If a company buys preferred stock in another company, 70% of the dividends are excluded from taxes.
Therefore, the after-tax return will be:
After-tax dividend yield = Preferred dividend rate[1 – (1 – Div. exclusion %)(T)]
Cash $ 100 Accounts payable $ 200
Accounts receivable 650 Accruals 350
Inventory 550 Notes payable 350
Current assets $1,300 Current liabilities $ 900
Net fixed assets 1,000 Long-term debt 600
Common equity 300
Retained earnings 500
Total assets $2,300 Total liab. & equity $2,300
Net operating working capital = Current assets – (Current liabilities – Notes payable)
NOWC = $1,300.00 – $550
NOWC = $750
This problem can be worked very easily—just multiply the increase in depreciation by (1 – T) to get
the decrease in net income:
Change in depreciation $0.700
Tax rate 0.350
Reduction in net income $0.455
We can also get the answer a longer way, which explains things more clearly:
Old New Change
Bonds $5.000 $5.000 $0.000
Interest rate 0.065 0.065 0.000
Tax rate 0.350 0.350 0.000
Sales $10.500 $10.500 $0.000
Operating costs excluding depreciation $6.250 $6.250 $0.000
Depreciation $1.300 $2.000 $0.700
Operating income (EBIT) $2.950 $2.250 -$0.700
Interest charges $0.325 $0.325 $0.000
Taxable income $2.625 $1.925 -$0.700
Taxes $0.919 $0.674 -$0.245
Net income $1.706 $1.251 -$0.455
Sales $2,850.00
Costs 1,850.00
Depreciation 192.00
EBIT $ 808.00
Interest expense 285.00
EBT $ 523.00
Taxes: rate = 35% 183.05
Net income $ 339.95
EBIT $808.00
Tax rate 35%
EBIT(1 − T) = $525.20
Sales $2,250
Costs 1,400
Depreciation 250
EBIT $ 600
Interest expense 70
EBT $ 530
Taxes: rate = 40% 212
Net income $ 318
EBIT $600.00
Tax rate 40%
EBIT(1 − T) = $360
EBIT(1 − T) 2011 2012 Change = Net invest. in FA + NOWC
Total assets $2,000 $2,500 $500
2012 FCF = EBIT(1 − T) − Net investment in FA + NOWC
2012 FCF = $925 − $500
2012 FCF = $425
Bonds $3,500.00
Interest rate 6.25%
Tax rate 35.00%
Sales $10,750.00
Operating costs excluding depreciation 5,500.00
Depreciation 1,250.00
Operating income (EBIT) $ 4,000.00
Capex + NOWC= $1,550.00
Tax rate = 35%
FCF = EBIT(1 – T) + Deprec. – (Capex + ΔNOWC)
FCF = $2,600 + $1,250 – $1,550
Free cash flow = $2,300
Tax rate 35%
Required addition to net operating working capital $6,850
Required capital expenditures (fixed assets) $15,250
Sales $185,250
Operating costs excluding depreciation 140,500
Depreciation 9,250
Operating income (EBIT) $ 35,500
FCF = EBIT(1 − T) + Deprec. – Capex – ΔNOWC
FCF = $23,075.00 + $9,250 – $15,250 – $6,850
Net income $600,000
Interest expense $20,000
Investor-supplied operating capital $9,000,000
Tax rate 40%
After-tax cost of capital 10%
EBT = Net income/(1 – T)
EBT = $1,000,000
EBIT = EBT + Interest
EBIT = $1,200,000
EVA = EBIT(1 – T) – (WACC × Total investor-supplied capital)
EVA = $720,000 – $900,000
EVA = -$180,000
Tax rate 40%
EBT After Unused
Taxable Carry-Forward Forward Carryable
Year Income Used Applied Amount
2008 -$4,000,000 $0 $0 $4,000,000
2009 $1,000,000 $1,000,000 $0 $3,000,000
2010 $2,000,000 $2,000,000 $0 $1,000,000
2011 $3,000,000 $1,000,000 $2,000,000 $0
2012 $5,000,000 $0 $5,000,000 $0
2011 Tax liability = EBT × Tax rate
2011 Tax liability = $800,000
Tax rate 34%
EBT After Unused
Carry-Forward Forward Carryable
Year Income Used Applied Amount
2009 -$3,200,000 $0 $0 $3,200,000
2010 $200,000 $200,000 $0 $3,000,000
