0 CHAPTER 8 Risk Analysis, Real Options, and Capital Budgeting.

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


Market size (Units) 10,000

Market share (Units) 23.15% 2,315

Price per unit (in million dollar)/Revenue 2 $4,630




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


Price per unit (in million dollar)/Revenue 2 $4,767.5




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%.


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


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 = $?


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


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


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 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


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

60

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)

61

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


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


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.

0 CHAPTER 8 Risk Analysis, Real Options, and Capital Budgeting.

Documents

cost of capital

fixed cost depreciation

millionthe npv

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capital investment decision

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