Is Widget healthy?
• Cash flow
• Changes in accts
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A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Cash flow analysis
From Operating Activities
• Net income
• Decrease (increase) in accts receivable
• Decrease (increase) in inventories
• Decrease (Increase) in prepaid expenses
• Increase (Decrease) in accounts payable
• Increase (Decrease) in accrued expenses payable
• Depreciation
From Investing Activities
• Sales (Purchases) of machinery
• Sales (Purchases) of office equipment
From Financing Activities
• Increase (Decrease) in short-term borrowings
• Increase (Decrease) in long-term borrowings
Increase (Decrease) in Cash Position
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
What happened?
FY 2
($175,000)
FY 1
$16,000
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Cash flow analysis
From Operating Activities
• Net income
• Decrease (increase) in accts receivable
• Decrease (increase) in inventories
• Decrease (Increase) in prepaid expenses
• Increase (Decrease) in accounts payable
• Increase (Decrease) in accrued exp payable
• Depreciation
FY 2
$390,000
($235,000)
($205,000)
($5,000)
$75,000
$15,000
$250,000
FY 1
$254,000
($34,000)
($28,000)
($3,000)
$25,000
$7,000
$240,000
From investing Activities
• Sales (Purchases) of machinery
($65,000)
($378,000)
Why did accounts receivable
increase by $201,000?
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Cash flow analysis
From Operating Activities
• Net income
• Decrease (increase) in accts receivable
• Decrease (increase) in inventories
• Decrease (Increase) in prepaid expenses
• Increase (Decrease) in accounts payable
• Increase (Decrease) in accrued exp payable
• Depreciation
FY 2
$390,000
($235,000)
($205,000)
($5,000)
$75,000
$15,000
$250,000
FY 1
$254,000
($34,000)
($28,000)
($3,000)
$25,000
$7,000
$240,000
From investing Activities
• Sales (Purchases) of machinery
($65,000)
($378,000)
Why did inventories
increase by $177,000?
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Cash flow analysis
From Operating Activities
• Net income
• Decrease (increase) in accts receivable
• Decrease (increase) in inventories
• Decrease (Increase) in prepaid expenses
• Increase (Decrease) in accounts payable
• Increase (Decrease) in accrued exp payable
• Depreciation
FY 2
$390,000
($235,000)
($205,000)
($5,000)
$75,000
$15,000
$250,000
FY 1
$254,000
($34,000)
($28,000)
($3,000)
$25,000
$7,000
$240,000
From investing Activities
• Sales (Purchases) of machinery
($65,000)
($378,000)
Why did machinery purchases
decrease by $313,000?
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Group hypos
[click here]
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
Page 31
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Module IV – Corporate Finance
Chapter 9
Numeracy for Corporate Lawyers
Bar
exam
Corporate
practice
Law
profession
Citizen of
world
Corporations:
A Contemporary Approach
• Financial accounting
– Fundamental formula
– Accounting statements: Balance
sheet, income statement, cash flow
statement
– Accounting statement analysis
Workshop 1
• Business valuation
–
–
–
–
Future vs. present value
Accounting value vs. market value
Income vs. cash flow
Discounted cash flow
Workshop 2
Chapter 9
Numeracy for Corporate Lawyers
Page 32
of 52
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
Page 33
of 52
What is the value of $1,000?
Which would you prefer –
$800 today or $1,000 in three years?
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Time value of money
Invest $800
Year 1
Year 2
Year 3
10%
$80.00
$88.00
$96.80
Balance
$880.00
$968.00
$1,064.80
$800 * (1+ .10)3 = $1064.80
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Time value of money
Invest $800
Year 1
Year 2
Year 3
5%
$40.00
$42.00
$44.10
Balance
$840.00
$882.00
$926.10
$800 * (1+ .05)3 = $926.10
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Future value
FV = PV * (1+ i)n
FV
7
PV
0
Corporations:
A Contemporary Approach
1
2
3
4
5
Chapter 9
Numeracy for Corporate Lawyers
6
Page 37
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You are offered $1,000
in three years from now.
What is its present value?
Why is this called “discounting”?
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Discounting to present value
Discount
$1,000
Year 3
Year 2
Year 1
End of year
20%
$1,000
$833
$694
$167
$139
$115
Start of year
(divide by 1.20)
$833
$694
$579
$1,000 / (1+ .20)3 = $579
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Present value
PV = FV / (1+ i)n
FV
7
6
5
Corporations:
A Contemporary Approach
4
3
2
Chapter 9
Numeracy for Corporate Lawyers
1
0
PV
Page 40
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Pop Quiz
[answers]
1.
You put $10,000 in the
bank at 3.6% annual
interest. How much will
you have after 20 years?
What about 7.2% in 10
years?
3.
You consider buying a
vineyard that has annual
cash flow of $300,000. It’s
risk is similar to that of an
apple orchard (discount
20%). Value the vineyard.
2.
You are a superstar at your
law firm. You are
promised an $85,000
bonus if you stay at the
firm for 5 years. How
much is it worth now? (Law
firm’s borrowing rate is
12%.)
4.
You look at another vineyard.
