Comparison of Alternatives

1
Comparison of Alternatives
2
Introduction

• What will we learn in the class?
• Defining Investment Alternatives.
• Defining the Planning Horizon.
• Developing Cash Flow Profiles.
• Specifying the MARR.

3
Introduction

• Most organizations, including Lamar, go through a
  "Capital Budgeting" cycle, which means the
  organization is deciding what projects to fund
  for the coming budget period (usually a physical
  year).
• In most cases, several projects are considered at
  one time. Only a few will be selected for
  funding.
• If your organization had 100,000 to spend, it is
  likely that several projects could be funded.
  Why?
• By spreading out your money, you diversify your
  investments and reduce your risk.
• If one of the investments goes bad, then you
  still have the remaining investments to provide
  returns, therefore reducing your risk.

4
Introduction

• An alternative is a collection of zero or more
  investments (projects to be considered).
• The null alternative is to do no investments.
• What is the danger of doing nothing?
• If the number of independent investments is m,
  then 2m alternatives can be formed.
• What is meant by mutually exclusive?
• Mutually exclusive alternatives means the
  alternatives cannot occur together.

5
Introduction
For example assume there are 3 independent
investments, A, B and C. Then there are 23 8
alternatives to select from. The alternatives are
best shown in Boolean table as follows
6
Introduction
Alternative 1 is to do none of the investment
opportunities Alternative 2 is to do investment A
but not to do B or C. Alternative 3 is to do
investment B but not to do A or C. Alternative 4
is to do investment C but not to do A or B.
Alternative 5 is to do investments A and B but
not to do C. Alternative 6 is to do investments
A and C but not to do B. Alternative 7 is to do
investments B and C but not to do A. Alternative
8 is to do investments A, B and C.
Assumes Projects are independent Enough money
exists for all projects
7
Introduction
Dependencies Mutually exclusive - A are mutually
exclusive if A and B cannot occur together
Contingent - Suppose project B is contingent on
project A. If you select B, then you must also
select A. If you select A, then you do not have
to select B.
8
Introduction
Suppose that projects A and B are mutually
exclusive. What changes must we make to our
Boolean Table?
9
Introduction
Suppose that project C was contingent on A.
What changes must we make to our Boolean Table?
For a more complete discussion of developing
investment alternatives see example 5.2 and Table
5.1 on page 146
10
Introduction

• If PWj lt 0, do we reject it immediately?
• No. Why? PWj could be a contingent project that
  has a huge PW.
• For example
• Mach 3 razors. Might be sold as a loss, but once
  customers have it, Gillet will profit from
  selling the blades.
• PWj could be thrown out immediately if it is not
  contingent on other projects (it is independent)
  or other projects are not contingent upon it

11
Introduction

• If an investment decision involves more than one
  project or investment options then it is wise to
  follow the systematic procedure of page 143.
• Define the set of feasible mutually exclusive
  alternatives.
• Define the planning horizon.
• Develop cash flow profiles for each alternative.
• Specify the MARR to be used.
• Compare the alternatives using a specified
  measure of worth.
• Perform supplementary analyses. (simulation,
  scenarios - not in this course)
• Select the preferred alternative. 

12
Defining The Planning Horizon

• Why can defining the planning horizon present a
  major challenge?
• Because it is common for the individual projects
  which make upon alternative to each have a
  different life length.
• A simple answer does not exist.

13
Defining The Planning Horizon

• Four common methods for dealing with unequal
  lives as presented at the bottom of page 149 are
  as follows
• Least common multiple of lives for the set of
  feasible alternatives, denoted T.
• Shortest life among alternatives, denoted Ts.
• Longest life among alternatives, denoted Tl.
• Some other period of time.
• None of these methods is completely satisfactory
  and this problem must be carefully solved by the
  engineer using sound logic.
• Illustrations of each of the four methods are
  presented in Table 5.3 on page 152-153.

