Taxation
The Effect of Taxation on Value
M&M
Modigliani-Miller Theorem - 1958
Franco Modigliani &
Merton Miller
Both Nobel Laureates
M&M
Start with a perfect world in which there are
no taxes; corporate or individual.
The value of a firm is unaffected by corporate
structure, i.e. how much debt or equity it has.
Leverage has no affect.
However with corporate tax, leverage
increases the value of the firm.
Company Data
10 Equity Partners holding 1 million shares
each
10 million shares outstanding
Perpetual stream of revenue of $13 million
per annum
Constant COGS of 80%
Un-levered equity beta of 0.9
Risk free rate is 4%
Re of the Market: 14%
1st Situation
D/E = 0
T=0
EBIT from operations = $2.6 million
EBIT
Revenue $13,000,000.00
COGS
(@ 80% of Revenue) ($10,400,000.00)
EBIT $2,600,000.00
1st Situation
D/E = 0
T=0
EBIT from operations = $2.6 million
Earnings after taxes & interest = $2.6 million
ru = 13%
ru
CAPM = Re = RFR + β(Rm – RFR)
re = .04 + .9(.14 - .04 )
re = .13
re = r u
ru = 13%
1st Situation
D/E = 0
T=0
EBIT from operations = $2.6 million
Earnings after taxes & interest = $2.6 million
ru = 13%
WACC = 13%
WACC
WACC = (1-L) x re + L x (1-T) x rd
No debt; L = 0; (1-L) = 1
T or Tax rate = 0; (1-T) = 1
ru = re = .13
rd = .04
WACC = (1 x .13) + (0 x 1 x .04) = .13
1st Situation
D/E = 0
T=0
EBIT from operations = $2.6 million
Earnings after taxes & interest = $2.6 million
ru = 13%
re = 13%
rd = 4%
WACC = 13%
Firm Value
Vu = FCF/re
FCF = 2.6 million
re = 13%
V = 2.6/.13
V = 20
Firm value = $20 million
1st Balance sheet
Assets Liability
$20,000,000 -$0-
Equity
$20,000,000
Liability plus Equity
$20,000,000
2nd Situation
Company wants to obtain a $2 million loan to retire
shares of stock
Perpetual loan of $2 million at 4% interest
10 million shares outstanding
$20 million value
Stock price = $2/share
Buy back 1 million shares
Equity = $8 million
Debt =$2 million
D/E = 1/9
2nd Situation
D/E = 1/9
T=0
EBIT from operations = $2.6 million
Earnings after taxes & interest
EBIT $2,600,000.00
Loan = $2,000,000.00
Times
Interest rate = .04
Interest ($8,000.00)
Earnings after
taxes & interest $2,520,000.00
2nd Situation
D/E = 1/9
T=0
EBIT from operations = $2.6 million
Earnings after taxes & interest = $2.52 million
ru = 13%
re = 14%
re
re = ru + D/E (ru-rd)(1-T)
re = .13 + 1/9 (.13 - .04) (1-0)
re = .14
2nd Situation
D/E = 1/9
T=0
EBIT from operations = $2.6 million
Earnings after taxes & interest = $2.52 million
ru = 13%
re = 14%
WACC = 13%
WACC
WACC = (1-L) x re + L x (1-T) x rd
Debt!
L = D/(D+E)
L = 2M/20M = .1
T or Tax rate = 0; (1-T) = 1
re = .14
rd = .04
WACC = (1 - .1) x .14 + (.1 x 1 x .04) = .13
Firm Value
VL = Vu + DT
Vu = FCF/re
FCF = 2.52 million
re = 14%
Vu = 2.52/.14 = 18 million
DT = Debt = 2 million
Firm value Leveraged = $20 million
2nd Balance sheet
Assets Liability
$20,000,000 $2,000,000
Equity
$18,000,000
Liability plus Equity
$20,000,000
Situation 1 & 2
$20 $2 million
million Debt
Equity
$18
million
Equity
Total Firm Value = $20 Total Firm Value = $20
Million Million
3rd Situation
The same conditions as the first; un-
leveraged, no debt
TAXES!
