0 chapter 8 risk analysis, real options, and capital budgeting
TRANSCRIPT
1
CHAPTER
8Risk Analysis, Real Options, and Capital
Budgeting
2
Chapter Outline
8.1 Decision Trees
8.2 Sensitivity Analysis,
8.3 Break-Even Analysis
8.4 Scenario Analysis, Options
8.5 Monte Carlo Simulation
8.6 Summary and Conclusions
3
8.1 Decision Trees
• Allow us to graphically represent the alternatives available to us in each period and the likely consequences of our actions.
• This graphical representation helps to identify the best course of action.
4
Example of Decision Tree
Do not study
Study finance
Squares represent decisions to be made.Circles represent
receipt of information e.g. a test score.
The lines leading away from the squares
represent the alternatives.
“C”
“A”
“B”
“F”
“D”
5
Capital Investment Decision: (SEC)
• Solar Electronics Corporation (SEC) has recently developed the technology for solar powered jet engines and presently is considering test marketing of the engine. A corporate planning group, including representatives from production, marketing, and engineering, has recommended that the firm go ahead with the test and development phase.
• This preliminary phase will last one year and cost $100 million. Furthermore, the group believes that there is a 75% chance that tests will prove successful.
• Cost of capital is 15%.• If the initial tests are successful, Solar Electronics Corporation can go
ahead with full-scale production. This investment phase will cost $1500 million. Production will occur over the next 5 years. Annual sales would be 30% of the market of 10,000. Sales price is $2 million per unit.
• If the initial tests are not successful, and Solar Electronics Corporation still goes ahead with full-scale production; the investment will cost $1500 million, and annual sales would then be 682 units over the next 5 years.
6
Assumption Year 1 Year 2-6 (yearly)
Market size (Units) 10,000
Market share (Units) 30% 3,000
Price per unit (in million dollar)/Revenue 2 $6,000
Variable cost in $m (per plane) 1 ($3,000)
Fixed cost (per year) $m 1791 ($1,791)
Depreciation (Investment/Life) ($300)
EBIT/Pretax Profit $909
Tax (34%) ($309)
Net Profit $600
Cash Flow ($1,500) ($900)
517,1$)352155.3(900$500,1$)15.1(
900$500,1$
5
11
tt
NPV
SEC: NPV of Full-Scale ProductionFollowing Successful Test
7
SEC: NPV of Full-Scale ProductionFollowing Failure of Test
Year 1 Year 2 –Year 6
Investment (1500)
Sales (No) 682
Total Revenue 1364
Total Variable Cost (682)
Fixed Cost (1791)
Depreciation (300)
Pretax Profit (1409)
Tax (34%) (479)
Net profit (930)
Cash Flow (630)
612,3$)15.1(
)630($)500,1($
5
11
tt
NPV
8
Decision Tree for SEC
Do not test
Test
Failure
Success
Do not invest
Invest
Invest
The firm has two decisions to make:To test or not to test.To invest or not to invest.
0$NPV
NPV = $1,517
NPV = $0
NPV = –$3,612 (Sales units=682)
75% prob.
25% prob.
9
NPV of the project
millionNPV 890$15.1
1138$100$
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.
10
Calculation of accounting BEP
Investment
Sales units
Revenues
Variable cost
Fixed cost
Depreciation
Taxable income Taxes
Net profit
Operating cash flow
NPV Date1
1500 0 0 0 -1791 -300 -2091 711 -1380 -1080 ($5,120)
1500 1,000 2,000 -1,000 -1,791 -300 -1091 371 -720 -420 ($2,908)
1500 3,000 6,000 -3,000 -1,791 -300 909 -309 600 900 $1,517
1500 4,000 8,000 -4,000 -1,791 -300 1,909 -649 1,260 1,560 $3,729
1500 10,000 20,000 -10,000 -1,791 -300 7,909 -2,689 5,220 5,520 $17,004
1500 2,091 4,182 -2,091 -1791 -300 0 0 0 300 (494)
BEPQ =Net Fixed charges/Net Contribution
=(Fixed cost + Depreciation) *(1-Tc)/(Sales Price-Variable cost)*(1-Tc)
=[(1791+300)*(1-.34)]/[(2-1)*(1-.34)]
=1380/.66=2,091 engines is the break-even point for an accounting profit
11
Sensitivity Analysis: SEC
%25000,8$
000,8$000,6$Rev%
• We can see that NPV is very sensitive to changes in revenues. For example, when sales drop from 4,000 units to 3,000, a 25% drop in revenue leads to a 59% drop in NPV.