2011 $500,000 $500,000 $0 $2,500,000
2012 $2,800,000 $2,500,000 $300,000 $0
2012 Tax liability = EBT × Tax rate
2012 Tax liability = $102,000
Preferred dividend rate 7.00%
Tax rate 38%
Dividend exclusion % 70%
After-tax dividend yield = Preferred dividend rate[1 – (1 – Div. exclusion %)(T)]
After-tax dividend yield = 6.20%
Bond yield 8.50%
Municipal bond yield 5.50%
Municipal yield = After-tax bond yield
5.50% = 8.50% × (1 – T)
0.6471 = (1 – T)
T = 35.29%
Municipal bond yield 4.80%
Tax rate 27.00%
Municipal yield = After-tax bond yield
4.80% = BT yield × (1 – T)
4.80% = BT yield × 73.00%
BT yield = 6.58%
Municipal bond yield 9.00%
Tax rate 35.00%
Municipal yield = After-tax bond yield
9.00% = BT yield × (1 – T)
9.00% = BT yield × 65.00%
BT yield = 13.85%
Treasury bond yield 6.00%
Tax rate 40.00%
Remember that municipal bonds are tax exempt, so their BT yield = AT yield.
Municipal yield = AT bond yield
Municipal yield = BT bond yield × (1 – T)
Municipal yield = 3.60%
BT Bond yield 9.00%
Municipal bond yield 6.50%
Remember that municipal bonds are tax exempt, so their BT yield = AT yield.
Municipal yield = After-tax bond yield
6.50% = 9.00% × (1 – T)
0.7222 = (1 – T)
T = 27.78%
BT project return 11.00%
BT preferred return 9.00%
Tax rate 25.00%
Dividend exclusion % 70.00%
After-tax return on project = BT project return × (1 – T)
After-tax return on project = 8.25%
After-tax return on pref. = BT pref. return[1 – (1 – Div. exclusion %)(T)]
After-tax return on pref. = 8.33%
BT bond yield 11.00%
BT municipal bond yield 8.00%
BT preferred yield 9.00%
Tax rate 40.00%
Dividend exclusion % 70.00%
Since municipal bonds are exempt from federal taxes, its BT return = AT return
AT municipal bond yield = 8.00%
AT bond yield = BT bond yield × (1 – T)
AT bond yield = 6.60%
AT preferred yield = BT pref. return[1 – (1 – Div. exclusion %)(T)]
AT preferred yield = 7.92%
Highest AT yield = 8.00%
BT Preferred stock yield 8.50%
Municipal yield 7.50%
Dividend exclusion % 70.00%
Remember that municipal bonds are tax exempt, so their BT yield = AT yield.
Municipal yield = After-tax preferred yield
7.50% = BT pref. return × [1 – (1 – Div. exclusion %)(T)]
7.50% = 8.50% × [1 – 30.00% × (T)]
88.24% = [1 – 30.00% × (T)]
T = 39.22%
BT Preferred stock yield 7.00%
Dividend exclusion % 70.00%
BT bond yield 10.00%
AT bond yield = After-tax preferred yield
BT bond yield × (1 – T) = BT pref. return × [1 – (1 – Div. exclusion %)(T)]
10.00% × (1 – T) = 7.00% × [1 – 30.00% × (T)]
3.00% = 7.900%(T)
T = 37.97%
BT municipal bond yield 8.50%
BT bond yield 10.50%
BT preferred yield 9.25%
Tax rate 35.00%
Dividend exclusion % 70.00%
Since municipal bonds are exempt from federal taxes, its BT return = AT return
AT municipal bond yield = 8.500%
AT bond yield = BT bond yield × (1 – T)
AT bond yield = 6.825%
AT preferred yield = BT pref. return[1 – (1 – Div exclusion%)(T)]
AT preferred yield = 8.279%
Highest AT yield = 8.500%
BT municipal bond yield 8.80%
BT bond yield 11.75%
BT preferred yield 9.80%
Tax rate 25.00%
Dividend exclusion % 70.00%
Since municipal bonds are exempt from federal taxes, its BT return = AT return
AT municipal bond yield = 8.800%
AT bond yield = BT bond yield × (1 – T)
AT bond yield = 8.813%
AT preferred yield = BT pref. return[1 – (1 – Div. exclusion %)(T)]
AT preferred yield = 9.065%
Highest AT yield = 9.065%
