Transcript Document 7448342

Advanced Corporate Finance
Finance 7330
Lecture 2&3
Ronald F. Singer
Practical Problems in Capital
Budgeting
• We have stated that we want the firm to
take all projects that generate positive
NPV and reject all projects that have a
negative NPV. Capital budgeting
complications arise when you cannot,
either physically or financial undertake all
positive NPV projects. Then we have to
devise methods of choosing between
alternative positive NPV projects.
Mutually Exclusive Projects
• IF,AMONG A NUMBER OF PROJECTS, THE
FIRM CAN ONLY CHOOSE ONE, THEN THE
PROJECTS ARE SAID TO BE MUTUALLY
EXCLUSIVE.
• For example: Suppose you have the choice of
modifying an existing machine, or replacing it
with a brand new one. You could not do both
and produce the desired amount of output.
Thus, these projects are mutually exclusive.
Given the cash flows below, which of these
projects do you choose?
Mutually Exclusive Projects
Time
Modify
0
-100,000
1
105,000
2
49,000
IRR
.40
NPV(@ 10%) 36,000
Replace
-250,000
130,000
253,500
.30
77,700
Difference
-150,000
25,000
204,500
.25
41,700
• Notice the conflict that can exist between NPV and IRR.
EXAMPLES OF CAPITAL BUDGETING
COMPLICATIONS
1.Optimal Timing
2.Long versus Short Life
3.Replacement Problem
4.Excess Capacity
5.Peak Load Problem (Fluctuating Load)
6.Capital Constraints
EXAMPLES OF CAPITAL BUDGETING
COMPLICATIONS
• These Capital Budgeting Complications
will stop the Firm from taking all possible
positive NPV PROJECTS. Thus, the firm
is faced with the choice of two possibilities.
• Remember: Goal is still Max NPV of all
possibilities
EXAMPLES OF CAPITAL BUDGETING
COMPLICATIONS
• We can divide these problems into three separate classes,
each with their own method of solutions.
(1) Once and for all deal.
Choose the one alternative having the highest NPV.
(2) Repetitive Deal.
Choose the one alternative having the highest
equivalent annual cash flow.
(3) Capital Budgeting Constraint
Choose the combination of projects having the highest
NET PRESENT VALUE.
Once and For all Deals
• INVESTMENT TIMING:
When is the optimal time to take on an
investment project? Consider T possible times,
where,
t = 1, ...T.
• Then each "starting time" can be considered a
different project in a set of T mutually exclusive
projects. Then find that t which Max:
NPV(t)
(1+r)t
Once and For all Deals
• Example You are in the highly competitive area of
producing laundry soap and detergents. You have a new
product which you feel does a superior job in washing
clothes, but you anticipate that the product will have
difficulty being accepted by the consumer. Thus you
expect that if you introduce the product now, you will
have to suffer a few years of losses until the product is
accepted by the consumer. A competitor is about to
come out with a similar product. You feel that if you
allow your competitor to come out with the product first,
you can benefit from the time he spends acclimating
your potential customers. However, you will then be
giving up your competitive edge.
Once and For all Deals
• The initial investment in the product has
already been spent, is a sunk cost and can
be ignored for this problem. The
anticipated life of the productive process is
ten years from the time the product is first
produced. Thereafter, there will be so
much competition that any new investment
in this product will have a zero NPV. The
discount rate is 15%.
Once and For all Deals
• Expected cash flows are:
CASH FLOW
($ MILLIONS )
year (from
start of
project
1
2
3
4-10
_______________________________________________
immediately
-4
-3
-2
20
If introduced after
one year
-1
1
3.5
If introduced after
two years
0
2
4
• WHAT SHOULD YOU DO?
19.5
19
Once and For all Deals
• NPV(0) (Introduced Immediately) is: 47.649 million
NPV(1) (Introduced in one year's time) is: 55.531 million
NPV(2) (Introduced in two year's time) is: 56.118 million
• WHICH ONE OF THESE THREE OPTIONS SHOULD
BE TAKEN?
47.649 55.531 56.118
|
|
|
0
1
2
3
4
5
Calculate NPV from time 0.
Once and For all Deals
• Shortcut
Calculate the annualized rate of change of
NPV. If delaying causes the NPV to
increase by more than the discount rate,
the project should be delayed. If not, the
project should not be delayed.
