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8/3/2019 December 13 Problems-1
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What is the NPV of this project?
It requires an initial investment of $5,000
Revenues will be $2,000 in year one, growing by $5,00Operating expenses will be $1,000 in year one, growin
Depreciation will be $1,000 in year 1 doubling each ye
Capital investment required to maintain the facility will
The company expects to sell $1,000 less than it collects
The company's stock is consistently 15% less risky tha
The overall stock market is expected to grow at 15% anThe short end of the yield curve is currently at 5%
The company's bonds current have a YTM of 7%
The company is in the 30% tax bracket
The company finances itself with 3 times as much equit
8/3/2019 December 13 Problems-1
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8/3/2019 December 13 Problems-1
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annually through year 5by 25% annually through year 5
r
be $8,000 in years 3, 4 and 5
in years 2 to 5
the market
nually
y as debt
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8/3/2019 December 13 Problems-1
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5
22,000$2,441$
19,559$
16,000$
3,559$
1,068$
2,491$
16,000$
18,491$
(8,000)$
1,000$11,491$
6,713$
8/3/2019 December 13 Problems-1
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What is the NPV of this project?
It requires an initial investment of $10,000
Revenues will be $0 in year one, growing to $1,000 in year 2
Operating expenses will be $100 in year 2, growing by 15% aDepreciation will be $1,000 in years 3, 4 and 5
Capital investment required to maintain the facility will be $1
At the end of year 5, the company will sell the facility for exa
The company builds $750 of additional inventory every year
The company's stock has consistently delivered twice the mar
The market currently quotes the company's bonds at YTM of
The company is in the 40% tax bracket
The company finances itself with 4 times as much debt as equ
The stock market has grown by 12% per year
Treasuries yield 5%
8/3/2019 December 13 Problems-1
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and $3,000 in years 3 to 5
nually through year 5
000 every year
tly $2,000
et's return
1% over treasury bonds
ity
8/3/2019 December 13 Problems-1
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What is the NPV of this project?
It requires an initial investment of $10,000
Revenues will be $0 in year one, growing to $1,000 in year 2 and $3,000 in years
Operating expenses will be $100 in year 2, growing by 15% annually through yea
Depreciation will be $1,000 in years 3, 4 and 5
Capital investment required to maintain the facility will be $1,000 every year
At the end of year 5, the company will sell the facility for exactly $2,000The company builds $750 of additional inventory every year
The company's stock has consistently delivered twice the market's return
The market currently quotes the company's bonds at YTM of 1% over treasury bo
The company is in the 40% tax bracket
The company finances itself with 4 times as much debt as equity
The stock market has grown by 12% per year
Treasuries yield 5%
0 1 2 3
Revenues -$ 1,000$ 3,000$OPEX 100$ 115$
Op Inc. 900$ 2,885$
Depreciation 1,000$
Taxable Income -$ 900$ 1,885$
Tax -$ 360$ 754$
After-tax Income -$ 540$ 1,131$
Depreciation -$ -$ 1,000$
NOPAT -$ 540$ 2,131$
CAPEX (10,000)$ (1,000)$ (1,000)$ (1,000)$
WC (750)$ (750)$ (750)$FCF (10,000)$ (1,750)$ (1,210)$ 381$
PV = (10,000)$ (1,640)$ (1,063)$ 314$
NPV = (10,397)$
Cost of Equity = 19.0%
Cost of Debt = 3.6%
WACC = 6.7%
8/3/2019 December 13 Problems-1
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3 to 5
r 5
nds
4 5
3,000$ 3,000$132$ 152$
2,868$ 2,848$
1,000$ 1,000$
1,868$ 1,848$
747$ 739$
1,121$ 1,109$
1,000$ 1,000$
2,121$ 2,109$
(1,000)$ 1,000$
(750)$ (750)$371$ 2,359$
286$ 1,707$
8/3/2019 December 13 Problems-1
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What is the NPV of this project?