Tax rate 34%
EBT After Unused
Taxable Carry-Forward Forward Carryable
Year Income Used Applied Amount
2009 -$3,000,000 $0 $0 $3,000,000
2010 -$5,200,000 $0 $0 $8,200,000
2011 $4,200,000 $4,200,000 $0 $4,000,000
2012 $8,300,000 $4,000,000 $4,300,000 $0
2012 Tax liability = EBT × Tax rate
2012 Tax liability = $1,462,000
Tax rate 35%
EBT After Unused
Taxable Carry-Forward Forward Carryable
Year Income Used Applied Amount
2009 -$50,000,000 $0 $0 $50,000,000
2010 -$150,000,000 $0 $0 $200,000,000
2011 -$100,000,000 $0 $0 $300,000,000
2012 $700,000,000 $300,000,000 $400,000,000 $0
2012 Tax liability = EBT × Tax rate
2012 Tax liability = $140,000,000
Tax rate 40%
EBT After Unused
Taxable Carry-Forward Forward Carryable
Year Income Used Applied Amount
2008 -$700,000 $0 $0 $700,000
2009 -$500,000 $0 $0 $1,200,000
2010 -$200,000 $0 $0 $1,400,000
2011 $800,000 $800,000 $0 $600,000
2012 $1,000,000 $600,000 $400,000 $0
2012 Tax liability = EBT × Tax rate
2012 Tax liability = $160,000
Tax rate 34%
EBT After Unused
Taxable Carry-Forward Forward Carryable
Year Income Used Applied Amount
2008 -$3,600,000 $0 $0 $3,600,000
2009 -$2,000,000 $0 $0 $5,600,000
2010 -$1,000,000 $0 $0 $6,600,000
2011 $1,200,000 $1,200,000 $0 $5,400,000
2012 $7,000,000 $5,400,000 $1,600,000 $0
2012 Tax liability = EBT × Tax rate
2012 Tax liability = $544,000
Tax rate 40%
EBT After Unused
Taxable Carry-Forward Forward Carryable
Year Income Used Applied Amount
2007 $50,000 $0 $50,000 $0
2008 $40,000 $0 $40,000 $0
2009 $30,000 $0 $30,000 $0
2010 $20,000 $0 $20,000 $0
2011 -$100,000 $0 $0 $100,000
2012 $60,000 $100,000 $10,000 $0
2012 Tax liability = EBT × Tax rate
Operating income $10,000,000
Interest expense $1,500,000
Taxable income = Operating income – Interest expense
Taxable income = Operating income – Interest expense
Taxable income = $8,500,000
Taxable Tax on Base % on
Income of Bracket Excess above Base
$0 $0 15%
$50,000 7,500 25%
$75,000 13,750 34%
$100,000 22,250 39%
$335,000 113,900 34%
$10,000,000 3,400,000 35%
$15,000,000 5,150,000 38%
$18,333,333 6,416,667 35%
Tax on base = $113,900
Tax on excess base = $2,776,100
Tax liability = $2,890,000
Net income = Taxable income – Taxes
Taxable income $80,000
Interest income $5,000
Dividend income $30,000
Dividend exclusion % 70%
Total taxable income = Taxable income + Interest income + Taxable dividend income
Total taxable income = Taxable income + Interest income + Dividend income (1 – Dividend exclusion %)
Total taxable income = $94,000
Taxable Tax on Base % on
Income of Bracket Excess above Base
$0 $0 15%
$50,000 7,500 25%
$75,000 13,750 34%
$100,000 22,250 39%
$335,000 113,900 34%
$10,000,000 3,400,000 35%
$15,000,000 5,150,000 38%
$18,333,333 6,416,667 35%
Tax on base = $13,750
Tax on excess base = $6,460
Tax liability = $20,210
Operating income $20,000,000
Interest payments $1,750,000
Dividend income $1,000,000
Dividend exclusion % 70%
Taxable income = Operating income – Interest payments + Taxable dividend income
Taxable income = Operating income – Interest payments + Dividend income × (1 – Dividend exclusion %)
Taxable income = $18,550,000
Taxable Tax on Base % on
Income of Bracket Excess above Base
$0 $0 15%
$50,000 7,500 25%
$75,000 13,750 34%
$100,000 22,250 39%
$335,000 113,900 34%
$10,000,000 3,400,000 35%
$15,000,000 5,150,000 38%
$18,333,333 6,416,667 35%
