Transcript Chapter 8

CHAPTER
8
Risk Analysis, Real
Options, and Capital
Budgeting
0
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
1
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.
2
Example of Decision Tree
Squares represent decisions to be made.
Circles represent
“A”
receipt of information
e.g. a test score.
Study
“B”
finance
“C”
Do not
study
The lines leading away
from the squares
“D”
represent the alternatives.
“F”
3
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.
4
SEC: NPV of Full-Scale Production
Following Successful Test
Assumption
Market size (Units)
Year 1
Year 2-6 (yearly)
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)
1791
($1,791)
Fixed cost (per year) $m
Depreciation (Investment/Life)
($300)
EBIT/Pretax Profit
$909
Tax (34%)
($309)
Net Profit
$600
Cash Flow
($1,500)
($900)
5
$900
NPV1  $1,500 
 $1,500 $900(3.352155)  $1,517
t
t 1 (1.15)
5
SEC: NPV of Full-Scale Production
Following Failure of Test
Year 1
Investment
Year 2 –Year 6
(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)
5
($630)
NPV1  ($1,500)  
 $3,612
t
t 1 (1.15)
6
Decision Tree for SEC
The firm has two decisions to make:
To test or not to test.
To invest or not to invest.
Success
Invest
NPV = $1,517
75% prob.
Test
Do not
invest
NPV = $0
Failure
25% prob.
NPV = –$3,612
(Sales units=682)
Do not
test
NPV  $0
Invest
7
NPV of the project
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
$1138
NPV  $100 
 $890 million
1.15
Since NPV is positive, so we should test.
8
Calculation of accounting BEP
Invest
ment
Sales
units
Reven
ues
Variable
cost
Fixed
cost
Deprec
iation
Taxable
income
Net
profit
Operating
cash flow
NPV
Date1
Taxes
0
-1791
-300
-2091
711
-1380
-1080 ($5,120)
1500
0
0
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
-300
0
300
(494)
2,091
4,182
-2,091
-1791
0
0
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
9
Sensitivity Analysis: SEC
• 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.
$6,000  $8,000
 25%
$8,000
$1,517  $3,729
%NPV 
 59.3%
$3,729
%Rev 
For every 1% drop in revenue, we can expect roughly a 2.4% drop
in NPV:
 59.3%
2.37% 
 25%
Similarly, when sales drop from 3,000 to 2,500 units then 1% drop
in revenue makes 4.4% drop in NPV.
10
Figure: Accounting BEP
$ in million
Total
Revenue
Total Cost
$4,182
Fixed cost (including depreciation)=$2,091
2,091
Output (sales units)
11
Present Value BEPQ
• The Equivalent Annual Cost (EAC) of the investment of $1,500 (in
million) is:
Initial Investment Initial Investment 1,500



 $447.5
5 yearannuityfactor
PVIFA( n5, i .15)
3.3522
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
EAC  Fixed Costs  (1  Tc )  Depreciation  Tc

( Sales Pr ice  Variable Costs)  (1  Tc )
$1,528
$1,528


 2,315
($2  $1)  (1  .34) $0.66
12
Break-Even Revenue SEC
Work backwards from OCFBE to Break-Even Revenue
Total Revenue
+ TVC
Total Variable cost
Fixed cost
Depreciation
EBIT
Tax (34%)
Net Income
+D
+FC
$147.5
0.66
OCF =$147.5 + $300
$4,630
$2,315
$1,791
$300
$223.5
$76.0
$147.5
$447.5
13
SEC: NPV of Full-Scale Production
Following Successful Test
Assumption
Market size (Units)
Year 1
Year 2-6 (yearly)
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)
1791
($1,791)
Fixed cost (per year) $m
Depreciation (Investment/Life)
($300)
EBIT/Pretax Profit
$224
Tax (34%)
($76)
Net Profit
$148.5
Cash Flow
($1,500)
$448.5
5
$448.5
NPV1  $1,500 
 $1,500 $448.5(3.352155)  $0
t
t 1 (1.15)
14
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
15
SEC: Financial BEP of Full-Scale Production
Following Successful Test
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)
1791
($1,791)
Fixed cost (per year) $m
Depreciation (Investment/Life)
($300)
EBIT/Pretax Profit
$292.75
Net Profit
$193.2
Cash Flow
($1,500)
5
$493.2
$493.2
 $1,500 $493.2(3.352155)  $153
t
t 1 (1.15)
Payoff at date1  (.75*153)  (.25* 0)  115
115
T heNP V of the test ingcomput edat dat e 0 (in million)is : - 100
0
1.15 16
NPV1  $1,500 
Sensitivity Analysis
Pessimistic Expected
Market size
Optimistic
5,000
10,000
20,000
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
-1802
1,517
$8,154
-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
17
Market share
NPV
Market size
Market share
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
18
following 4 years.
NPV Following Successful Test
Investment
Year 1
Years 2-5
$7,000
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
(700 m*$10)
Variable Costs
Fixed Costs
Depreciation
(3,000)
(1,800)
(400)
Pretax profit
Tax (34%)
$1,800
(612)
Net Profit
Cash Flow
$1,188
t 1
$1,588 NPV 1  $3,433.75
-$1,600
PVIFA=3.1699
4
NPV 1  $1,600  
$1,588
(1.10)t
19
NPV Following Unsuccessful Test
Investment
Year 1
Years 2-5
Revenues
Variable Costs
Fixed Costs
Depreciation
$4,050
(1,735)
(1,800)
(400)
Pretax profit
Tax (34%)
Net Profit
$115
(39.10)
$75.90
Cash Flow
-$1,600
$475.90
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%.
4
$475.90
t
t 1 (1.10)
NPV 1  $1,600  
NPV 1  $91.461
20
Decision Tree for Stewart Pharmaceutical
The 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
Do not
test
NPV  $0
NPV = –$91.46 m
Invest
21
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:
Payoff
Payoff
 Prob.
  Prob.
  