14
Defining The Planning Horizon

• Working life of equipment actual period of time
  the equipment is capable of being used
• Depreciable life of equipment allowable period
  of time for depreciating the asset
• Length of the planning horizon may have no
  relationship to these time periods.
• Only a time period for comparing alternatives
• Should be realistic
• Must be the same for each alternative

15
Defining The Planning Horizon

• Least common multiple
• Each alternative's cash flow profile is assumed
  to repeat in the future until a time is reached
  when all alternatives under consideration
  conclude at the same time.
• Relying on this approach alone is not advised.
• Shortest life
• Considers each alternative based on the shortest
  life on the alternatives under consideration.
• What is wrong with this approach?
• It ignores the cash flows in years beyond

16
Defining The Planning Horizon

• Longest life
• Alternatives with shorter life spans must be
  replaced by new alternatives when their time
  expires.
• What is wrong with this approach?
• Since predicting what technology will be
  available at that time, this method is not used
  often.

17
Example 5.3
Alternative 1 No investment required, probably
just keep on doing what we are doing Alternative
2 30,000 in revenues, 10,000 in costs and 20,000
in net cash flow for 6 years Alternative 3
various amounts in revenues, 7500 in costs and
various amounts in net cash flow for 5 years
18
Example 5.3
What if we use the least common multiple
approach? The least common multiple for T 3, 5,
and 6 30. Thus Alternative 1 is repeated 10
times, Alternative is repeated 6 times and
alternative 3 is repeated 5 times. What are the
drawbacks to this approach? Inflation and
technological improvements are ignored. What if
we use the shortest life approach? Years 4-5 for
Alternative 2 and years 4-6 for Alternative 3 are
ignored. What if we use the longest life
approach? How do we project the cash flow for
Alternative 1 in years 4-6? We could assume that
more used equipment is bought in year 4, or that
a new unit is bought in year 4.
19
Example 5.4

• Consider Figure 5.1 on page 154.
• Based on the numerical results, Alternative 2 is
  the best choice
• Never trust numbers alone!
• Balance logic with economic numbers.

6000
4500
5000
4000
3500
3500
3500
3000
2000
1000
1
2
3
4
1
2
3
4
5
6
Alternative 1
Alternative 2
Figure 5.1
4000
5000
20
Example 5.4

• Why should we consider Alternative 1?
• Shorter time period thus less risk in later
  years.
• The longer you try to predict into the future,
  the less accurate the prediction
• Only about 300 difference between alternatives -
  6 years in the future - so these projects are
  very close
• How did the engineers come up with these cash
  flows in figure 5.1?
• Educated guesses and calculations - thus a lot of
  error - and more risk!

21
Developing Cash Flow Profiles

• Specify the MARR to be used.
• Organizations normally decide at a high level of
  management the value of the minimum attractive
  rate of return (MARR).
• For Example, Wal-Marts MARR 21 (Spring 2003)
• The author presents a worked example in section
  5.4, Developing cash flow profiles.
• You should read example 5.5 on page 155 and the
  associated Tables 5.5 and 5.6 on page 156.

22
Developing Cash Flow Profiles

• What issues contribute to determining the MARR?
• This number is a function of companys
• Cost of capital
• Risk level
• Desired minimum return after accounting for the
  cost of capital and risk (profit).
• Once the MARR is decided upon it is normally
  passed down to the engineers who must design
  projects whose projected return exceeds the MARR.

23
MARR

• The value of the MARR should be greater than the
  cost of capital.
• Should represent the opportunity cost associated
  with investing the candidate alternatives as
  opposed to other available alternatives.