It requires an initial investment of $100,000
Revenues will be $50,000 in year one, growing by 35% throu
Operating expenses will always be 60% of revenues
Depreciation will always be 10% of revenuesCapital expenditures will be $50,000, growing at the same rat
The company adds an additional 1% of each year's revenues t
The company's stock has consistently delivered 150% of the
The market currently quotes the company's bonds at 2% over
The company is in the 40% tax bracket
The company finances itself with twice as much debt as equit
The stock market has grown by 20% per year
Treasuries yield 5%
After year 5, FCF grows at 5% forever
8/3/2019 December 13 Problems-1
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h year 5.
as revenues for that year
Accounts Receivable
arket's return
reasury bonds
8/3/2019 December 13 Problems-1
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What is the NPV of this project?
It requires an initial investment of $100,000
Revenues will be $50,000 in year one, growing by 35
Operating expenses will always be 60% of revenues
Depreciation will always be 10% of revenuesCapital expenditures will be $5,000 in year 1, growing
The company adds an additional 1% of each year's rev
The company's stock has consistently delivered 150%
The market currently quotes the company's bonds at 2
The company is in the 40% tax bracket
The company finances itself with twice as much debt
The stock market has grown by 20% per year
Treasuries yield 5%
After year 5, FCF grows at 5% forever
0 1 2 3
Revenues 50,000$ 67,500$ 91,125$
OPEX 30,000$ 40,500$ 54,675$
Op Inc. 20,000$ 27,000$ 36,450$
Depreciation 5,000$ 6,750$ 9,113$
Taxable Income 15,000$ 20,250$ 27,338$
Tax 6,000$ 8,100$ 10,935$
After-tax Income 9,000$ 12,150$ 16,403$
Depreciation 5,000$ 6,750$ 9,113$
NOPAT 14,000$ 18,900$ 25,515$CAPEX (100,000)$ (5,000)$ (6,750)$ (9,113)$
WC (500)$ (675)$ (911)$
FCF (100,000)$ 8,500$ 11,475$ 15,491$
PV = (100,000)$ 8,500$ 11,475$ 15,491$
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NPV = 226,422$
Cost of Equity = 27.5%
Cost of Debt = 4.2%
WACC = 12.0%
8/3/2019 December 13 Problems-1
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through year 5.
at the same rate as revenues each year
enues to Accounts Receivable
of the market's return
over treasury bonds
s equity
4 5 Terminal
123,019$ 166,075$
73,811$ 99,645$
49,208$ 66,430$
12,302$ 16,608$
36,906$ 49,823$
14,762$ 19,929$
22,143$ 29,894$
12,302$ 16,608$
34,445$ 46,501$(12,302)$ (16,608)$
(1,230)$ (1,661)$
20,913$ 28,233$ 29,644$
20,913$ 28,233$ 241,810$
8/3/2019 December 13 Problems-1
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What is the NPV of this project?
It requires an initial investment of $15,000
Revenues will be $25,000 in years 3 to 6
Operating expenses will be $10,000 every year
Depreciation will be $5,000 growing by 10% every yearCapital expenditures will be $2,000 every year that there are r
The company adds an additional $5,000 every year to Accoun
The company's stock has consistently been half as risky as th
The market currently quotes the company's bonds at double t
The company is in the 20% tax bracket
The company finances itself with twice as much equity as deb
The stock market has grown by 10% per year
Treasuries yield 5%
FCF grows by 2% forever
8/3/2019 December 13 Problems-1
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8/3/2019 December 13 Problems-1
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evenues
ts Payable
market
e yield of treasury bonds
t
8/3/2019 December 13 Problems-1
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What is the NPV of this project?
