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8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
1/27
NPV 2,862,082$
Initial
Sales forecast (units per year) 50,000 50,000
Product life (years) 4 4
Expected wholesale price ($ unit) 260 260Production cost ($ unit) 110 110
Selling, General and Administrative Costs ($ per year) 2,800,000 2,800,000
New equipment cost ($) 7,500,000 7,500,000
Years of depreciation 5 5
tax rate 40% 40%
Receivables (% of sales) 15% 15%
Payables (% of COGS) 15% 15%
WACC 12% 12%
Item Formula Year
Incremental Revenue =50000*260
Production Costs =-50000*110
Selling, General and Administrative Costs
Depreciation =-7500000/5
Incremental Cost
Incremental EBIT
Tax, 40% =EBIT*40%
Incremental Earnings
Receivables =15%*Sales
Payables =15%*COGS
Net Working Capital
Change in Net Working Capital
Add back Depreciation
Purchase Equipment
Incremental Free Cash Flow
WACC = 12%
Present Value of FCF
NPV
Comments:
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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- Even though the project lasts for 4 years, the equipment has a 5-year life, so we must account fo
- Negative EBIT provides a tax credit => has positive impact on after-tax earnings and cash flows a
- Why do we ignore interest expenses?
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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worst case best case
35,000 65,000
4 4
240 280120 100
2,800,000 2,800,000
7,500,000 7,500,000
5 5
40% 40%
15% 15%
15% 15%
15% 10%
0 1 2 3 4 5
13,000,000$ 13,000,000$ 13,000,000$ 13,000,000$
(5,500,000)$ (5,500,000)$ (5,500,000)$ (5,500,000)$
(2,800,000)$ (2,800,000)$ (2,800,000)$ (2,800,000)$
(1,500,000)$ (1,500,000)$ (1,500,000)$ (1,500,000)$ (1,500,000)$
(9,800,000)$ (9,800,000)$ (9,800,000)$ (9,800,000)$ (1,500,000)$
3,200,000$ 3,200,000$ 3,200,000$ 3,200,000$ (1,500,000)$
(1,280,000)$ (1,280,000)$ (1,280,000)$ (1,280,000)$ 600,000$
1,920,000$ 1,920,000$ 1,920,000$ 1,920,000$ (900,000)$
1,950,000$ 1,950,000$ 1,950,000$ 1,950,000$
(825,000)$ (825,000)$ (825,000)$ (825,000)$
1,125,000$ 1,125,000$ 1,125,000$ 1,125,000$
(1,125,000)$ -$ -$ -$ 1,125,000$
1,500,000$ 1,500,000$ 1,500,000$ 1,500,000$ 1,500,000$
(7,500,000)$
(7,500,000)$ 2,295,000$ 3,420,000$ 3,420,000$ 3,420,000$ 1,725,000$
(7,500,000)$ 2,049,107$ 2,726,403$ 2,434,288$ 2,173,472$ 978,811$
2,862,082$
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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r the final depreciation charge in the 5th year.