It has cash flow this year of
$250,000, but its cash flows
have been increasing each
year by 7.5%. Assume a
higher discount rate of 25%.
Value the vineyard.
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Business valuation
“Accounting is twodimensional;
valuation is threedimensional”
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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“Old Man and Apple Tree”
Consider the following valuations:
•
•
•
•
•
•
•
•
Corporations:
A Contemporary Approach
Salvage
Current production
Future production
Market price
Book value
Comparables (ratio)
Capitalization of earnings
Discounted cash flow
Chapter 9
Numeracy for Corporate Lawyers
Page 43
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“Old Man and Apple Tree”
The old man figures he’ll
have cash flows from
the tree of $50 for 5
years, then $40 for 10
years. And then sell the
tree as firewood for $50.
What is the present value
of cash flows?
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Value of Apple Tree
Present Value
Year
Cash flow
5%
8%
15%
25%
1
50.00
47.62
46.30
43.48
40.00
2
50.00
45.35
42.87
37.81
32.00
3
50.00
43.19
39.69
32.88
25.60
4
50.00
41.14
36.75
28.59
20.48
5
50.00
39.18
34.03
24.86
16.38
6
40.00
29.85
25.21
17.29
10.49
7
40.00
28.43
23.34
15.04
8.39
8
40.00
27.07
21.61
13.08
6.71
9
40.00
25.78
20.01
11.37
5.37
10
40.00
24.56
18.53
9.89
4.29
11
40.00
23.39
17.16
8.60
3.44
12
40.00
22.27
15.88
7.48
2.75
13
40.00
21.21
14.71
6.50
2.20
14
40.00
20.20
13.62
5.65
1.76
15
40.00
19.24
12.61
4.92
1.41
Salvage
50.00
24.05
15.76
6.14
1.76
Total
482.58
398.15
273.71
183.27
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Time value of “perpetuity”
Discount
rate (i)
3%
Capitalization
multiplier (1/i)
33.3
Mathematically
5%
20
8%
12.5
PV = Pymt / i
PV = Pymt * (1/i)
10%
10
15%
6.7
25%
4
40%
2.5
Corporations:
A Contemporary Approach
***
Suppose a business earns
$10,000 per year, with a
DR = 15%. It’s PV =
$66,666
Chapter 9
Numeracy for Corporate Lawyers
Page 46
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Time value of “growing perpetuity”
What if somebody offers
you $10 each year –
growing at 3%, forever!
How much do you pay for
it, assuming an 8%
discount rate?
Mathematically
(Gordon-Shapiro model)
PV = Pymt1 / (d – g)
$10 * 1.03 / (.08 - .03) =
$10.30 / .05 = $206
________________
approximately
PV = Pymt / (d – g)
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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End of Lecture
(group work in class)
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Valuation of Widget, Inc.
(for whom are we doing the valuation?)
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Valuation methods:
• Asset value
• Market comparables
• Income
– Earnings
• P/E multiplier
• Cap multiplier
– Discounted cash flow
• Perpetuity
• Spreadsheet
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Assets method
(Adjusted book value)
Balance Sheet
Assets
Liabilities
[adjusted – some
up, some down]
[already reflects
payout amount]
$3,750,000
$5,260,000
[$5,660,000]
Equity
$1,510,000
[$1,910,000]
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Market methods
(Comparable)
Similar companies
EBITDA = $10,000,000
Sales price = 23,000,000
Multiplier = 2.3
Widget Inc
EBITDA = $1,170,000
Price = 2,691,000
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Income methods
(Earnings)
Earnings
P/E multiplier:
Earnings * P/E =
$390,000 * 4 =
$1,560,000
Cap multiplier:
Earnings * Cap =
$390,000 * (1 / 30%) =
$390,000 * 3.33 =
$1,300,000
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
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Income methods
Discounted cash flow
(Cash Flow)
Net income
$390,000
Depreciation
$250,000
Accts rec’ble
($130,000)
Inventory
($ 80,000)
Bonuses
$120,000
Normalized (CF) $500,000
Discount rate
Growth rate
Capitalization rate
30%
5%
25%
(discount minus growth)
DCF
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
$2,000,000
Page 54
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What is Widget, Inc. worth?
Valuation methods:
• Asset value
$1.9 million
• Market
$2.7 million
• Earnings
$1.5 million
• Discounted cash flow
$2.00 million
Ah, let’s say $2.0 million
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
Page 55
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The end
Corporations:
A Contemporary Approach
Chapter 9
Numeracy for Corporate Lawyers
Page 56
of 52
Module IV – Corporate Finance
Chapter 9
Numeracy for Corporate Lawyers
Bar
exam
Corporate
practice
Law
profession
Citizen of
world
Corporations:
A Contemporary Approach
• Financial accounting
Day 1
Day 2
Day 3
Day 4
– Fundamental formula
– Accounting statements: Balance
sheet, income statement, cash flow
statement
– Financial statement analysis
• Business valuation
–
–
–
–
Future vs. present value
Accounting value vs. market value
Income vs. cash flow
Discounted cash flow
Chapter 9
Numeracy for Corporate Lawyers
Page 57
of 52