Transcript MBAC 6060 Chapter 7x

MBAC 6060
Chapter 7
Risk Analysis,
Real Options,
and Capital Budgeting
1
Chapter Overview:
7.1 Sensitivity Analysis, Scenario Analysis, and
Break-Even Analysis
– We will cover this section in detail
7.2 Monte Carlo Simulation
– Just some description
7.3 Real Options
– Just some description
7.4 Decision Trees
– A simple example
2
Sensitivity Analysis
• How sensitive are the calculated values to our
estimates?
• How wrong can we be and still make money?
Definition of Sensitivity Analysis
• Change one variable
• See how it changes a calculated value
– OCF, Total CF, NPV, IRR, Working Capital needs…
3
Scenario Analysis
• If one thing changes, lots of thing might
change
• Change multiple variables
• See how this changes a calculated value
– OCF, Total CF, NPV, IRR, Working Capital needs…
4
Sensitivity Analysis Example:
•
•
•
•
•
•
•
•
A machine costs $1,000
It will last 5 years
Depreciated straight-line to $0 over its life
Sales will be 150 units at $30 per unit
Variable costs will be $25 per unit
Fixed costs will be $400 per year
Tax rate is 30%
Required return is 10%
Calculate the NPV 
5
Sensitivity Analysis Example:
•
•
•
•
•
•
•
•
•
Cost = $1,000
Years = 5
Dep Exp = 1,000/5 = $200
Units = 150
Price = $30
VC = $25
FC = $400
T = 30%
R = 10%
OCF = (Sales – Costs)(1 – T) + Dep x T
= (30 x 150 – 25 x 150 – 400)(1 - .3) + 200 x .30 = $305
NPV = -PV(rate, nper, pmt, [fv], [type]) - Cost
= -PV(0.1,5,305) - 1000 = $156.19
Go to the Simple Sensitivity Analysis Spreadsheet 
6
Sensitivity Analysis Example Continued:
• How sensitive is the OCF and NPV to our estimates?
1. How good are the individual forecasts?
2. How important are the forecasts to the success of the project?
Things to Consider when looking at the forecasts:
• What are we forecasting?
– Revenue: Sales Price per Unit x Units Sold
• Must consider our sales price, competitors’ sales price…
• Must consider market size, market share…
– Costs:
• fixed, variable, labor, materials…
– Is it our decisions, competitors’ decisions, government’s
decisions…
• How far in the future are we forecasting?
– Today? One Year? Ten Years?
7
Accounting Break-Even
• First consider the units estimate of 150 per year
• How many units sold for a positive NI?
NI = (Units x Price – Units x VC – FC – Dep)(1 – T)
• So set NI equal to zero and solve for Units…
[Units x (Price – VC) – FC – Dep](1 – T) = 0
Units x (Price – VC) – FC – Dep = 0
Units = (FC + Dep)/(Price – VC)
= (400 + 200)/(30 – 25)
= 600/5 = 120
Back to the spreadsheet 
8
Financial (or NPV) Break-Even
• How many units for a positive NPV?
• First Estimate (and then use Solver or Goal Seek)
NPV at 150 units  $156.19
•
•
•
•
Re-calc NPV at 151 units  $169.46
ΔNPV/ΔUnits = (169.46 – 156.19)/1 = $13.27
For NPV to change by $13.27, Units change by 1
For NPV to change by $156.19, Units change by
156.19/13.27 = 11.77
• If Units = 150 – 11 = 139  NPV > 0
• If Units = 150 – 12 = 138  NPV < 0
Back to the spreadsheet 9
NPV Break-Even for Each Input
• Solver and Goal Seek are iterative solvers in Excel
Cost
Years
Dep
Units
Price
VC
FC
Tax
R
OCF
NPV
%Δ
Base
1000
5
200
150
30
25
400
30%
10%
305
$156.19
Units
1000
5
200
138
30
25
400
30%
10%
263.80
$0.00
-7.85%
Price
1000
5
200
150
29.61
25
400
30%
10%
263.80
$0.00
-1.31%
VC
1000
5
200
150
30
25.39
400
30%
10%
263.80
$0.00
1.57%
FC
1000
5
200
150
30
25
458.86
30%
10%
263.80
$0.00
14.72%
10
More about Break-Even
• The text shows how to calculate the break-even
point using EAC and algebra
• I don’t like this method because it only works for
simple situations
– Same sales and costs estimates in each year
• The Excel-model based methods (Solver or Goal
Seek) work for more complex situations
• We’ll see this in a few minutes with the Baldwin
Example…
11
Scenario Analysis (New Example):
• 5 Year Project costs $200k
• Straight-Line to zero with no salvage (Dep = $40k per
year)
• Tax rate is 34%, R = 12%
Sales and Cost Estimates (for all 5 years):
Unit Sales
Sale Price per Unit
Variable Cost per Unit
Fixed Costs
6,000
$80
$60
$50,000
12
Scenario Analysis
• In each year
OCF = (Sales – Costs)(1 – T) + Dep x T
– Sales = 6k x $80 = $480k
– VC = 6k x $60 = $360k
OCF = ($480 – $360 - $50)(1 – 0.34) + $40(0.34) = $59.8
13
Scenario Analysis Example Continued:
• CF0 = -$200, CF1 through CF5 = $59.8
• NPV @ 12% = $15,566
• So how good is our NPV estimate?