long as long as the firm has other profitable projects
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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2,862,082$
0 (10,439,881)$
5000 (9,109,685)$
10000 (7,779,489)$
15000 (6,449,292)$
20000 (5,119,096)$25000 (3,788,900)$
30000 (2,458,703)$
35000 (1,128,507)$
40000 201,689$
45000 1,531,886$
50000 2,862,082$
55000 4,192,278$
60000 5,522,474$
65000 6,852,671$
70000 8,182,867$
75000 9,513,063$
2,862,082$
180 (4,232,298)$
190 (3,345,501)$
200 (2,458,703)$
210 (1,571,906)$
220 (685,108)$
230 201,689$
240 1,088,487$
250 1,975,284$260 2,862,082$
270 3,748,879$
280 4,635,677$
2,862,082$
80 5,522,474$85 5,079,076$
90 4,635,677$
95 4,192,278$
100 3,748,879$
105 3,305,481$
110 2,862,082$
115 2,418,683$
120 1,975,284$
$(15,000,000)
$(10,000,000)
$(5,000,000)
$-
$5,000,000
$10,000,000
$15,000,000
0
5,0
00
10,0
00
15,0
00
20,0
00
25,0
00
30,0
00
NPV as fun
$(5,000,000)
$(4,000,000)
$(3,000,000)
$(2,000,000)
$(1,000,000)
$-$1,000,000
$2,000,000
$3,000,000
$4,000,000
$5,000,000
$6,000,000
180
190
200
210
220
NPV as function
$3,000,000
$4,000,000
$5,000,000
$6,000,000
NPV as function
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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125 1,531,886$
130 1,088,487$
135 645,088$
140 201,689$
2,862,082$
9.0% 3,668,864$
9.5% 3,527,696$
10.0% 3,389,302$
10.5% 3,253,611$
11.0% 3,120,554$
11.5% 2,990,066$
12.0% 2,862,082$
12.5% 2,736,539$
13.0% 2,613,378$
13.5% 2,492,539$
14.0% 2,373,965$
14.5% 2,257,602$
15.0% 2,143,395$
15.5% 2,031,293$
16.0% 1,921,245$
16.5% 1,813,202$
17.0% 1,707,117$
$-
$1,000,000
$2,000,000
80
85
90
95
100
105
Pr
$-
$500,000
$1,000,000
$1,500,000
$2,000,000
$2,500,000
$3,000,000
$3,500,000
$4,000,000
9.0% 9.5% 10.0% 10.5% 11.0% 11.5% 12.0% 1
NPV as func
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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35,0
00
40,0
00
45,0
00
50,0
00
55,0
00
60,0
00
65,0
00
70,0
00
75,0
00
Units sold
tion of sales
230
240
250
260
270
280
holesale Price
f wholesale price
f production cost
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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110
115
120
125
130
135
140
oduction cost
.5% 13.0%13.5% 14.0% 14.5%15.0% 15.5% 16.0%16.5% 17.0%
roduction cost
tion of WACC
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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tax rate 40%
WACC 10%
the market value of old machine 70,000$
Item Formula Year
1. Sell old machine
depreciation =130,000/13 = 10,000
book value today =130,000 - (130,000/13)*3 = 100,000
the market value =70,000
tax paid =0.4*(70000-100000)=-12000
net proceedings from selling the old machine =70,000 + 12000
2. Incremental Earnings
New machine
Old machine
Increase in depreciation =(150000-5000)/10 - 10000 = 4500
Cost of three engineers
Incremental EBIT
tax, 40%
Incremental Earnings
3. Incremental cash flow
Change in Net Working CapitalAdd back increase in Depreciation
Purchase Equipment
Salvage value =5000
Incremental Free Cash Flow
Present Value of FCF
NPV