24
The Cost Of Capital

• It costs money to obtain money for investment.
• Funding may come from two types
• Debt
• Equity funds.
• Two common debt investments are loans and bonds.
• The interest paid for the use of money is a cost
  of capital.
• Interest is deductible from income for tax
  purposes

25
The Cost Of Capital
The cost of capital (after taxes) for funds
obtained by bank or other loans is given by
Equation 5.1.   kl (1 r/m)m 1 (1 T)
. . . Eq. 5.1 r loans nominal annual interest
rate m number of payment periods Where the
bracketed term is the effective interest rate
payable on the loan and T is the organizations
tax rate. Any business interest is tax
deductable, thus we use (1-T)
26
The Cost Of Capital
The equation for bonds, Eq. 5.2, is exactly the
same as the equation for loans because bonds are
loans.   kb (1 r/m)m 1 (1 T) . . .
Eq. 5.2 The cost of equity capital is given by
Equation 5.3 and 5.4. Equation 5.3 is the cost of
capital for common stock. The cost of capital for
common for common stock is   ks D / Ps . . .
Eq. 5.3 D is the annual dividend per share of
stock and Ps is the price per share. The cost of
capital for retained earnings is   kr D / Ps .
. . Eq. 5.4 Why is this a measure that will
change quickly? Based on stock price, which
changes everyday.
27
The Cost Of Capital

• Why is the cost of capital for retained earnings
  the same as the cost of capital for common stock?
• Because the money belongs to the same person
  the stockholder.
• An organizations total cost of capital is a
  weighted average of the cost of debt and equity
  as shown in equation 5.5.
• ka kl pl kb pb ks ps kr pr . . . Eq. 5.5
• Where ki is the proportion of the organizations
  assets obtained by funding source i (loans,
  bonds, stock, or retained earnings) and
• kl kb ks kr 1

28
Example 5.8
29
Example 5.8
30
Approaches to Establish MARR

• Add a fixed percentage of return to the firms
  cost of capital
• Average rate of return over the past 5 years is
  used as this years MARR
• Use different MARR for different planning
  horizons
• Use different MARR for different magnitudes of
  initial investment
• Use different MARR for new ventures rather than
  for cost-improvement projects
• Use as a management tool to stimulate or
  discourage capital investments depending on the
  overall economic condition of the firm
• Use the average stockholders return on
  investment for all companies in the same industry
  group

31
Comparison of Alternatives

• There are two approaches for evaluating
  alternatives
• Ranking Approach
• Incremental Approach.
• The ranking approach can be use only with the PW,
  AW and FW criterion.
• The incremental approach is a little more complex
  and time consuming but it can be used with all
  criterion. (PW, AW, FW, I, I, and SIR)
• The ranking approach simply calculates the PW, AW
  or FW of each feasible alternative and selects
  the one that Ranks the highest.
• The incremental approach requires a number of
  steps which are presented in the flow chart of
  Figure 5.5 on page 167.

32
Comparison of Alternatives

• The process of solving an investment analysis
  problem involving more than one project can be
  described as follows
• Determine the time horizon.
• Determine the set of feasible mutually exclusive
  alternatives.
• Number the alternatives so that the lowest
  costing alternative is number 1 and the second
  lowest is number 2 and so on.
• Compare alternatives 1 and 2 by obtaining the
  cash flow of alternatives 2 minus the cash flow
  of alternative 1 and applying the appropriate
  measure of merit (PW, AW, FW, IRR, ERR, or SIR)
  to the differential cash flow.
• Select the preferred alternative and compare it
  with the next higher numbered alternative.
  Continue until the highest numbered alternative
  has been considered.
• Consider Example 5.9, p.167 - 168

33
Comparison of Alternatives
5.6.1 Present Worth method 5.6.2 Annual Worth
Method 5.6.3 Future Worth Method All of these
methods are the same, meaning they will product
the same final decision.
34
Comparison of Alternatives
An example application of the incremental rate of
return is Problem 5.10 page 230-231(See Table
12.1 below). A firm has available four proposals
A, B, C and D. Proposal A is contingent on
acceptance of either Proposal C or Proposal D. In
addition , Proposal C is contingent on Proposal
D, while D is contingent on either Proposal A or
Proposal B. The firm has a budget limitation of
500,000. The cash flows are as
follows Table 12.1 Problem 5.10 Data
35
Comparison of Alternatives