 


payoff
 sucess given success   failure given failure
Expected



Expected
 .60  $3,433.75  .40  $0  $2,060.25
payoff
The NPV evaluated at date 0 is:
NPV  $1,000 
$2,060.25
 $872.95
1.10
So, we should test.
22
Sensitivity Analysis: Stewart
• 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.
%Rev 
$6,000  $7,000
 14.29%
$7,000
$1,341.64  $3,433.75
%NPV 
 60.93%
$3,433.75
For every 1% drop in revenue, we can expect roughly a
4.26% drop in NPV:
 60.93%
 4.26 
14.29%
23
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.
24
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
25
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
26
Accounting BEPQ
• BEP=(1,800+200)*(.66)/($10-($3,000/700))*(.66)=385
TR
TC
$3,850
385
Quantity of sales
27
Break-Even Revenue: Stewart
Work backwards from OCFBE to Break-Even Revenue
Revenue
+ VC
Variable cost
Fixed cost
Depreciation
EBIT
Tax (34%)
Net Income
+D
+FC
$104.75
0.66
OCF =$104.75 + $400
$5,358.71
$3,000
$1,800
$400
$158.71
$53.96
$104.75
$504.75
28
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 =
$5,358.71
700
= $7.66 / dose
29
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%.
30
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
$60,000
Book value
0
Profit (Loss)
$60,000
Tax (34%)
($20,400)
Net salvage value
$39,600
31
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
100,000 ÷ 3 =
$25,000
$33,333
Fixed cost
Depreciation
EBIT
$1,041,666.67
Tax (34%)
Net Income
OCF =$687,500 + $33,333
$354,166.67
$687,500
$720,833.33
32
Dorm Beds OCF3
Revenue
Variable cost
Fixed cost
Depreciation
EBIT
Tax (34%)
Net Income
10,000× $200 =
10,000 × $90 =
100,000 ÷ 3 =
OCF = $687,500 + $33,333 =
$2,000,000
$900,000
$25,000
$33,333
$1,041,666.67
$354,166.67
$687,500
$720,833.33
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
33
NPV of Dorm Beds
 720,833.33  720,833.33  737,433.33
NPV  149,600 



2
3

 1.08   1.08   (1.08) 
 $1,721,235
34
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.
35
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.
$16,600
Cost  $149,600
 $136,422
3
(1.08)
Let us find out the Equivalent Annual Cost (EAC) of the
investment:
EAC 
$136,422.4
$136,422.4