%3.59729,3$
729,3$517,1$%
NPV
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.
%25
%3.59%37.2
12
Figure: Accounting BEP
$ in million
Fixed cost (including depreciation)=$2,091
2,091 Output (sales units)
$4,182
Total Revenue
Total Cost
13
Present Value BEPQ
• The Equivalent Annual Cost (EAC) of the investment of $1,500 (in million) is:
5.447$3522.3
500,1
5 )15.,5(
inPVIFA
InvestmentInitial
factorannuityyear
InvestmentInitial
After tax fixed charges: =EAC + (Fixed costs x(1-Tc))-(Depreciation*Tc)
=$447.5 +($1,791*.66 - $300*.34)=$1,528
So, present value BEPQ =After tax fixed charges/After tax contribution
315,266.0$
528,1$
)34.1()1$2($
528,1$
)1()Pr(
)1(
c
cc
TCostsVariableiceSales
TonDepreciatiTCostsFixedEAC
14
Break-Even Revenue SEC
Work backwards from OCFBE to Break-Even RevenueTotal Revenue $4,630
Total Variable cost
$2,315
Fixed cost $1,791
Depreciation $300
EBIT $223.5
Tax (34%) $76.0Net Income $147.5
OCF = $147.5 + $300 $447.5
$147.5
0.66
+D+FC
+ TVC
15
Assumption Year 1 Year 2-6 (yearly)
Market size (Units) 10,000
Market share (Units) 23.15% 2,315
Price per unit (in million dollar)/Revenue 2 $4,630
Variable cost in $m (per plane) 1 ($2,315)
Fixed cost (per year) $m 1791 ($1,791)
Depreciation (Investment/Life) ($300)
EBIT/Pretax Profit $224
Tax (34%) ($76)
Net Profit $148.5
Cash Flow ($1,500) $448.5
0$)352155.3(5.448$500,1$)15.1(
5.448$500,1$
5
11
tt
NPV
SEC: NPV of Full-Scale ProductionFollowing Successful Test
16
Financial Break-even
• Expected pay-off at date 1=(.75*0)+(.25*0)=0• We fail to finance the test of $100.• For that we need a pay-off of $115 at date 1• Thus the NPV needed at date 1 is 115/.75=$153million• The cost of investment becomes=$1,500+$153=$1,653m• EAC=1653/3.352155=$493• Net profit required is ($493-$300(dep))=$193• Before tax profit is (net profit/(1-T))=$193/.66=$292.75• Total contribution needed=$292.75+$300+$1,791=$2,383.75• So, (P-VC)Q=2,383.75• (2-1)2,383=2,383.75
17
Assumption Year 1 Year 2-6 (yearly)
Price per unit (in million dollar)/Revenue 2 $4,767.5
Variable cost in $m (per plane) 1 ($2,382)
Fixed cost (per year) $m 1791 ($1,791)
Depreciation (Investment/Life) ($300)
EBIT/Pretax Profit $292.75
Net Profit $193.2
Cash Flow ($1,500) $493.2
01.15
115100- :is million)(in 0 dateat computed testing theof NPV The
115)0*25(.)153*75(.1
153$)352155.3(2.493$500,1$)15.1(
2.493$500,1$
5
11
dateatPayoff
NPVt
t
SEC: Financial BEP of Full-Scale ProductionFollowing Successful Test
18
Sensitivity AnalysisPessimistic Expected Optimistic
Market size 5,000 10,000 20,000
Market share 20% 30% 50%
Price (in million dollar) 1.9 2 2.2
Variable cost in $m (per plane) 1.2 1 0.8
Fixed cost (per year) $m 1,891 1,791 1,741
Investment in million dollar 1,900 1,500 1,000
NPV
Market size -1802 1,517 $8,154
Market share -695 1,517 5,942
Price (in million dollar) 853 1,517 2,844
Variable cost in $m (per plane) 189 1,517 2,844
Fixed cost (per year) $m 1,295 1,517 1,627
Investment $m 1,208 1,517 1,903
19
Example 2: Stewart Pharmaceuticals • Stewart Pharmaceuticals Corporation is considering investing
in the development of a drug that cures the common cold.• A corporate planning group, including representatives from
production, marketing, and engineering, has recommended that the firm go ahead with the test and development phase.