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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0 1 2 3 4 5 6 7 8
82,000$
40,000$ 40,000$ 40,000$ 40,000$ 40,000$ 40,000$ 40,000$ 40,000$
(25,000)$ (25,000)$ (25,000)$ (25,000)$ (25,000)$ (25,000)$ (25,000)$ (25,000)$
(4,500)$ (4,500)$ (4,500)$ (4,500)$ (4,500)$ (4,500)$ (4,500)$ (4,500)$
-$ -$ -$ -$ -$ -$ -$ -$
10,500$ 10,500$ 10,500$ 10,500$ 10,500$ 10,500$ 10,500$ 10,500$
(4,200)$ (4,200)$ (4,200)$ (4,200)$ (4,200)$ (4,200)$ (4,200)$ (4,200)$
6,300$ 6,300$ 6,300$ 6,300$ 6,300$ 6,300$ 6,300$ 6,300$
5,000$ -$ -$ -$ -$ -$ -$ (5,000)$ -$4,500$ 4,500$ 4,500$ 4,500$ 4,500$ 4,500$ 4,500$ 4,500$
(150,000)$
(63,000)$ 10,800$ 10,800$ 10,800$ 10,800$ 10,800$ 10,800$ 5,800$ 10,800$
(63,000)$ 9,818$ 8,926$ 8,114$ 7,377$ 6,706$ 6,096$ 2,976$ 5,038$
2,723$
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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9 10
40,000$ 40,000$
(25,000)$ (25,000)$
(4,500)$ (4,500)$
-$ -$
10,500$ 10,500$
(4,200)$ (4,200)$
6,300$ 6,300$
-$ -$4,500$ 4,500$
5,000$
10,800$ 15,800$
4,580$ 6,092$
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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Sales forecast (units per year) 50,000
Product life (years) 4
Expected wholesale price ($ unit) 260
Production cost ($ unit) 110
Selling, General and Administrative Costs ($ per year) 2,800,000
New equipment cost ($) 7,500,000Years of depreciation 5
tax rate 40%
Receivables (% of sales) 15%
Payables (% of COGS) 15%
WACC 12%
Item Formula Year
Incremental Revenue =50000*260
Production Costs =-50000*110
Selling, General and Administrative Costs
Depreciation =-7500000/5
Incremental Cost
Incremental EBIT
Tax, 40% =EBIT*40%
Incremental Earnings
Receivables =15%*Sales
Payables =15%*COGS
Net Working Capital
Change in Net Working Capital
Add back Depreciation
Selling the equipment =7500000-7500000/5*1
Incremental Free Cash Flow
WACC = 12%
Present Value of FCF
NPV
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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0 1 2 3 4
(13,000,000)$ (13,000,000)$ (13,000,000)$
5,500,000$ 5,500,000$ 5,500,000$
2,800,000$ 2,800,000$ 2,800,000$
1,500,000$ 1,500,000$ 1,500,000$ 1,500,000$
9,800,000$ 9,800,000$ 9,800,000$ 1,500,000$
(3,200,000)$ (3,200,000)$ (3,200,000)$ 1,500,000$
1,280,000$ 1,280,000$ 1,280,000$ (600,000)$
(1,920,000)$ (1,920,000)$ (1,920,000)$ 900,000$
(1,950,000)$ (1,950,000)$ (1,950,000)$ -$
825,000$ 825,000$ 825,000$ -$
(1,125,000)$ (1,125,000)$ (1,125,000)$ -$
1,125,000$ -$ -$ (1,125,000)$
(1,500,000)$ (1,500,000)$ (1,500,000)$ (1,500,000)$
6,000,000$
6,000,000$ (2,295,000)$ (3,420,000)$ (3,420,000)$ (1,725,000)$
6,000,000$ (2,049,107)$ (2,726,403)$ (2,434,288)$ (1,096,269)$
(2,306,067)$
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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Units 50,000.00
Whole sale price 260.00
Cost per unit 110.00
Capital expenditures (7,500,000.00)
Years - 1 2
Revenue 13,000,000.00 13,000,000.00
COGS (5,500,000.00) (5,500,000.00)
SG&A (2,800,000.00) (2,800,000.00)
(1,500,000.00) (1,500,000.00)
EBIT 3,200,000.00 3,200,000.00