Once and For all Deals
•
Caution
This method assumes that the project cannot be reproduced at a positive NPV after
the initial life of the project. Otherwise, you have to also account for the fact that the
project that is started earlier can also be reproduced earlier. In that case, the
alternatives look like:
START IMMEDIATELY
0
10
20
30
_______________________________
ONE YEAR DELAY
0 1
11
21
31
_________________________________
•
THIS LEADS TO THE SECOND CLASS OF PROBLEMS:
Repetitive Deals
• Mutually exclusive projects with different
Starting Times
• Mutually exclusive projects with different
Economic Lives
• Replacement Decision
• Management of Excess of Peak Capacity
•
examples:
Alternatives with Different Lives
3 Little Pigs
Brick vs. Wood vs. Straw.
Alternatives with Different Lives
• Example: YOU HAVE THE OPTION OF
UNDERTAKING ONE OF TWO DIFFERENT
WAYS OF ACHIEVING SOME GOAL. WHICH
ONE SHOULD YOU TAKE?
(A) A Bridge costing 5M lasts 15 years
(B) A Bridge costing 4M lasts 10 years
Both generate $1 Million in net revenues per year.
Let the Discount rate = 12% for each alternative.
• NPV (A) = $1.81 Million
NPV (B) = $1.65 Million
Alternatives with Different Lives
Conceptually
• The NPV rule would say, take the project
with the highest Net Present Value. This
may be wrong.
• Consider what happens after ten years.
In particular by year 30.
Alternatives with Different Lives
A
1.81
1.81
1.81.....
_____________________________________
0
5 10 15 20 25 30
35
B
1.65 1.65
1.65
1.65
_____________________________________
0 5 10
15 20
25 30
35
• PV(A) over infinite horizon:
PV(A) = 1.81 + 1.81
+ 1.81 + … = 2,214,900
(1.12)15
(1.1)30
• PV(B) over infinite horizon:
PV(B) = 1.65 + 1.65__
+ 1.65__ + ….. = 2,435,700
(1.12)10
(1.12)20
Alternatives with Different Lives
ALTERNATIVE
EQUIVALENT ANNUAL CASH FLOW
(EACF) or (NUS in Hewlett Packard)
• Note: BMA talk about Equivalent Annual Cost, this is a more general
concept.
• Consider the annuity having the same NPV and life of the project.
EACF (A) = That annuity having a Present Value of 1.81, lasting 15
years at a discount rate of 12%.
• (A): PV(A) = Annuity x PVFA(r%, T)
Annuity(A) =
PV(A)____
PVFA(12%,15)
Annuity(A) = 1.81 Million = 265,700 = EACF(A)
6.811
Annuity(B) = 1.65 Million = 292,000 = EACF(B)
5.650
Alternatives with Different Lives
• This "Equivalent Annual Cash Flow" (or Cost) is a
convenient way of examining the host of complicated,
mutually exclusive capital budgeting problems listed
above: These all involve
A TIMING PROBLEM
(1) When to start project
(2) When to "cash in"
Forestry
Wine
(3) Replacement
(4) Short vs. Long lived Project
(5) When and how to increase capacity
Can all be dealt with in a similar way?
Mutually exclusive projects with
different Starting Times
• Instead of assuming that this is a once and
for all deal, assume that the alternatives
can be reproduced indefinitely. Note that
this case differs from the Laundry Detergent
Example treated above:
1. How?
2. What impact will this have on the timing
decision?
Mutually exclusive projects with
different Starting Times
• Consider an example: The mutually exclusive decision,
when to cut down a forest:
In ten years with NCF of
47,000
In eleven years with NCF of
53,000
In twelve years with NCF of
58,000
• If this were a one-time-only deal, you would simply
calculate the NPV of each alternative:
NPV of cutting in ten years:
15,132.74
NPV of cutting in eleven years:
15,236.23
NPV of cutting in twelve years:
14,887.16
Mutually exclusive projects with
different Starting Times
• But, more realistically, you will be able to continue
cutting down these trees every ten, eleven, or
twelve years. Which is the best alternative as a
repetitive procedure?
• The question is, what is better:
(1) receiving an annuity of 47,000 every ten years
(2) receiving an annuity of 53,000 every eleven years
(3) receiving an annuity of 58,000 every twelve years
Mutually exclusive projects with
different Starting Times
• For any set of reproducible mutually exclusive projects with
different lives, you can:
Find the NPV of each project through one repetition, and then find
its Equivalent Annual Cash Flow (EACF), and choose the one with
the highest EACF.