• This preliminary phase will last one year and cost $1 billion. Furthermore, the group believes that there is a 60% chance that tests will prove successful.
• If the initial tests are successful, Stewart Pharmaceuticals can go ahead with full-scale production. This investment phase will cost $1.6 billion. Production will occur over the following 4 years.
20
NPV Following Successful Test
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
Investment Year 1 Years 2-5
Revenues
(700 m*$10)
$7,000
Variable Costs (3,000)
Fixed Costs (1,800)
Depreciation (400)
Pretax profit $1,800
Tax (34%) (612)
Net Profit $1,188
Cash Flow -$1,600 $1,588 75.433,3$
)10.1(
588,1$600,1$
1
4
1
1
NPV
NPVt
t
21
NPV Following Unsuccessful Test
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%.
Investment Year 1 Years 2-5
Revenues $4,050
Variable Costs (1,735)
Fixed Costs (1,800)
Depreciation (400)
Pretax profit $115
Tax (34%) (39.10)
Net Profit $75.90
Cash Flow -$1,600 $475.90461.91$
)10.1(
90.475$600,1$
1
4
1
1
NPV
NPVt
t
22
Decision Tree for Stewart Pharmaceutical
Do not test
Test
Failure
Success
Do not invest
Invest
Invest
The firm has two decisions to make:To test or not to test.To invest or not to invest.
0$NPV
NPV = $3.4 b
NPV = $0
NPV = –$91.46 m
23
Decision to Test
• Let’s move back to the first stage, where the decision boils down to the simple question: should we invest?
• The expected payoff evaluated at date 1 is:
failuregiven
Payoff
failure
Prob.
successgiven
Payoff
sucess
Prob.
payoff
Expected
25.060,2$0$40.75.433,3$60.payoff
Expected
95.872$10.1
25.060,2$000,1$ NPV
The NPV evaluated at date 0 is:
So, we should test.
24
Sensitivity Analysis: Stewart
%29.14000,7$
000,7$000,6$Rev%
• We can see that NPV is very sensitive to changes in revenues. In the Stewart Pharmaceuticals example, a 14% drop in revenue leads to a 61% drop in NPV.
%93.6075.433,3$
75.433,3$64.341,1$%
NPV
For every 1% drop in revenue, we can expect roughly a 4.26% drop in NPV:
%29.14
%93.6026.4
25
Scenario Analysis: Stewart• A variation on sensitivity analysis is scenario
analysis.
• For example, the following three scenarios could apply to Stewart Pharmaceuticals:1. The next years each have heavy cold seasons, and
sales exceed expectations, but labor costs skyrocket.
2. The next years are normal, and sales meet expectations.
3. The next years each have lighter than normal cold seasons, so sales fail to meet expectations.
• For each scenario, calculate the NPV.
