CHAPTER. 8. Risk Analysis, Real Options, and Capital Budgeting. Chapter Outline. 8.1 Decision Trees 8.2 Sensitivity Analysis, 8.3 BreakEven Analysis 8.4 Scenario Analysis, Options 8.5 Monte Carlo Simulation 8.6 Summary and Conclusions. 8.1 Decision Trees.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
8.1 Decision Trees
8.2 Sensitivity Analysis,
8.3 BreakEven Analysis
8.4 Scenario Analysis, Options
8.5 Monte Carlo Simulation
8.6 Summary and Conclusions
“B”
“C”
“D”
“F”
Example of Decision TreeSquares represent decisions to be made.
Circles represent receipt of information e.g. a test score.
Study finance
The lines leading away from the squares represent the alternatives.
Do not study
=
NPV
$
0
Decision Tree for SECThe firm has two decisions to make:
Invest
To test or not to test.
To invest or not to invest.
NPV = $1,517
Success
75% prob.
Test
Do not invest
NPV = $0
Failure
NPV = –$3,612 (Sales units=682)
25% prob.
Do not test
Expected payoff at date 1= (Prob. of success x Payoff if successful) +(Prob. Of failure x Payoff if failure)
=(.75x$1,517)+(.25x0)
=$1,138 million
The NPV of the testing computed at date 0 (in million) is
Since NPV is positive, so we should test.
BEPQ =Net Fixed charges/Net Contribution
=(Fixed cost + Depreciation) *(1Tc)/(Sales PriceVariable cost)*(1Tc)
=[(1791+300)*(1.34)]/[(21)*(1.34)]
=1380/.66=2,091 engines is the breakeven point for an accounting profit
For every 1% drop in revenue, we can expect roughly a 2.4% drop in NPV:
Similarly, when sales drop from 3,000 to 2,500 units then 1% drop in revenue makes 4.4% drop in NPV.
$ in million
Total Revenue
Total Cost
$4,182
Fixed cost (including depreciation)=$2,091
2,091
Output (sales units)
After tax fixed charges: =EAC + (Fixed costs x(1Tc))(Depreciation*Tc)
=$447.5 +($1,791*.66  $300*.34)=$1,528
So, present value BEPQ =After tax fixed charges/After tax contribution
+D
+FC
$147.5
0.66
BreakEven Revenue SECWork backwards from OCFBE to BreakEven Revenue
Total Revenue
$4,630
Total Variable cost
$2,315
Fixed cost
$1,791
Depreciation
$300
EBIT
$223.5
Tax (34%)
$76.0
Net Income
$147.5
OCF =
$147.5+ $300
$447.5
Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. Assume a cost of capital of 10%.
PVIFA=3.1699
Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. Assume a cost of capital of 10%.
=
NPV
$
0
Decision Tree for Stewart PharmaceuticalThe firm has two decisions to make:
Invest
To test or not to test.
To invest or not to invest.
NPV = $3.4 b
Success
Test
Do not invest
NPV = $0
Failure
NPV = –$91.46 m
Do not test
The NPV evaluated at date 0 is:
So, we should test.
For every 1% drop in revenue, we can expect roughly a 4.26% drop in NPV:
+D
+FC
$104.75
0.66
BreakEven Revenue: StewartRevenue
$5,358.71
Variable cost
$3,000
Fixed cost
$1,800
Depreciation
$400
EBIT
$158.71
Tax (34%)
$53.96
Net Income
$104.75
OCF =
$104.75+ $400
$504.75
PBE
=
= $7.66 / dose
700
BreakEven Analysis: PBE$5,358.71 million = 700 million × PBE
What is the OCF in year zero for this project?
Cost of New Equipment $100,000
Net Working Capital Investment $10,000
Opportunity Cost of Old Equipment* $39,600
$149,600
*Calculation of Opportunity Cost of Old Equipment:
Market value $60,000
Book value 0
Profit (Loss) $60,000
Tax (34%) ($20,400)
Net salvage value $39,600
What is the OCF in years 1 and 2 for this project?
Revenue
10,000× $200 =
$2,000,000
Variable cost
10,000 × $90 =
$900,000
Fixed cost
$25,000
Depreciation
100,000 ÷ 3 =
$33,333
EBIT
$1,041,666.67
Tax (34%)
$354,166.67
Net Income
$687,500
OCF =
$687,500 + $33,333
$720,833.33
Revenue
10,000× $200 =
$2,000,000
10,000 × $90 =
Variable cost
$900,000
$25,000
Fixed cost
100,000÷ 3 =
Depreciation
$33,333
$1,041,666.67
EBIT
$354,166.67
Tax (34%)
$687,500
Net Income
$720,833.33
OCF =$687,500 + $33,333 =
We get our NWC back and sell the equipment. Since the book value and market value of net working capital is same, so there is no tax effect. Thus, and net cash flow becomes $10,000. The salvage value of equipment $10,000 and the book value is zero. So the capital gain of $10,000 is taxable. Thus, the aftertax salvage value is $6,600 = $10,000 × (1 – .34)
Thus, OCF3 = $720,833.33 + $10,000 + $6,600 = $737,433.33
The PV of the cost of this project is the sum of $149,600 today less $6,600 of net salvage value and $10,000 as return of NWC in year 3.
Let us find out the Equivalent Annual Cost (EAC) of the investment:
0.66
BreakEven RevenueWork backwards from OCFBE to BreakEven Revenue
Revenue
10,000× $PBE =
$988,035.04
Variable cost
10,000 × $90 =
$900,000
Fixed cost
$25,000
Depreciation
100,000 ÷ 3 =
$33,333
EBIT
$29,701.71
Tax (34%)
$10,098.58
Net Income
$19,603.13
OCF =
$19,603.13 + $33,333
$52,936.46
PBE× 10,000 = $988,035.34
PBE= $98.80
988
,
035
.
04
=
=
Break