Tax rate (40%) 40% (1,280,000.00) (1,280,000.00)
Incremental Earnings 1,920,000.00 1,920,000.00
Recievables (15%) 1,950,000.00 1,950,000.00
Payables (15%) (825,000.00) (825,000.00)
Net working capital 0 1,125,000.00 1,125,000.00
EBIT(1-T) 1,920,000.00 1,920,000.00
Depreciation 1,500,000.00 1,500,000.00
+Change in Net working Capital (1,125,000.00) -
2,295,000.00 3,420,000.00
WACC 12%
(7,500,000.00) 2,049,107.14 2,726,403.06
NPV 2,862,081.81
1.) Tax rate lowering makes NPV higher
2.) Product life infinite makes NPV higher since you're creating value every 5 years
3.) Would lower NPV due to losing value and losing out on debt
4.) CHECK, does opportunity cost play a part, sunk costs too? Interesting
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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3 4 5
13,000,000.00 13,000,000.00
(5,500,000.00) (5,500,000.00)
(2,800,000.00) (2,800,000.00)
(1,500,000.00) (1,500,000.00) (1,500,000.00)
3,200,000.00 3,200,000.00 (1,500,000.00)
(1,280,000.00) (1,280,000.00) 600,000.00
1,920,000.00 1,920,000.00 (900,000.00)
1,950,000.00 1,950,000.00 -
(825,000.00) (825,000.00) -
1,125,000.00 1,125,000.00 - 0
1,920,000.00 1,920,000.00 (900,000.00)
1,500,000.00 1,500,000.00 1,500,000.00
- - 1,125,000.00
3,420,000.00 3,420,000.00 1,725,000.00
2,434,288.45 2,173,471.83 978,811.33
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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Units 50,000.00
Price 260.00
Cost 110.00
0 1 2 3
Facility (7,500,000.00)Sales 13,000,000.00 13,000,000.00 13,000,000.00
COGS (5,500,000.00) (5,500,000.00) (5,500,000.00)
SG&A (2,800,000.00) (2,800,000.00) (2,800,000.00)
Depreciation (1,500,000.00) (1,500,000.00) (1,500,000.00)
EBIT 3,200,000.00 3,200,000.00 3,200,000.00
Taxes - 40% (1,280,000.00) (1,280,000.00) (1,280,000.00)
Earnings 1,920,000.00 1,920,000.00 1,920,000.00
Receivables 1,950,000.00 1,950,000.00 1,950,000.00
Payables (825,000.00) (825,000.00) (825,000.00)
NWC 1,125,000.00 1,125,000.00 1,125,000.00
Change in NWC (1,125,000.00) 0.00 0.00
EBIT(1-T) 1,920,000.00 1,920,000.00 1,920,000.00
Change in NWC (1,125,000.00) 0.00 0.00
Depreciation 1,500,000.00 1,500,000.00 1,500,000.00
FCF 2,295,000.00 3,420,000.00 3,420,000.00
WACC - 12% 12%
(7,500,000.00) 2,049,107.14 2,726,403.06 2,434,288.45
NPV 2,862,081.81
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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4 5
13,000,000.00
(5,500,000.00)
(2,800,000.00)
(1,500,000.00) (1,500,000.00)
3,200,000.00 (1,500,000.00)
(1,280,000.00) 600,000.00
1,920,000.00 (900,000.00)
1,950,000.00 0.00
(825,000.00) 0.00
1,125,000.00 0.00
0.00 1,125,000.00
1,920,000.00 (900,000.00)
0.00 1,125,000.00
1,500,000.00 1,500,000.00
3,420,000.00 1,725,000.00
2,173,471.83 978,811.33
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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machine (130,000.00) new machine 150,000.00
mkt value 70,000.00 new depr 14,500.00
deprc (10,000.00)
3yrs (100,000.00)
Tax benefit 12000
0 1 2 3
New machine (150,000.00)
Sell machine 82,000.00
New GM 40,000.00 40,000.00 40,000.00