26
Break-Even Analysis
• Common tool for analyzing the relationship between sales volume and profitability
• There are two common break-even measures– Accounting break-even: sales volume at which net
income = 0– Financial break-even: sales volume at which net
present value = 0
27
Break-Even Analysis: Stewart
• Another way to examine variability in our forecasts is break-even analysis.
• In the Stewart Pharmaceuticals example, we could be concerned with break-even revenue, break-even sales volume, or break-even price.
• To find zero NPV, we start with the break-even operating cash flow.
• EAC=1600/3.1699=504
28
Accounting BEPQ
• BEP=(1,800+200)*(.66)/($10-($3,000/700))*(.66)=385
385 Quantity of sales
$3,850
TR
TC
29
Break-Even Revenue: Stewart
Work backwards from OCFBE to Break-Even Revenue
Revenue $5,358.71
Variable cost $3,000
Fixed cost $1,800
Depreciation $400
EBIT $158.71
Tax (34%) $53.96Net Income $104.75
OCF = $104.75 + $400 $504.75
$104.75
0.66
+D+FC
+ VC
30
Break-Even Analysis: PBE
• Now that we have break-even revenue of $5,358.71 million, we can calculate break-even price.
• The original plan was to generate revenues of $7 billion by selling the cold cure at $10 per dose and selling 700 million doses per year,
• We can reach break-even revenue with a price of only:
$5,358.71 million = 700 million × PBE
PBE = = $7.66 / dose 700
$5,358.71
31
Dorm Beds Example• Consider a project to supply the University of Missouri with
10,000 dormitory beds annually for each of the next 3 years. • Your firm has half of the woodworking equipment to get the
project started; it was bought years ago for $200,000: is fully depreciated and has a market value of $60,000. The remaining $100,000 worth of equipment will have to be purchased.
• The engineering department estimates that you will need an initial net working capital investment of $10,000.
• The project will last for 3 years. Annual fixed costs will be $25,000 and variable costs should be $90 per bed.
• The initial fixed investment will be depreciated straight line to zero over 3 years. It also estimates a (pre-tax) salvage value of $10,000 (for all of the equipment).
• The marketing department estimates that the selling price will be $200 per bed.
• You require an 8% return and face a marginal tax rate of 34%.
32
Dorm Beds OCF0
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 $60,000Book value 0Profit (Loss) $60,000Tax (34%) ($20,400)Net salvage value $39,600
33
Dorm Beds OCF1,2
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 $25,000Depreciation 100,000 ÷ 3 = $33,333
EBIT $1,041,666.67
Tax (34%) $354,166.67Net Income $687,500
OCF = $687,500 + $33,333 $720,833.33
34
Dorm Beds OCF3
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 after-tax salvage value is $6,600 = $10,000 × (1 – .34)
Thus, OCF3 = $720,833.33 + $10,000 + $6,600 = $737,433.33
Revenue 10,000× $200 = $2,000,000
Variable cost 10,000 × $90 = $900,000Fixed cost
$25,000Depreciation 100,000 ÷ 3 = $33,333
EBIT $1,041,666.67
Tax (34%)
$354,166.67
Net Income
$687,500
OCF = $687,500 + $33,333 = $720,833.33
35
NPV of Dorm Beds
235,721,1$
)08.1(
33.433,737
08.1
33.833,720
08.1
33.833,720600,149
32
NPV
36
Dorm Beds Break-Even Analysis
• In this example, we should be concerned with break-even price.
• Let’s start by finding the revenue that gives us a zero NPV.
• To find the break-even revenue, let’s start by finding the break-even operating cash flow (OCFBE) and work backwards through the income statement.
37
Dorm Beds Break-Even Analysis
The PV of the cost of this project is the sum of $149,600 today less $6,600 of net salvage value and $10,000 as return of NWC in year 3.