even
sales
volume
4
,
941
beds
$
200
Common Mistake in BreakEvenAs a check, you can plug 4,941 beds into the problem and see if the result is a zero NPV.
0.66
Don’t Forget that Variable Cost VariesRevenue
QBE× $200 =
$88,035.04 + QBE×$110
Variable cost
QBE× $90 =
$?
Fixed cost
$25,000
Depreciation
100,000 ÷ 3 =
$33,333
EBIT
$29,701.71
Tax (34%)
$10,098.58
Net Income
$19,603.13
OCF =
$19,603.13 + $33,333
$52,936.46
QBE
=
= 801 beds
$110
BreakEven AnalysisCMBE ×10,000 = $88,035.04
CMBE = $8.80
$
2
,
550
å
=

+
=

NPV
$
30
,
000
$
21
,
916
.
84
t
(
1
.
10
)
=
t
1
Campusteria pro forma Income StatementWe plan to sell 25 meal plans at $200 per month with a 12month contract.
Variable costs are projected to be $3,500 per month.
Fixed costs (the lease payment) are projected to be $1,500 per month.
We can depreciate our capitalized leaseholder improvements.
NPV is $4,730 which is positive
Value of the managerial option=21,916+4,730=$26,646
M = NPV + Opt
Prob. Success
Successful Payoff
Prob. Failure
Failure Payoff
=
×
+
×
$287.50
= –$38.64
NPV =
Expected Payoff
–$300 +
= (0.50×$575) + (0.50×$0) = $287.50
1.10
The Option to Abandon: ExampleTraditional NPV analysis would indicate rejection of the project.
Sit on rig; stare at empty hole: PV = $0.
Drill

$
300
Failure
Sell the rig; salvage value = $250
Do not drill
=
NPV
$
0
The Option to Abandon: ExampleTraditional NPV analysis overlooks the option to abandon.
The firm has two decisions to make: drill or not, abandon or stay.
Prob. Success
Successful Payoff
Prob. Failure
Failure Payoff
=
×
+
×
$412.50
= $75.00
NPV =
Expected Payoff
–$300 +
= (0.50×$575) + (0.50×$250) = $412.50
1.10
The Option to Abandon: ExampleWhen we include the value of the option to abandon, the drilling project should proceed:
M = NPV + Opt
$75.00 = –$38.61 + Opt
$75.00 + $38.61 = Opt
Opt = $113.64
7
,
900
=
$
6
,
529
2
(
1
.
10
)
The Option to Delay: ExampleWe should delay the investment. We should make the investment in 2013.
Taking net salvage value under consideration, we should make the investment in 2010 rather than 2011.
Taken 65% terminal market value of investment, the project should be started in 2010.
Taken 65% terminal market value of investment, the project should be started in 2010.