• Specify the net cash flow profile associated with
  each alternative.
• Clearly show the alternatives to be considered.
• Use an incremental approach and internal rate of
  return to determine the preferred alternative
  assuming the MARR is 20.
• Table 1
• 2.2 Boolean Table of
  Alternatives

36
Comparison of Alternatives
Table 12.2 shows that alternatives 2(D), 3(C),
4(CD), 7(BC), 9(A), 11(AC) and 13(A B) are
all infeasible because of contingencies.
Alternatives 14, 15 and 16 are over budget. So of
the sixteen alternatives only alternatives 1, 5,
6, 8, 10 and 12 are feasible. The next step is to
renumber the feasible alternatives from lowest
investment required. In doing this alternative 10
becomes 2, 12 becomes 3, 5 becomes 4, 6 becomes 5
and 8 becomes 6. These alternatives have cash
flows as shown in Table 12.3.
37
Comparison of Alternatives
Table 12.3 Cash Flows for Feasible
Alternatives The analysis is presented below the
Table 12.4. The cash flow for alternative 2 minus
1 is simply the cash flow of alternative 2 since
alternative 1 is the null alternative and has no
cash flow.   IRR2-1 PW2-1(i) -288,000
88,000(P/A, i, 5) 5,000(P/G, i, 5)
65,000(P/F, i, 5) 0   I used the Excel function
IRR(range) to solve for i and obtained 24.
Since 24 is greater than the MARR select the
higher costing alternative.
38
Comparison of Alternatives
Table 12.4 Incremental Cash Flow of Alternatives
2 minus 1 Now compare alternatives 3 and 2
IRR3-2 PW3-2(i) -50,000 10,000(P/A, i,
5) The rate of return of 3 2 is 0 because the
positive cash flows equal the negative cash
flows. Since 0 is less than the MARR select 2,
the lower costing alternative.
39
Comparison of Alternatives
Now compare alternatives 4 and 2. The cash flow
and IRR from Excel are as shown in Table 12.5
below. The IRR is 29 which is greater than the
MARR. Therefore, choose alternative 4 and
compare 5 with 4. The cash flow and IRR for 5
minus 4 is 16. Since the IRR5-4 is less than the
MARR select 4 and compare 6 and 4. Again the
IRR6-4 is 8 which is below the MARR so select 4.
Alternative 4 is the final selection, since there
are no additional feasible alternatives Table
12.5 Incremental Cash Flows
40
Replacement Analysis

• Two choices
• Maintain the status quo
• Various replacement options
• Why consider replacement Analysis?
• Current asset (defender) may have a number of
  deficiencies such as high set-up costs, excessive
  maintenance, declining production efficiency,
  high energy consumption or physical impairment
• Example Your car is becoming expensive to
  operate or may need a major repair. Ryan replaced
  his 1997 Grand Am when the transmission started
  to slip (thus a major was likely because a
  transmission overhaul would be needed).

41
Replacement Analysis

• Why consider replacement Analysis?
• Potential replacement assets (challengers) may
  take advantage of new technology and be easily
  set-up, maintained a low cost, high in output,
  energy efficient, and posses increased
  capabilities
• Environmental impacts
• Customer preference change present equipment
  may not be capable of adapting to new demands
• Low utilization sell equipment and outsource
  such as lease, rent, or contract to another
  company
• What are some examples of challengers who fit
  this description?