It requires an initial investment of $15,000
Revenues will be $25,000 in years 3 to 6
Operating expenses will be $10,000 every year
Depreciation will be $5,000 in year 1 growing by 10%Capital expenditures will be $2,000 every year that there
The company adds an additional $5,000 every year to Ac
The company's stock has consistently been half as risky
The market currently quotes the company's bonds at dou
The company is in the 20% tax bracket
The company finances itself with twice as much equity a
The stock market has grown by 10% per year
Treasuries yield 5%
FCF grows by 2% forever
0 1 2 3 4
Revenues -$ -$ 25,000$ 25,000$
OPEX 10,000$ 10,000$ 10,000$ 10,000$
Op Inc. (10,000)$ (10,000)$ 15,000$ 15,000$
Depreciation 5,000$ 5,500$ 6,050$ 6,655$
Taxable Income (15,000)$ (15,500)$ 8,950$ 8,345$
Tax (3,000)$ (3,100)$ 1,790$ 1,669$
After-tax Income (12,000)$ (12,400)$ 7,160$ 6,676$
Depreciation 5,000$ 5,500$ 6,050$ 6,655$NOPAT (7,000)$ (6,900)$ 13,210$ 13,331$
CAPEX (15,000)$ -$ (2,000)$ (2,000)$
WC 5,000$ 5,000$ 5,000$ 5,000$
FCF (15,000)$ (2,000)$ (1,900)$ 16,210$ 16,331$
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PV = (15,000)$ (1,858)$ (1,639)$ 12,988$ 12,153$
NPV = 220,629$
Cost of Equity = 7.5%
Cost of Debt = 8.0%
WACC = 7.7%
8/3/2019 December 13 Problems-1
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are revenues
counts Payable
s the market
le the yield of treasury bonds
debt
5 6 Terminal
25,000$ 25,000$
10,000$ 10,000$
15,000$ 15,000$
7,321$ 8,053$
7,680$ 6,947$
1,536$ 1,389$
6,144$ 5,558$
7,321$ 8,053$13,464$ 13,611$
(2,000)$ (2,000)$
5,000$ 5,000$
16,464$ 16,611$ 16,943$
8/3/2019 December 13 Problems-1
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11,380$ 10,663$ 191,941.05$
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What is the NPV of this project?
It requires an initial investment of $5,000
Revenues will be $10,000 growing by 25% through year
Operating expenses will be 60% of revenues
Depreciation will be $5,000 in year 1 growing by 10%Capital expenditures will be $1,000 and the company wil
The company adds an additional $500 every year to Inve
The company's stock has consistently tracked the market
The market currently quotes the company's bonds at thre
The company is in the 20% tax bracket
The company finances itself with five times as much deb
The stock market has grown by 25% per year
Treasuries yield 5%
8/3/2019 December 13 Problems-1
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6
l sell all equipment for $5,000 on the last day of year 6
tory
times the yield of treasury bonds
as equity
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What is the NPV of this project?
It requires an initial investment of $5,000
Revenues will be $10,000 growing by 25% through year
Operating expenses will be 60% of revenues
Depreciation will be $5,000 in year 1 growing by 10%Capital expenditures will be $1,000 every year and the c
The company adds an additional $500 every year to Inve
The company's stock has consistently tracked the market
The market currently quotes the company's bonds at thre
The company is in the 20% tax bracket
The company finances itself with five times as much deb
The stock market has grown by 25% per year
Treasuries yield 5%
0 1 2 3 4
Revenues 10,000$ 12,500$ 15,625$ 19,531$
OPEX 6,000$ 7,500$ 9,375$ 11,719$
Op Inc. 4,000$ 5,000$ 6,250$ 7,813$
Depreciation 5,000$ 5,500$ 6,050$ 6,655$
Taxable Income (1,000)$ (500)$ 200$ 1,158$
Tax (200)$ (100)$ 40$ 232$
After-tax Income (800)$ (400)$ 160$ 926$
Depreciation 5,000$ 5,500$ 6,050$ 6,655$
NOPAT 4,200$ 5,100$ 6,210$ 7,581$CAPEX (5,000)$ (1,000)$ (1,000)$ (1,000)$ (1,000)$
WC (500)$ (500)$ (500)$ (500)$
FCF (5,000)$ 2,700$ 3,600$ 4,710$ 6,081$
PV = (5,000)$ 2,400$ 2,844$ 3,308$ 3,796$
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NPV = 19,002$
Cost of Equity = 15.0%
Cost of Debt = 12.0%
WACC = 12.5%
8/3/2019 December 13 Problems-1
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6
mpany will sell all equipment for $5,000 on the last day of year 6
tory
times the yield of treasury bonds
as equity
5 6
24,414$ 30,518$
14,648$ 18,311$
9,766$ 12,207$
7,321$ 8,053$
2,445$ 4,154$
489$ 831$
1,956$ 3,324$
7,321$ 8,053$
9,277$ 11,376$(1,000)$ 4,000$
(500)$ (500)$
7,777$ 14,876$
4,315$ 7,338$