422,136$)08.1(
600,16$600,149$
3Cost
Let us find out the Equivalent Annual Cost (EAC) of the investment:
46.936,52$
08.)308.1(
11
4.422,136$4.422,136$
3,08.
niPVIFA
EAC
38
Break-Even Revenue
Work backwards from OCFBE to Break-Even Revenue
Revenue 10,000× $PBE = $988,035.04
Variable cost 10,000 × $90 = $900,000
Fixed cost $25,000Depreciation 100,000 ÷ 3 = $33,333
EBIT $29,701.71
Tax (34%) $10,098.58Net Income $19,603.13
OCF = $19,603.13 + $33,333 $52,936.46
$19,603.13
0.66
39
Break-Even Analysis
• Now that we have break-even revenue we can calculate break-even price• If we sell 10,000 beds, we can reach break-even revenue with a price of
only:
PBE × 10,000 = $988,035.34
PBE = $98.80
40
Common Mistake in Break-Even
• What’s wrong with this line of reasoning?• With a price of $200 per bed, we can reach
break-even revenue with a sales volume of only:
beds 941,4200$
04.035,988$ volumesaleseven -Break
As a check, you can plug 4,941 beds into the problem and see if the result is a zero NPV.
41
Don’t Forget that Variable Cost Varies
Revenue QBE × $200 = $88,035.04 + QBE× $110
Variable cost QBE × $90 = $?
Fixed cost $25,000Depreciation 100,000 ÷ 3 = $33,333
EBIT $29,701.71
Tax (34%) $10,098.58Net Income $19,603.13
OCF = $19,603.13 + $33,333 $52,936.46
$19,603.13
0.66
42
Break-Even Analysis
• With a contribution margin of $110 per bed, we can reach break-even revenue with a sales volume of only:
QBE = = 801 beds$110
$88,035.04
If we sell 10,000 beds, we can reach break-even gross profit with a contribution margin of only $8.80:
CMBE ×10,000 = $88,035.04
CMBE = $8.80If variable cost = $90, then break-even price (PBE) = $98.80
If we sell 10,000 beds, we can reach break-even gross profit with a contribution margin of only $8.80:
CMBE ×10,000 = $88,035.04
CMBE = $8.80If variable cost = $90, then break-even price (PBE) = $98.80
43
8.4 Options
• One of the fundamental insights of modern finance theory is that options have value. The phrase “We are out of options” is surely a sign of trouble. Because corporations make decisions in a dynamic environment, they have options that should be considered in project valuation.
• The Option to Expand– Has value if demand turns out to be higher than expected.
• The Option to Abandon– Has value if demand turns out to be lower than expected.
• The Option to Delay– Has value if the underlying variables are changing with a
favorable trend.
44
The Option to Expand
• Imagine a start-up firm, Campusteria, Inc. which plans to open private (for-profit) dining clubs on college campuses.
• The test market will be your campus, and if the concept proves successful, expansion will follow.
• The start-up cost of the test dining club is only $30,000 (this covers leaseholder improvements and other expenses for a vacant restaurant near campus).
45
Campusteria pro forma Income Statement
Investment Year 0 Years 1-4
Revenues $60,000
Variable Costs ($42,000)
Fixed Costs ($18,000)
Depreciation 30,000/4= ($7,500)
Pretax profit ($7,500)
Tax shield 34% $2,550
Net Profit –$4,950
Cash Flow –$30,000 $2,550
We plan to sell 25 meal plans at $200 per month with a 12-month contract.
Variable costs are projected to be $3,500 per month.
Fixed costs (the lease payment) are projected to be $1,500 per month.
We can depreciate our capitalized leaseholder improvements.84.916,21$
)10.1(
550,2$000,30$
4
1
t
tNPV
46
The Option to Expand:
• Note that while the Campusteria test site has a negative NPV, we now evaluate the possibility of expansion of sales. If sales grows at the rate 40% annually over the next 4 years, and the investment has the excess capacity to produce the higher level of sales, Then cost benefit takes following form. Find out the value of the expansion option.