– Forecasting: Units, Sale Price, Unit Cost, Fixed Costs
– What if we are wrong?
– We can do sensitivity analysis like before
But also try a Scenario Analysis:
• Best guess for all variables is called the Base Case
• First forecast Upper Bound and Lower Bound for each variable
• Second create two new scenarios:
– Best Case is best of each variable (high revs, low costs)
– Worst Case is worst of each variable (low revs, high costs)
14
OCF for the Three Scenarios:
• First estimate the Upper and Lower Bound for each variable:
Units
Sale Price Per unit
Variable Costs Per Unit
Fixed Costs
Lower
5,500
$75
$58
$45,000
Base
6,000
$80
$60
$50,000
Upper
6,500
$85
$62
$55,000
• Next calculate the Best Case (high revs and low costs) and the
Worst Case (low revs and high costs):
Units
Sale Price Per unit
Variable Costs Per Unit
Fixed Costs
Sales
Variable Costs
Best
6,500
$85
$58
$45,000
$552,500
$377,000
Base
6,000
$80
$60
$50,000
$480,000
$360,000
Worst
5,500
$75
$62
$55,000
$412,500
$341,000
15
OCF for the Three Scenarios:
• Now calculate the OCF for the Best, Base and Worst case:
Units
Sale Price Per unit
Variable Costs Per Unit
Fixed Costs
Sales
Variable Costs
Best
6,500
$85
$58
$45,000
$552,500
$377,000
Base
6,000
$80
$60
$50,000
$480,000
$360,000
Worst
5,500
$75
$62
$55,000
$412,500
$341,000
OCF = (Sales – Costs)(1 – T) + Dep x T
Best OCF = ($552.5 - $337 - $45)(0.66) + $40(0.34) = $99.73
Base OCF = ($480 - $360 - $50)(0.66) + $40(0.34) = $59.8
Worst OCF = ($412.5 - $341 - $55)(0.66) + $40(0.34) = $24.49
Note that OCF is the same in each year of the project
16
NPV for the Three Scenarios:
• Best: CF0 = -$200, CF1 through CF5 = $99.73, NPV = $159.50
• Base: CF0 = -$200, CF1 through CF5 = $59.80, NPV = $15.57
• Worst: CF0 = -$200, CF1 through CF5 = $24.49, NPV = -$111.72
• These scenarios use the “best” and “worst” of the “upper”
and “lower” bounds of the variable estimates
• That is why they are called the “Best Case” and “Worst Case”
• Obviously not the best and worst possible outcomes
Go to “Scenario Example” tab on spreadsheet 
17
Baldwin Example (From Chapter 6)
•
•
•
•
•
•
•
•
•
•
•
•
•
Bowling balls will be manufactured for 5 years
Use a building with market value of $150,000
Building market value will be $150,00 after this project
The cost of the bowling ball machine is $100,000
Market value of machine in five years is $30,000
Units per year: 5,000, 8,000, 12,000, 10,000 and 6,000
Price of bowling is $20 and will increase at 2% per year
VC is $10, increase at 10% per year
Tax Rate is 34%
NWC of $10,000 is required at time zero
NWC at year end will equal 10% of sales for that year
NWC will decline to $0 at project’s end
Cost of Capital (Required Rate) = 10%
Lets consider these estimates 
18
Baldwin Example
How important are the assumptions :
• Market value of the machine in 5 years
($30,000)?
