Title: Chapter 8: Project Analysis
1Topic Project Analysis and Evaluation
Objectives
- NPV estimates depend on projected future cash
flows - Use sensitivity, scenario, and break-even
analysis to see how project profitability would
be affected by a change in forecasting - Explain the concept of operating leverage
2Project Analysis
- Some What If Analyses
- Scenario Analysis
- Sensitivity Analysis
- Simulation Analysis
- Break-Even Analysis
- Additional Considerations in Capital Budgeting
- Managerial Options
- Capital Rationing
3Scenario Analysis
- The determination of what happens to NPV
estimates when we ask what-if questions - Allow managers to look at different but
consistent combinations of variables, and compare
one particular combination with another - Forecasters usually prefer to give an estimate of
revenues or costs under a particular scenario
rather than giving some absolute optimistic or
pessimistic value - Scenario analysis allows variables to be
interdependent
4Sensitivity Analysis
- Investigation of what happens to NPV when only
one variable is changed - e.g., sales, variable costs, fixed costs...
- Sensitivity analysis is useful in pinpointing
those variables that deserve the most attention - Sensitivity analysis assumes that the
individual variables are independent of each
other - Simulation analysis a combination of scenario
and sensitivity analyses
5Break-Even Analysis
- Question How bad do sales have to get before we
actually loose money? - Examines the relationship between sales volume
and profitability - Variable Costs costs that change when the
quantity of output changes - Fixed Costs costs that do not change when the
quantity of output changes during a particular
period
6Example A-Sensitivity Analysis
- A project currently generates sales of
10million, variable - costs equal to 50 of sales, and fixed costs of
2million. The - firms tax rate is 35. What are the effects of
the following - changes on after-tax profits and cash flows?
- a) Sales increase from 10million to 11million
- b) Variable costs increase to 60 of sales
7Example A
8Example A
9Operating Leverage
- Operating leverage the degree to which a project
or firm is committed to fixed costs - Degree of Operating Leverage (DOL) the change
in operating cash flow relative to the change
in the quantity sold - DOL measures the sensitivity of OCF to the
quantity sold. Since FC do not vary with sales, a
small change in Q can be magnified into a large
change in OCF - The danger from incorrectly forecasting sales is
directly related to its DOL. The higher the fixed
costs, the greater the variation in operating
cash flows given a change from estimated sales
10Operating Leverage
- Given that
- Can you prove (ignoring taxes) that
- Hint OCF(P-v)Q-FC, ignoring taxes, where P is
unit price, v is unit cost, Q is sales and FC is
fixed cost. Think about what happens when sales
increases by 1.
11Operating Leverage
12NPV Break-Even Analysis
- NPV Break-Even analysis calculates the level of
sales that generates an NPV of zero the
textbook calls this the financial break-even. - Sales higher than the zero NPV sales will produce
positive NPV - This is equivalent to finding the sales level for
which the cost of the project equals the present
value of the cash flows
13Simple Example, based on pp359
- Victoria Sailboats Limited is considering
whether to launch its new Mona-class sailboat.
The selling price would be 40,000 per boat and
the cost per boat would be 20,000. Fixed costs
would be 500,000 per year. The total investment
needed to undertake this project would be 3.5 M
for factory improvements. This amount will be
depreciate straight-line over the 5-yr life of
the equipment. The salvage value is zero, and
there are no working capital consequences.
Victoria has 20 required return on new projects. - Calculate the NPV break-even ignoring taxes.
- Calculate the NPV break-even, assuming a tax rate
of 35.
14Simple Example, based on pp359
- The initial investment is 3.5 M
- Ignoring taxes, the annual OCF is (P-v)Q-FC
(40,000-20,000)Q- 500,000
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18Example B
- Emperors Clothes Fashions can invest 5 million
in a new plant for producing invisible makeup.
The plant has an expected life of 5 years, and
expected sales are 6 million jars of makeup a
year. Fixed costs are 2 million a year, and
variable costs are 1 per jar. The product will
be priced at 2 per jar. The plant will be
depreciated straight-line over 5 years to a
salvage value of zero. The opportunity cost of
capital is 12 and Tc is 40. - a) What is the project NPV under the base-case
assumptions? - b) What is the NPV if variable costs turn out to
be 1.20 per jar? - c) At what price per jar would the NPV equal
zero? - d) Whats the NPV break-even sales per year?
19Example B,Part a)
20Example B,Part b)
21Example B,Part c)
22Example B,Part d)
23Topic Project Analysis and Evaluation
Objectives
- Analyze projects with alternative sequential
decisions and possible outcomes by using decision
trees - Make investment timing decisions
- Choose between projects with different lives by
comparing the equivalent annual costs of the
projects - Use equivalent annual costs to decide whether to
replace an aging machine with a new one
24Example of a Decision Tree
- Your midrange guess as to the amount of oil in a
prospective field is 10 million barrels, but in
fact there is a 50 percent chance that the amount
of oil is 15 million barrels, and a 50 percent
chance of 5 million barrels. If the actual
amount of oil is 15 million barrels, the present
value of the cash flows from drilling will be 8
million. If the amount is only 5 million
barrels, the present value will be only 2
million. It costs 3 million to drill the well.