 $52,936.46
PVIFAi .08,n 3 1  1
(1.08)3
.08
36
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
100,000 ÷ 3 =
$25,000
$33,333
Fixed cost
Depreciation
EBIT
Tax (34%)
Net Income
$19,603.13
0.66
OCF =$19,603.13 + $33,333
$29,701.71
$10,098.58
$19,603.13
$52,936.46
37
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
38
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:
Break - even sales volume 
$ 988, 035 . 04
 4, 941 beds
$ 200
As a check, you can plug 4,941 beds into the
problem and see if the result is a zero NPV.
39
Don’t Forget that Variable Cost Varies
Revenue
QBE × $200 =
Variable cost
QBE × $90 =
Fixed cost
Depreciation
EBIT
Tax (34%)
Net Income
$88,035.04 + QBE× $110
100,000 ÷ 3 =
$19,603.13
0.66
OCF =$19,603.13 + $33,333
$?
$25,000
$33,333
$29,701.71
$10,098.58
$19,603.13
$52,936.46
40
Break-Even Analysis
• With a contribution margin of $110 per bed,
we can reach break-even revenue with a
sales volume of only:
$88,035.04
QBE =
= 801 beds
$110
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 = $8.80
If variable cost = $90, then break-even price (PBE) = $98.80
41
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.
42
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).
43
Campusteria pro forma Income Statement
Investment
Year 0
Revenues
Years 1-4
$60,000
Variable Costs
($42,000)
Fixed Costs
($18,000)
Depreciation
30,000/4=
Pretax profit
($7,500)
Tax shield 34%
$2,550
–$4,950
Net Profit
Cash Flow
($7,500)
–$30,000
NPV  $30,000 
4
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.
$2,550
$2,550
 $21,916.84

t
t 1 (1.10)
We can depreciate our
capitalized leaseholder
improvements.
44
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.
45
The Option to Expand:
Investment
0
Revenues
1
2
3
4
$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)
Depreciation
$30,000/4=
($18,000)
($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 positive
Value of the managerial option=21,916+4,730=$26,646
46
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.
47
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.
48
The Option to Abandon: Example
Traditional NPV analysis would indicate rejection of the
project.
Expected
=
Payoff
Prob.
Successful
×
Success
Payoff
Prob.
Failure
+
×
Failure
Payoff
Expected
= (0.50×$575) + (0.50×$0) = $287.50
Payoff
NPV = –$300 +
$287.50
1.10
= –$38.64
49
The Option to Abandon: Example
Traditional NPV analysis overlooks the option to abandon.
Success: PV = $575
Sit on rig; stare
at empty hole:
PV = $0.
Drill
 $300
Failure
Do not
drill
NPV  $0
Sell the rig;
salvage value
= $250
The firm has two decisions to make: drill or not, abandon or stay.
50
The Option to Abandon: Example
When we include the value of the option to abandon, the
drilling project should proceed:
Expected = Prob. ×Successful + Prob. × Failure
Payoff
Success Payoff
Failure Payoff
Expected
= (0.50×$575) + (0.50×$250) = $412.50
Payoff
NPV = –$300 +
$412.50
1.10
= $75.00
51
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
52
The Option to Delay: Example
Year
Year
00
11
22
33
44
Cost
Cost PV (cashflow)
PV
20,000 $ $ 25,000
25,000
$$20,000
18,000 $ $ 25,000
25,000
$$18,000
17,100 $ $ 25,000
25,000
$$17,100
16,929 $ $ 25,000
25,000
$$16,929
16,760 $ $ 25,000
25,000
$$16,760
NPV
NPV tt
$$ 5,000
$$ 7,000
7,900
$$ 7,900
8,071
$$ 8,071
8,240
$$ 8,240
NPV 0
$ 5,000
$ 6,364
$ 6,529
$ 6,064
$ 5,628
$7,900
$6,529 
(1.10)2
• 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.
53
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
54
Calculation of NPVt
(Investment=Tk.10,00)
Source
Investment
Sales
Year0
-10,000
Year2-Year5
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
NPV
3,028
-402
55
Calculation of NPVt
(Investment=Tk.8,600)
Source
Investment
Sales
Variable costs
Fixed costs
Depreciation
Taxable income
After tax income
Cash flow
NPV
Year0
-8,600
Year2-Year5
8,000
-3200
-1500
-2150
1,150
759
2,909
621
56
Delay option
Year
2010
2011
2012
2013
2014
Investment
10,000
9,400
8,600
8,400
8,300
NPVt
-402
37
621
767
840
NPV0
-402
34
513
576
574
We should delay the investment. We should make the
investment in 2013.
57
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
58
Option to delay (with salvage value)
Year
Investment Net salvage Value
NPVt
NPV0
2010
10000
3690
502
502
2011
2012
9400
8600
3468
3173
886
1398
805
1155
2013
2014
8400
8300
3100
3062
1526
1590
1147
1086
Taking net salvage value under consideration, we should
make the investment in 2010 rather than 2011.
59
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
60
Option to delay (with 65% salvage value)
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.
61
PV (Cash flow)
y1-y4
sales
8000
VC
3200
FC
1500
Dep
1000
Taxable income
2300
Net income
1518
Cash flow
2518
Salvage: book value
6000
Market value
6500
Gain
500
Tax
170
NSV
6330
Total Cash inflow
NPV
7981.808
4323.39
12305.2
62
2,305
Option to delay (with 65% salvage value)
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.
63
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.
64