Old GM (25,000.00) (25,000.00) (25,000.00)
Engr costs - - -
Depreciation increase (4,500.00) (4,500.00) (4,500.00)
EBIT 10,500.00 10,500.00 10,500.00
Tax - 40% (4,200.00) (4,200.00) (4,200.00)
Earnings 6,300.00 6,300.00 6,300.00
NWC 5,000.00 5,000.00 5,000.00 5,000.00
Change in NWC 5,000.00 - - -
EBIT(1-T) 6,300.00 6,300.00 6,300.00
Change in NWC - - -
Deprc 4,500.00 4,500.00 4,500.00
Salvage value
FCF (63,000.00) 10,800.00 10,800.00 10,800.00
WACC -10% (63,000.00) 9,818.18 8,925.62 8,114.2010%
NPV 2,723.25
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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4 5 6 7 8 9 10
40,000.00 40,000.00 40,000.00 40,000.00 40,000.00 40,000.00 40,000.00
(25,000.00) (25,000.00) (25,000.00) (25,000.00) (25,000.00) (25,000.00) (25,000.00)
- - - - - - -
(4,500.00) (4,500.00) (4,500.00) (4,500.00) (4,500.00) (4,500.00) (4,500.00)
10,500.00 10,500.00 10,500.00 10,500.00 10,500.00 10,500.00 10,500.00
(4,200.00) (4,200.00) (4,200.00) (4,200.00) (4,200.00) (4,200.00) (4,200.00)
6,300.00 6,300.00 6,300.00 6,300.00 6,300.00 6,300.00 6,300.00
5,000.00 5,000.00 5,000.00 - - - -
- - - (5,000.00) - - -
6,300.00 6,300.00 6,300.00 6,300.00 6,300.00 6,300.00 6,300.00
- - - (5,000.00) - - -
4,500.00 4,500.00 4,500.00 4,500.00 4,500.00 4,500.00 4,500.00
5,000.00
10,800.00 10,800.00 10,800.00 5,800.00 10,800.00 10,800.00 15,800.00
7,376.55 6,705.95 6,096.32 2,976.32 5,038.28 4,580.25 6,091.58
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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0 1 2 3
Facility 6,000,000.00
Sales (13,000,000.00) (13,000,000.00) (13,000,000.00)
COGS 5,500,000.00 5,500,000.00 5,500,000.00
SG&A 2,800,000.00 2,800,000.00 2,800,000.00
Depreciation 1,500,000.00 1,500,000.00 1,500,000.00EBIT (3,200,000.00) (3,200,000.00) (3,200,000.00)
Taxes - 40% 1,280,000.00 1,280,000.00 1,280,000.00
Earnings (1,920,000.00) (1,920,000.00) (1,920,000.00)
Receivables (1,950,000.00) (1,950,000.00) (1,950,000.00)
Payables 825,000.00 825,000.00 825,000.00
NWC 1,125,000.00 1,125,000.00 1,125,000.00
Change in NWC 1,125,000.00 0.00 0.00
EBIT(1-T) (1,920,000.00) (1,920,000.00) (1,920,000.00)
Change in NWC 1,125,000.00 0.00 0.00
Depreciation (1,500,000.00) (1,500,000.00) (1,500,000.00)
FCF (2,295,000.00) (3,420,000.00) (3,420,000.00)
WACC - 12% 12%
6,000,000.00 (2,049,107.14) (2,726,403.06) (2,434,288.45)
NPV (2,306,067.34)
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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4
1,500,000.001,500,000.00
(600,000.00)
900,000.00
(1,950,000.00)
825,000.00
(1,125,000.00)
900,000.00
(1,125,000.00)
(1,500,000.00)
(1,725,000.00)
(1,096,268.69)
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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investment 10,000,000.00
annual cf 1,300,000.00
market risk 7.00%
risk-free 2.00%
corp tax 35.00%
beta 1.70
Equity cost 13.90000%
Equity only use the cost of equity 13.90000%
1
NPV (10,000,000.00) 1,300,000.00
9,352,517.99
(647,482.01)
Use same wacc - underlying riskiness of business remains same
No - company should use Bu and Wacc that corresponds to risk of project
