1. Risk Analysis, Real Options, and Capital Budgeting
MBAC 6060 Chapter 7
Risk Analysis,
Real Options,
and Capital Budgeting

2. 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
7.4 Decision Trees
A simple example

3. 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…

4. 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…

5. 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 

6. 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) x .30 = $305
NPV = -PV(rate, nper, pmt, [fv], [type]) - Cost
= -PV(0.1,5,305) = $156.19
Go to the Simple Sensitivity Analysis Spreadsheet 

7. Sensitivity Analysis Example Continued:
How sensitive is the OCF and NPV to our estimates?
How good are the individual forecasts?
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?

8. 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)
= ( )/(30 – 25)
= 600/5 = 120
Back to the spreadsheet 

9. 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 = ( – )/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 

10. NPV Break-Even for Each Input
Solver and Goal Seek are iterative solvers in Excel
Base
Units
Price VC FC
Cost
1000
Years 5
Dep
200
150
138 30
29.61 25
25.39
400
458.86
Tax
30% R
10%
OCF
305
263.80
NPV
$156.19
$0.00 %Δ
-7.85%
-1.31%
1.57%
14.72%

11. 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…

12. 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 ,000
Sale Price per Unit $80
Variable Cost per Unit $60
Fixed Costs $50,000

13. 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

14. Scenario Analysis Example Continued:
CF0 = -$200, CF1 through CF5 = $59.8
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)

15. OCF for the Three Scenarios:
First estimate the Upper and Lower Bound for each variable:
Next calculate the Best Case (high revs and low costs) and the Worst Case (low revs and high costs):

16. OCF for the Three Scenarios:
Now calculate the OCF for the Best, Base and Worst case:
OCF = (Sales – Costs)(1 – T) + Dep x T
Best OCF = ($ $337 - $45)(0.66) + $40(0.34) = $99.73
Base OCF = ($480 - $360 - $50)(0.66) + $40(0.34) = $59.8
Worst OCF = ($ $341 - $55)(0.66) + $40(0.34) = $24.49
Note that OCF is the same in each year of the project

17. 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 

18. 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 

19. 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 

20. 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

21. Monte Carlo Simulation
Plug all this into Monte Carlo simulation software
Crystal
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

22. Monte Carlo Simulation Results
Figure 7.4 , Page 218
(Distribution of Total Cash Flows from year 3)

23. 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”

24. 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%

25. Decision Tree 80% prob of NPV = $22 Delay 1 year 20% prob of NPV = $9
Test (Pay $1.5)
50% prob of NPV = $22
If you don’t invest, the NPV = 0, even if you test first, because the cost of testing becomes a sunk cost.
If you are so unwise as to invest in the face of a failed test, you incur lots of additional costs, but not much in the way of revenue, so you have a negative NPV as of date 1.
Referring back to slide 7 (Decision to Test) may help to clarify the application of decision trees.
Not Test
(Launch)
50% prob of NPV = $9

26. 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 $ x $9 = $15.5
NPV of Test Marketing First
Pay $1.5 at time 0 to increase probability of launch-time 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

27. 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.

28. 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

29. Where do we go from here?
We have been looking at Capital Budgeting Decisions
Using the NPV Framework:
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?