Tax on base = $6,416,667
Tax on excess base = $75,833
Tax liability = $6,492,500
Operating income $500,000
Interest income $50,000
Dividend income $100,000
Dividend exclusion % 70%
Taxable income = Operating income + Interest income + Taxable dividend income
Taxable income = Operating income + Interest income + Dividend income × (1 – Dividend exclusion %)
Taxable income = $580,000
Taxable Tax on Base % on
Income of Bracket Excess above Base
$0 $0 15%
$50,000 7,500 25%
$75,000 13,750 34%
$100,000 22,250 39%
$335,000 113,900 34%
$10,000,000 3,400,000 35%
$15,000,000 5,150,000 38%
$18,333,333 6,416,667 35%
Tax on base = $113,900
Tax on excess base = $83,300
Tax liability = $197,200
Operating income $125,000
Interest expense $40,000
Interest income $25,000
Dividend income $70,000
Dividend exclusion % 70%
Taxable income = Operating income – Interest expense + Interest income + Taxable dividend income
Taxable income = Operating income – Interest expense + Interest income + Div. income (1–Div. exclusion %)
Total taxable income = $131,000
Taxable Tax on Base % on
Income of Bracket Excess above Base
$0 $0 15%
$50,000 7,500 25%
$75,000 13,750 34%
$100,000 22,250 39%
$335,000 113,900 34%
$10,000,000 3,400,000 35%
$15,000,000 5,150,000 38%
$18,333,333 6,416,667 35%
Tax on base = $22,250
Tax on excess base = $12,090
Tax liability = $34,340
This problem can be worked very easily—just multiply the increase in depreciation by (1 – T) to get the
decrease in net income, and then subtract this value from the change in depreciation to get the change in
free cash flow:
Change in depreciation $725
Tax rate 35.00%
Reduction in net income = Change in Deprec. (1 − Tax rate) -$471.25
Increase in free cash flow = Change in Deprec. − Reduction in NI $253.75
We can also get the answer the long way, which explains things in more detail:
Old New Change
Bonds $3,500 $3,500 $0.00
Interest rate 6.50% 6.50% 0.00
Tax rate 35% 35% 0.00
Capex + NOWC $2,000 $2,000 $0.00
Sales $11,250 $11,250 $0.00
Operating costs excluding depreciation $4,500 $4,500 $0.00
Depreciation $1,250 $1,975 $725.00
Operating income (EBIT) $5,500 $4,775 -$725.00
Interest charges $228 $228 $0.00
Taxable income $5,273 $4,548 -$725.00
Taxes $1,845 $1,592 -$253.75
Net income $3,427 $2,956 -$471.25
Free cash flow = EBIT(1 − T) + Deprec − [Capex + NOWC] $2,825 $3,079 $253.75
Check on FCF: Δ FCF = Change in depreciation × Tax rate $253.75
We like this problem because it illustrates that an increase in depreciation will decrease the firm’s net
income yet increase its free cash flow, and cash is king.
Bonds $3,200
Interest rate 5%
Tax rate 35%
Required capital expenditures (fixed assets) $1,250
Required addition to net operating working capital $300
Sales $8,250.00
Operating costs excluding depreciation 5,750.00
Depreciation 650.00
Operating income (EBIT) $1,850.00
Interest charges 160.00
Taxable income (EBT) $1,690.00
Taxes 591.50
Net income $1,098.50
FCF = EBIT(1 − T) + Deprec. – Capex – ΔNOWC
FCF = $1,202.50 + $650 – $1,250 – -$300 = $302.50
Difference between net income and FCF = $796.00
WACC 10.00%
Investor-supplied capital $20,500
Sales $11,500
Operating costs including depreciation $5,000
Tax rate 40%
EBIT = Sales – Operating costs
EBIT = $6,500
EVA = EBIT(1 – T) – (WACC × Total investor-supplied capital)
EVA = $3,900 – $2,050
EVA = $1,850