47
The Option to Expand:Investment 0 1 2 3 4
Revenues $60,000 $84,000 $117,600 $164,640
Variable Costs ($42,000) ($58,800) ($82,320) ($115,248)
Fixed Costs ($18,000) ($18,000) ($18,000) ($18,000)
Depreciation $30,000/4= ($7,500) ($7,500) ($7,500) ($7,500)
Pretax profit ($7,500) ($300) $9,780 $23,892
Tax/ shield (34%) ($2,550) ($102) $3,325 $8,123
Net Profit ($4,950) ($198) $6,455 $15,769
Cash Flow ($30,000) $2,550 $7,302 $13,955 $23,269
PV (Cash flow) ($30,000) $2,318 $6,035 $10,484 $15,893
NPV is $4,730 which is positiveValue of the managerial option=21,916+4,730=$26,646
48
Discounted Cash Flows and Options
• We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project.
M = NPV + Opt• A good example would be comparing the desirability of a
specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time the more versatile machine is more valuable because it comes with options.
49
The Option to Abandon: Example
• Suppose that we are drilling an oil well. The drilling rig costs $300 today and in one year the well is either a success or a failure.
• The outcomes are equally likely. The discount rate is 10%.
• The PV of the successful payoff at time one is $575.• The PV of the unsuccessful payoff at time one is $0.
50
The Option to Abandon: Example
Traditional NPV analysis would indicate rejection of the project.
NPV = = –$38.641.10
$287.50–$300 +
Expected Payoff
= (0.50×$575) + (0.50×$0) = $287.50
=Expected
PayoffProb.
Success× Successful
Payoff+
Prob. Failure
×Failure Payoff
51
The Option to Abandon: Example
The firm has two decisions to make: drill or not, abandon or stay.
Do not drill
Drill
0$NPV
300$
Failure
Success: PV = $575
Sell the rig; salvage value
= $250
Sit on rig; stare at empty hole:
PV = $0.
Traditional NPV analysis overlooks the option to abandon.
52
The Option to Abandon: Example
When we include the value of the option to abandon, the drilling project should proceed:
NPV = = $75.001.10
$412.50–$300 +
Expected Payoff
= (0.50×$575) + (0.50×$250) = $412.50
=Expected Payoff
Prob. Success
× Successful Payoff
+ Prob. Failure
× Failure Payoff
53
Valuation of the Option to Abandon
• Recall that we can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project.
M = NPV + Opt
$75.00 = –$38.61 + Opt
$75.00 + $38.61 = Opt
Opt = $113.64
54
The Option to Delay: Example
• Consider the above project, which can be undertaken in any of the next 4 years. The discount rate is 10 percent. The present value of the benefits at the time the project is launched remain constant at $25,000, but since costs are declining the NPV at the time of launch steadily rises.
• The best time to launch the project is in year 2—this schedule yields the highest NPV when judged today.