cost of debt 2.0%
split 50%
Beta(L) 2.805
cost of equity 21.63500%
WACC 11.46750%
1.00
FCF (10,000,000.00) 1,300,000.00
NPV (10,000,000.00) 11336385.44
1,336,385.44
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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2008 2009 2010 2011
10% 9.00%
sales 19,200,000,000.00 21,120,000,000.00 23,020,800,000.00
EBIT 2,112,000,000.00 2,302,080,000.00
Capex/Deprc - -
Tax 24% (506,880,000.00) (552,499,200.00)Earnings 1,605,120,000.00 1,749,580,800.00
Change in NWC (192,000,000.00) (190,080,000.00)
EBIT(1-T) 1,605,120,000.00 1,749,580,800.00
Change in NWC (192,000,000.00) (190,080,000.00)
FCF 1,413,120,000.00 1,559,500,800.00
WACC - 10% 1,284,654,545.45 1,288,843,636.36
Enterprise 32,542,444,954.48
Cash 2,300,000,000.00
Debt (32,000,000.00)
Equity value 34,810,444,954.48
Shares outstanding 486,000,000
Price 71.63$
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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2012 2013 2014 2015 TV
8.00% 7.00% 6.00% 5.00%
24,862,464,000.00 26,602,836,480.00 28,199,006,668.80 29,608,957,002.24
2,486,246,400.00 2,660,283,648.00 2,819,900,666.88 2,960,895,700.22
- - - -
(596,699,136.00) (638,468,075.52) (676,776,160.05) (710,614,968.05)1,889,547,264.00 2,021,815,572.48 2,143,124,506.83 2,250,280,732.17
(184,166,400.00) (174,037,248.00) (159,617,018.88) (140,995,033.34)
1,889,547,264.00 2,021,815,572.48 2,143,124,506.83 2,250,280,732.17
(184,166,400.00) (174,037,248.00) (159,617,018.88) (140,995,033.34)
1,705,380,864.00 1,847,778,324.48 1,983,507,487.95 2,109,285,698.83 44,294,999,675.35
1,281,277,884.30 1,262,057,458.15 1,231,602,093.71 26,194,009,336.50
8/10/2019 Fin 321 Midterm Review Problems - Capital Budgeting, DCF Valuation
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WACC
Beta 0.5
YTM Debt 6%
Debt 18%
Equity 82%
Risk-free 3%
Market-risk P 5%Tax rate 30%
Equity return 5.500%
WACC 5.26600%
New beta 0.61
New cost of equit 6.05%
WACC 5.71600%
Capital Budgeting
0 1 2 3 4
New Sales 3 3.50 3.00 2.50 2.00
Old Sales (2.50) (2.00) (1.50) (1.00)
Incr in cost (0.75) (0.70) (0.65) (0.40)
Kitchens (0.15)
Depreciation (0.05) (0.05) (0.05)
EBIT 0.20 0.25 0.30 0.60
Tax rate - 30% (0.06) (0.08) (0.09) (0.18)
Earnings 0.14 0.18 0.21 0.42
NWC 0.30 0.35 0.30 0.25 0.20
Change in NWC (0.30) (0.05) 0.05 0.05 0.05
EBIT(1-T) 0.14 0.18 0.21 0.42
Deprc 0.05 0.05 0.05
Change in NWC (0.05) - - 0.05
FCF 0.14 0.23 0.26 0.47
WACC 10% 0.13 0.19 0.20 0.32
(0.45) 0.13 0.19 0.20 0.32NPV 0.06
Valuation
0 1
5%
Sales 24,000,000,000.00 25,200,000,000.00
EBIT 2,400,000,000.00
Tax rate - 24 (576,000,000.00)
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EBIT(1-T) 1,824,000,000.00
Change in NWC (120,000,000.00)
CapEx/Deprc -
FCF 1,704,000,000.00
Enterprise Value 34,080,000,000.00
Cash 3,300,000,000.00Debt (364,000,000.00)
Mkt value 37,016,000,000.00
Shares 453,000,000
Price 81.71$
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5
1.00
(1.00)
(0.40)
(0.40)
0.12
(0.28)
0.10
0.10
(0.28)
-
(0.28)
(0.17)
(0.17)
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