Capital Budgeting
Investment Decision
Cash
Investment
opportunity
(real asset)
Firm
Invest
Shareholder
Pay dividend to
shareholders
Investment
opportunities
(financial assets)
Shareholders invest
for themselves
Investment return must exceed the return on investing in a
financial asset of equivalent risk to accept the project
Net Present Value

Project Market Value - Project Cost
1. Estimate all cash flows, positive and negative
2. Estimate project’s required return
3. Find the present value of the cash flows

Discount all future cash flows
n

t 0

CFt

NPV
t
1  k 
NPV > 0 : Accept
NPV < 0 : Reject
NPV: Value to Equity Holders

Investors:
– You $20,000 & Brother $30,000


Buy a thoroughbred horse $50,000
Present value of sale $60,000
– NPV =

Gain for equity holders
– Brother’s share =
– Your share =
Negative NPV


Air Quality Control Act requires a firm to
install 3 cleaner ventilation systems
Cash Flows
– Cost: $350,000/unit
– Value: Avoid $100,000/unit in fines annually
over the 5 year life of the units.

At r =14%, NPV = -$20,075
Project Analysis

Alternative analysis of cash flow estimates
– Payback
– Internal Rate of Return

Supplements to NPV analysis
–
–
–
–
Sensitivity Analysis
Break-even Analysis
Monte Carlo Simulation
Decision Trees
Payback

Payback Period
– Number of years it takes before the cumulative
forecasted cash flow equals the initial outlay

Payback Rule
– Only accept projects that “payback” in the
desired time frame
Fixed & Variable Costs

Total Costs = Fixed + Variable Costs
– Total variable costs = quantity * cost per unit
– Fixed costs are constant over some time period

Ex: Your firm pays $3000 per month in fixed costs.
You also pay $15 per unit to produce your product.
– What is your total cost if you produce 1000 units?
– What if you produce 5000 units?
Example

New experimental laser medical treatment
–
–
–
–

Purchase of new laser costs $250,000
Installation will cost $20,000
Hourly labor costs are $830 (doctor, nurse, tech)
Charge $3,000 vs. $1,500 for traditional treatment
Break-even Calculation
– Fixed costs =
– Variable costs =
– Break-even =
Internal Rate of Return
IRR is the discount rate that forces PV of the
inflows equal to the initial outflow (cost).
NPV:
Enter r, solve for NPV.
n
CFt
 NPV

t
t  0 1  r 
IRR:
Enter NPV=0, solve for IRR.
n
CFt

0

t
t  0 1  IRR 
IRR Rationale

IRR > Opportunity Cost of Capital
– Project’s rate of return is greater than its cost
– Extra return is left after repaying financing to boost
stockholders’ returns

IRR > r : Accept

IRR < r : Reject
Mutually Exclusive Projects
NPV: choose the project with the higher NPV
IRR: choose the project with the higher IRR
Period Project A Project B
0
1
-500
325
-400
325
2
325
200
IRR
19.43%
22.17%
NPV
64.05
60.74
Req. return for both
projects is 10%.
Which project
should you accept
and why?
Relevant Cash Flows

Incremental cash flows
– Any and all changes in cash flows due to
accepting a project
– “Will this cash flow occur ONLY if we accept the
project?”

Stand-alone principle
– Analyze each project in isolation from the firm
Common Cash Flows

Sunk costs
– Costs that have accrued in the past

Opportunity costs
– Costs of lost options

Side effects
– Positive: benefits to other projects
– Negative: costs to other projects

Taxes
Incremental Cash Flows

Luxury Car currently sells
– 30,000 cars at $45,000 and 12,000 SUVs at $85,000

Introduces a motorcycle


Expects to sell 21,000 at $12,000 = $252 mil
Changes brand
– SUVs decrease: -1,300 * $85,000 = - $110.5 mil
– Cars increase: 5,000 * $45,000 = $225 mil
– Net sales
Evaluating NPV Estimates

NPV estimates are just that – estimates
– NPV ≠ Actual Profitability

Forecasting risk
– More sensitive NPV estimates, the greater the
forecasting risk
– Sources of value
Sensitivity Analysis


NPV impact when vary one variable
Vary inputs separately
– Determines project’s realizations with
better/worse outcomes of key variables

Shows sensitivity to forecasting errors
Scenario
Unit Sales Cash Flow NPV
IRR
Baseline
6000
59,800
15,567
15.1%
Worst case
5500
53,200
-8,226
10.3%
Best case
6500
66,400
39,357
19.7%
Sensitivity Analysis

Must identify key variables
– Determines where additional information is needed
– Exposes confused forecasts

Results are often ambiguous
– Difficult to evaluate true probability distribution of
outcomes

How likely is each state of the world?
– Interactions?
 Strong demand
higher market size / price
Scenario Analysis

Alternative to sensitivity analysis

Examines outcome given certain events
– Ex: Increased oil prices and car market

Consider at least
– Best case: high revenues, low costs
– Worst case: low revenues, high costs
– Measure of the range of possible outcomes
Simulation Analysis

Managers can consider many possible
combinations

Generates a probability distribution and
estimates probability of positive NPV.
Discounting & Risk

High Risk Project with Cost of $125,000
– If successful, firm will build a $1 million plant which
would generate $250,000/yr after taxes
– Otherwise, project will be dropped
– 50% probability of success
Expected cash flows:
C0 = -125
C1 = .5(-1,000) + .5(0) = -500
Ct for t=2,3,…=.5(250) + .5(0) = 125
Discounting & Risk

High risk so management uses a project
discount rate of 25%.

NPV
– All: -125 - 500/1.25 +(125/.25)/1.252 =negative

Problematic approach
– If the test is a failure, then there is no risk at all!
– If successful, there may be normal risk afterwards.
Decision Tree Analysis

Low risk if pilot is successful
– Discount rate of 10%
Success
50%
NPV= -1000 + (250/.1)/1.1 = 1,272
Pilot production
and test marketing
50%
Failure
NPV = 0