Year Cost PV NPV t
0 20,000$ 25,000$ 5,000$ 1 18,000$ 25,000$ 7,000$ 2 17,100$ 25,000$ 7,900$ 3 16,929$ 25,000$ 8,071$ 4 16,760$ 25,000$ 8,240$
2)10.1(
900,7$529,6$
Year Cost PV (cashflow) NPV t NPV 0
0 20,000$ 25,000$ 5,000$ 5,000$ 1 18,000$ 25,000$ 7,000$ 6,364$ 2 17,100$ 25,000$ 7,900$ 6,529$ 3 16,929$ 25,000$ 8,071$ 6,064$ 4 16,760$ 25,000$ 8,240$ 5,628$
55
Option to delay
• When should we make the investment if annual sales revenue is Tk.8,000, variable cost 40% of sales, fixed costs Tk.1500 and project life 4 years. The cost of capital is 10%. The investment has zero salvage value and follows straight line depreciation. The amount of investment varies as following:
Year Amount of investment
2010 Tk.10,000
2011 Tk.9,400
2012 Tk.8,600
2013 Tk.8,400
2014 Tk.8,300
56
Calculation of NPVt (Investment=Tk.10,00)
Source Year0 Year2-Year5
Investment -10,000
Sales 8,000
Variable costs (40% of sales) -3,200
Fixed costs -1,500
Depreciation -2,500
Taxable income 800
After tax income 528
Cash flow 3,028
NPV -402
57
Calculation of NPVt
(Investment=Tk.8,600)
Source Year0 Year2-Year5
Investment -8,600
Sales 8,000
Variable costs -3200
Fixed costs -1500
Depreciation -2150
Taxable income 1,150
After tax income 759
Cash flow 2,909
NPV 621
58
Delay option
Year Investment NPVt NPV0
2010 10,000 -402 -402
2011 9,400 37 34
2012 8,600 621 513
2013 8,400 767 576
2014 8,300 840 574
We should delay the investment. We should make the investment in 2013.
59
Option to delay (with salvage value)
• When should we make the investment if annual sales revenue is Tk.8,000, variable cost 40% of sales, fixed costs Tk.1500 and project life 4 years. The cost of capital is 10%. The investment has 10 year life and will fetch 25% salvage value at the end of the project, and follows straight line depreciation. The amount of investment varies as following:
Year Amount
2010 10,000
2011 9,400
2012 8,600
2013 8,400
2014 8,300
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Year Investment Net salvage Value NPVt NPV0
2010 10000 3690 502 502
2011 9400 3468 886 805
2012 8600 3173 1398 1155
2013 8400 3100 1526 1147
2014 8300 3062 1590 1086
Taking net salvage value under consideration, we should make the investment in 2010 rather than 2011.
Option to delay (with salvage value)
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Option to delay (with 65% salvage value)
• When should we make the investment if annual sales revenue is Tk.8,000, variable cost 40% of sales, fixed costs Tk.1500 and project life 4 years. The cost of capital is 10%. The investment has 10 year life and will fetch 65% salvage value at the end of the project, and follows straight line depreciation. The amount of investment varies as following:
Year Amount
2010 10,000
2011 9,400
2012 8,600
2013 8,400
2014 8,300
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Year Investment Net salvage value NPVt NPV0
2010 10,000 6,330 2,305 2,305
2011 9,400 5,950 2,581 2,346
2012 8,600 5,444 2,949 2,437
2013 8,400 5,317 3,041 2,285
2014 8,300 5,254 3,087 2,108
Option to delay (with 65% salvage value)
Taken 65% terminal market value of investment, the project should be started in 2010.
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y1-y4 PV (Cash flow)
sales 8000
VC 3200
FC 1500
Dep 1000
Taxable income 2300
Net income 1518
Cash flow 2518 7981.808
Salvage: book value 6000
Market value 6500
Gain 500
Tax 170
NSV 6330 4323.39
Total Cash inflow 12305.2
NPV 2,305
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Year Investment Net salvage value NPVt NPV0
2008 10,000 6,330 2,305 2,305
2009 9,400 5,950 2,581 2,346
2010 8,600 5,444 2,949 2,437
2011 8,400 5,317 3,041 2,285
2012 8,300 5,254 3,087 2,108
Option to delay (with 65% salvage value)
Taken 65% terminal market value of investment, the project should be started in 2010.
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8.5 Summary and Conclusions• This chapter discusses a number of practical applications of capital
budgeting.
• We ask about the sources of positive net present value and explain what managers can do to create positive net present value.
• Sensitivity analysis gives managers a better feel for a project’s risks.
• Scenario analysis considers the joint movement of several different factors to give a richer sense of a project’s risk.
• Break-even analysis, calculated on a net present value basis, gives managers minimum targets.
• The hidden options in capital budgeting, such as the option to expand, the option to abandon, and timing options were discussed.