Where EACF is calculated as: EACF(t) = NET PRESENT VALUE
PVFA(r%,t)
So:
EACF(10) = 15,132 = 2,678.12
(5.650)
EACF(11) = 15,236 = 2,566.98
(5.938)
EACF(12)
You know this isn't the right one since it has a lower present value
but takes longer to produce
• Thus you want to take the shorter lived project now.
Replacement Decision
• Return to the first example, you choose project (2), and
now you are in the fifth year of that project. The project,
as expected, is returning $19.5 million this year. But
production difficulties have resulted in a machine which
is wearing out faster than anticipated. So that your
expected cash flow for the next five years will be:
0
Cash Flow
19.5
NPV of operating
Cash Flows
62.54
1
18
2
17
50.54
38.61
3
16
4
15
26.24 13.39
5
Replacement Decision
• A new production technology has been devised
which will cost $100 million and generate $39
million for the next 7 years, with an anticipated
scrap value of 3 million at the end of the seventh
year. Should you replace the machine now,
never, or plan to replace it some time in the
future?
• It is assumed that the scrap value of the old
machine will be 0 if not replaced during the next
5 years (the life of the old project), but can be
sold for 3 million at any time during the next five
years. The discount rate is assumed to be 12%.
Replacement Decision
• Find the equivalent annual cash flow for the new
machine, net of the current scrap value.
Net Cash Flow of Replacement Machine
0
-97
1
39
2
39
3
39
4
39
NET PRESENT VALUE
EQUIVALENT ANNUAL CASH FLOW:
IRR
5
39
6
39
7
42
82.344 million
18.043 million
35.56%
Replacement Decision
• Replace in the beginning of year 2. Note, simply
comparing NPV will not give the right answer, neither will
looking at incremental cash flow. This is because the
replacement has a different life than the current process
and they are obviously mutually exclusive.
Furthermore, and more important, the alternatives of
replacing now versus not replacing now is not the
appropriate alternatives. You can also replace next year,
the year after, etc. The alternative which gives the
greatest incremental value relative to all the other
possible alternatives could be calculated by looking at
the incremental cash flows from each alternative. But it
is easier to simply calculate the EACF and compare that
to the current cash flow to see what to do.
Replacement Decision
• In general, Equivalent Annual Cash Flow
or Cost is used to consider a problem
where the investment is considered
ongoing and you have to examine what
happens at the end of the project's life. All
that EACF does is help you discover the
decision which gives the highest NPV as a
whole.
Capital Rationing
• In this situation, the decision maker is faced with
a limited capital budget. As a result, it may not
be possible to take all positive net present value
projects. Under this scenario, the problem is to
find that combination of projects (within the
capital budgeting constraint) that leads to the
highest Net Present Value.
• The problem here is that the number of
possibilities become very large with a relatively
small number of projects. Thus, in order to
make the problem "manageable", we can
systematize the search.
Capital Rationing
• Since we have a constraint, what we want to do
is invest in those projects which gives us the
highest BENEFIT per dollar invested. (The
highest bang per buck). What is the benefit?, it
is the Present Value of the Cash Flows. So that
we would want to choose that set of projects
within the capital budgeting constraint that gives
the highest:
Net Present Value
INVESTMENT
• This ratio is called the profitability Index.
Capital Rationing
• For example, suppose we have a $13 million capital
budgeting constraint, with 7 alternative capital budgeting
projects with the following projections.
Project
NPV
Investment
A
10
15
B
8
10
C
4
2.5
D
6
5
E
5
2.5
F
7
5
G
4.5
3
Capital Rationing
• Rank by Profitability Index {(NPV/INV}
Project
Profitability Index Investment Total
E
C
G
F
D
B
A
2.0
2.6
2.5
2.4
2.2
1.8
1.667
2.5
2.5
3
5
5
10
15
2.5
5.0
8.0
13.0
• COMBINATION WITH HIGHEST PROFITABILITY INDEX WITHIN
THE CAPITAL BUDGET
• (E,C,G,F) has a NPV of $20.5 million, and a cost of $13 million.
Capital Rationing
• However, if the budget were 15 million rather than 13
million we would have a problem. Adding D would go
over the budget and be infeasible, but the combination
CDEF has a higher NPV ($22 million) than the chosen
combination of ECGF. This is because the amount spent
was only 13 million leaving 2 million in unspent funds. In
this case, we are better off choosing a combination
which spends all the funds.
• THE ONLY WAY TO DO THIS RIGHT IS TO DO A FULL
BLOWN LINEAR PROGRAMING PROBLEM WITH
CONSTRAINTS.