• Market value of the building in 5 years
($150,000)?
• Price ($20) and Price Growth (2%)?
• VC ($10) and VC Growth (10%)?
• NWC assumptions?
• The Tax Rate?
• The Discount Rate?
Go to “Baldwin Model” tab 
19
7.2 Monte Carlo Simulation
• Program the NPV model and Identify the Variables
– Market Size, Market Share, Price, VC, FC…
• Define a Distribution for each variable:
– One possible Distribution for Market Share:
• 20% probability of 2% market share
• 60% probability of 4% market share
• 20% probability of 5% market share
– Anther possible Distribution for Market Share:
• Market share will be Normally Distributed with a
4.0% mean and a 0.5% standard deviation
• Define the Interactions Between Variables
– If Market Size and Price are both related to economic
growth
– Set 40% correlation between them
20
Monte Carlo Simulation
• Plug all this into Monte Carlo simulation software
– Crystal Ball, @Risk…
• The machine “draws” values for each variable
• It then calculates an NPV using the programed model
• Then it starts over
– Draws new values for each variable
– Calculates a new NPV
• After 10,000 draws, you have distribution of NPVs
(or OCFs, Total CFs,…)
• From the distribution, calculate an Expected NPV
and Distribution Statistics
21
Monte Carlo Simulation Results
Figure 7.4 , Page 218
(Distribution of Total Cash Flows from year 3)
22
7.3 Real Options
Managerial Options:
• Not just accept or reject:
– Managers can wait
– See what competitors do
– See what government will do
• If a five-year project is losing money after 2 years
– If it is the worst case scenario
– QUIT!
– Or reduce the scale
• If it’s making money after 2 years:
– If it is the best case scenario
– EXPAND!
– Or extend the life of the project
• Options on Real Assets are called “Real Options”
23
7.4 Decision Trees
• A decision tree is a graphical representation of
alternatives
Example:
• A company has developed a new product
• If the product is successful (50% chance)
the NPV at time of product launch is $22m
• If the product fails (50% chance)
the NPV at time of product launch is $9m
• The company can delay the launch for one year and
spend $1.5m to test market the project
• Test marketing would increase the probability of a
successful product to 80%
• The discount rate is 11%
24
Decision Tree
80% prob of NPV = $22
20% prob of NPV = $9
50% prob of NPV = $22
50% prob of NPV = $9
Calculate NPV of Each Choice:
• NPV of going directly to market (Not Test)
– 50% chance of $22, 50% chance of $9
NPV = 0.50 x $22 + 0.50 x $9 = $15.5
• NPV of Test Marketing First
– Pay $1.5 at time 0 to increase probability of launchtime NPV of $22 to 80%
– Delay launch date one year
– So must discount launch-time NPV by 11%
NPV = -$1.5 + [(.80 x $22) + (.2 x $9)]/1.11
= -$1.5 + [$19.40]/1.11
= -$1.5 + $17.48
= $15.98
26
Decision:
• “Not Test” NPV = $15.5
• “Test Market” NPV = $15.98
• So better to pay $1.5 and delay launch in
order to increase probability of a
successful product.
27
Capital Rationing
A firm or division may have limited resources
• Soft rationing
– When business units are allocated only a certain
amount of capital by management
• Hard rationing
– When a firm is unable to raise the capital
28
Where do we go from here?
• We have been looking at Capital Budgeting Decisions
• Using the NPV Framework:
NPV  CF0 
CFN
CF1
CF2




1  r 1  r 2
1  r N
• We looked at the numerators
• Now we will look at the denominators
–
–
–
–
What is the correct discount rate?
How much does the firm need to earn on its projects?
How much do investors require the firm to earn?
What does it cost the firm to raise money (its cost of capital)?
• We’ll start with terminology and pricing models for bonds
and stocks
• Then move to risk and return
– The calculations and tradeoffs
• Then we’ll look at the financing mix for a company
– Sell ownership stakes or borrow?
29