Suppose that a seismic test that costs 100,000
can verify the amount of oil in the field. Is it
worth paying for the test? Use a decision tree
to justify your answer.
25Decision Tree
Big oil field (.5)
NPV 8 3 5 million
Test (cost .1m)
NPV 0 (abandon)
Small oil field (.5)
Big oil field (.5)
NPV 8 3 5 million
Do not test
NPV 2 3 - 1 million
Small oil field (.5)
EV(test) -.1M .5x5M .5x0 2.4M EV (no test)
.5x5M .5x(-1) 2.0M
26Decision Tree - Part II
- Suppose the probability of the oil field being
large is p. For what value of p would you be
indifferent between paying for the test and not
paying for it?
27Decision Tree - Part II
EV(test) -.1M px5M (1-p)x0 (5p-.1)M EV (no
test) px5M (1-p)x(-1)M (6p-1)M EV(test)
EV (no test) (5p-.1)M(6p-1)M p0.9
28Investment Timing Decision
- When to make an investment is a difficult
decision in a dynamic world, where new
cost-saving technology is always improving and
NPVs are greater if delayed until later. - Decision Rule
- - compute NPVs for each possible year of
investment - - compare NPVs computed all in t 0 values
- - choose the time that gives the highest NPV0
29Example on Investment Timing
- You can purchase an optical scanner today for
400. The - scanner provides benefits worth 60 a year. The
expected life - of the scanner is 10 years. Scanners are
expected to decrease - in price by 20 percent per year. Suppose the
discount rate is - 10. What is the best purchase time?
30Example on Investment Timing
- Time Cost PV of Benefits till Purchase
at Purchase Date - 60x(1/.1)x(1-1/1.110)
- 0 400 368.67
- 1 320 368.67
- 2 256 368.67
- 3 204.8 368.67
- 4 163.84 368.67
- 5 131.07 368.67
- 6 104.86 368.67
- 7 83.88 368.67
31Example on Investment Timing
- Time NPV at NPV at till
Purchase Purchase Date Time 0 - 0 -31.33 -31.33 -31.33
- 1 48.67 48.67/(1.1) 44.25
- 2 112.67 112.67/(1.1)2 93.12
- 3 163.87 163.87/(1.1)3 123.12
- 4 204.83 204.83/(1.1)4 139.90
- 5 237.60 237.60/(1.1)5 147.53
- 6 263.81 263.81/(1.1)6 148.91
- 7 284.79 284.79/(1.1)7 146.14
32Example on Investment Timing -II
- How does your answer change when the cost of
scanners decreases by 50 each year?
33Example on Investment Timing -II
34Long-lived versus Short-lived Equipment
- When comparing mutually exclusive projects that
have unequal project lives, one must analyze the
present value of investment outlays and operating
costs of the projects - Decision Rule (between two machines w/ different
lives) - - calculate the equivalent annual cost (EAC) of
both machines - - the equivalent annual cost is the cost per
period with the same PV as the cost of buying and
operating a machine -
- - choose the machine with the lowest EAC
35Example on Long- vs. Short-Lived Machines
- Suppose your firm must decide which machine to
buy to produce widgets. Machines A and B have
identical capacity and do exactly the same job.
Machine A costs 100,000, lasts 4 years, and
costs 20,000 per year to operate. Machine B
costs 75,000, will last only 3 years, and costs
35,000 per year to operate. Which machine would
you purchase? The opportunity cost of capital is
10.
36Example on Long- vs. Short-Lived Machines
- PV of costs for A
- PV of costs for B
- Why cant we compare A and B yet?
37To compare costs of projects with different lives
use EAC Project A (life of 4 years) Annuity
factor1-1/1.14/.103.17 EAC163,397/3.1751,5
47 Project B (life of 3 years) Annuity
factor1-1/1.13/.102.49 EAC162,040/2.4965,1
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38Replacing an Old Machine
- Most equipment is replaced before the end of its
useful economic life. Replacement decisions most
often involve replacing old by new with different
useful cash flow lives - Decision Rule
- calculate the EAC of the new project, and compare
to the period cost of the old project. - if the EAC of the new project is less than the
period cost of the old project, accept the new
39Example on Replacing an Old Machine
- Suppose that a new machine has developed and it
costs 20,000 and its economic life is 3 years.
The existing machine will last at most for 2 more
years. The annual operating costs of the two
machines are given below. Both machines produce
identical output. The opportunity cost of capital
is 10. When should you replace the existing
machine with the new one? - Annual Operating Cost
- Machine 1 2 3
- Old 10,000 15,000
- New 4,000 6,000 8,000
40Example on Replacing an Old Machine
- The firm has 3 mutually exclusive alternatives
- Replace immediately
- Replace in 1 year
- Replace in 2 years
- First step compute EACNEW
41Example on Replacing an Old Machine
- 1. Immediate replacement (today)
- 2. Replace in 1 year
- 3. Replace in 2 years!!
42Example on Replacing an Old Machine
43A Quick Summary
- Optimal investment timing
- - Compare the NPV0 of all future NPVs
- Mutually exclusive equipment with different
lives - - Compare the EACs of the two equipment pieces
- Replacing an old machine
- - Compare the EAC of a new machine with the
period cost of the old machine