Corporate tax rate = 34%
3rd Situation
D/E = 0
T = 34%
EBIT from operations = $2.6 million
Earnings after taxes & interest = $1.716
million
Earnings after taxes & interest
EBIT $2,600,000.00
Times
Tax rate = .34
Taxes ($884,000)
Earnings after
taxes & interest $1,716,000
3rd Situation
D/E = 0
T = 34%
EBIT from operations = $2.6 million
Earnings after taxes & interest = $1.716
million
ru = 13%
re = 13%
rd = 4%
WACC = 13%
Firm Value
Vu = FCF/re
FCF = 1.716 million
re = 13%
V = 1.716/.13
V = 13.2
Firm value = $13.2 million
3rd Balance sheet
Assets Liability
$13,200,000 -$0-
Equity
$13,200,000
Liability plus Equity
$13,200,000
4th Situation
The same conditions as the third
However
Firm borrows $2 million
TAXES!
Corporate tax rate = 34%
4th Situation
D/E = ?
T = 34%
EBIT from operations = $2.6 million
Earnings after taxes & interest = $1.6632
million
re = 14%
rd = 4%
WACC = ?
Earnings after interest
EBIT $2,600,000.00
Loan = $2,000,000.00
Times
Interest rate = .04
Interest ($8,000.00)
Earnings after
interest $2,520,000.00
Earnings after taxes & interest
Earnings after interest $2,520,000.00
Times
Tax rate = .34
Taxes ($856,800.00)
Earnings after
taxes & interest $1,663,200.00
Firm Value
VL = Vu + DT
Vu = FCF/re
FCF = 1.6632 million
re = 14%
Vu = 1.6632/.14 = 11.88 million
DT = Debt = 2 million
Firm value Leveraged = $13.88 million
D/E
D = $2,000,000.00
D + E = $13,880,000.00
E = $11,000,000.00
D/E = .1684 = 16.84%
WACC
WACC = (1-L) x re + L x (1-T) x rd
L = D/(D+E)
L = 2M/11.88M = .1441
T or Tax rate = .34; (1-T) = .66
re = .14
rd = .04
WACC = (1 - .1441) x .14 + (.1441 x .66 x
.04) = .12363 = 12.363%
4th Situation
D/E = 16.84%
T = 34%
EBIT from operations = $2.6 million
Earnings after taxes & interest = $1.6632
million
re = 14%
rd = 4%
WACC = 12.363%
4th Balance sheet
Assets Liability
$13,880,000 $2,000,000
Equity
$11,880,000
Liability plus Equity
$13,880,000
Situation 3 & 4
$6.12
$6,200,000
million
million
Taxes
Taxes
$11.88
million
Equity
$13.2 $2 million
million Debt
Equity
Total Firm Value = Total Firm Value =
$13.2 Million $13.88 Million
Leverage
Leverage Stops the Leakage From
Taxes!
Summary
Item #1 #2 $3 #4
D/E 0 1/9 0 2/11.88
T 0 0 .34 .34
EBIT $2.6M $2.6M $2.6M $2.6M
After T&I $2.6M $2.52M $1.716M $1.6632M
ru 13% 13% 13% 13%
re 13% 14% 13% 14%
WACC 13% 13% 13% 12.363%
rd 4% 4% 4% 4%
Value $20M $20M $13.2M $13.88M
Taxation
Taxation Entities
Taxable Entities
Individuals
Regular or “C” Corporations
Estates
Some Trusts
Non-Taxable Entities
Conduit Entities: report only
Partnerships
“S” Corporations
Conduits
Profit (Loss) of entity flows through the
conduit to the owner(s)
Owner(s) pay tax according to their personal
tax position
“C” Corp
Net Revenue
minus COGS
minus SAG
minus Depreciation & amortization
minus Interest
Earnings before taxes
minus Taxes
Net Earnings
“C” Corp
Dividends are subtracted from net earnings
Dividends have been taxed at the corporate
level
Dividends are included as ordinary income in
the individuals’ tax position
Double taxation!
“S” Corp
Net earnings are not subject to corporate tax
Net earnings profit (loss) flows through to
owner(s)
Single taxation!