42
Replacement Analysis

• Is replacement Analysis similar to alternative
  comparison?
• Yes- they follow the same systematic seven-step
  approach outlined in Ch5
• All six consistent measures of investment worth
  are also applicable
• What are some confounding issues related to
  Replacement Analysis?
• Personnel may have emotional attachment to the
  current equipment (particularly if they were
  involved in selecting, installing or operating
  it).
• Attempts to hold on to old equipment is often an
  attempt to recover sunk costs, which are past
  costs that are unrecoverable and should not be
  considered in a replacement analysis
• To include sunk costs penalizes or burdens the
  potential replacement asset and unfairly favors
  the current asset

43
Replacement Analysis

• What should sunk costs be excluded from
  Replacement Analysis?
• Sunk costs penalizes or burdens the potential
  replacement asset and unfairly favors the current
  asset
• What are the two approaches commonly used in
  replacement analysis?
• Cash flow approach actual cash flows associated
  with keeping, purchasing or leasing an asset are
  used directly
• Outsider viewpoint approach cash flow profiles
  faced by an objective outsider are used
• Are the two approaches equivalent?
• Both approaches are mathematically equivalent and
  yield consistent decisions

44
Replacement Analysis Cash Flow Approach

• Cash flow insider viewpoint
• No additional cost of capital if asset is kept
  (in most cases)
• Trade-in allowance for most assets
• How are cash flows developed?
• Decision maker must determine how much money
  will be spent and received if an alternative is
  adopted
• Past costs sunk costs - which are not included
  in economic studies that deal with the future
• Decision maker determines planning horizon, but
  the shortest life is often chosen because the
  existing asset will not likely last as long as
  the new asset under consideration

45
Replacement Analysis Cash Flow Approach

• For replacement analysis, the planning horizon is
  a window through which only the cash flows that
  occur during the planning horizon can be seen
• What about a salvage value that occur after the
  planning horizon?
• Even though a salvage value may occur later than
  the planning horizon, it is included in the
  calculations

46
Replacement Analysis Outsider Viewpoint Approach

• Outsider viewpoint is preferred in some cases
  because it forces the decision maker to view both
  the existing asset and its challengers from an
  objective point of view as would an outsider
• Outsiders
• Have no existing assets
• Free to choose either a used asset (the defender)
  available for the price of its market value
• Considers the salvage value of the existing asset
  to be its investment cost if it is retained in
  service
• Since the retention of the defender is equivalent
  to a decision to forego the receipt of the
  salvage value, then an opportunity cost is
  assigned to the defender

47
Replacement Analysis Outsider Viewpoint Approach

• What if there is little correspondence between
  the market value and the trade in value?
• Usually a high trade in value indicates that the
  seller is using an inflated selling price
• If a purchase was made without a trade in, then
  the selling price would likely be lower.
• When using the Outsider Approach decrease the
  inflated selling price of the asset by the
  difference between the trade in value and a lower
  market value

48
Example 5.32
49
Example 5.32
A chemical plant owns a filter press that was
purchased 3 years ago for 30,000. Actual OM
expenses (excluding labor) for the press have
been 4,000 , 5,000 and 6,000 each of the past 3
years. It is anticipated that the filter press
can be used for 5 more years and salvaged for
2,000. The undepreciated worth of the press as
indicated on our accounting books is 12,600,
however, new technological developments have
produced new presses that are very competitive,
thus the current press is worth only 9,000. A
new filter press is available and can be
purchased for 36,000. It has anticipated life of
10 years. Alternative 1 is to keep the old
press and Alternative 2 is to replace the old
press with the new press.
50
Example 5.32
Since the old press can only be used for 5 more
years, the planning horizon will be 5 years. The
salvage value of the new press in 5 years is
anticipated to be 12,000. Note that the 9,000
market value of the existing press is applied as
a positive cash flow for the challenger since the
old unit will be sold if the new unit is
purchased. Annual worth using a MARR
15 AW1(15) -7000 1000(AG, 15, 5)
2000(A\F, 15, 5) AW1(15) -7000 1000(1.7228)
2000(.1483) AW1(15) 8426.20/year
51
Example 5.32
Annual worth using a MARR 15 AW2(15)
-27000(AP, 15, 5) 1000(AG, 15, 5)
12000(AF, 15, 5) AW2(15) -27000(.2983)
1000(1.7228) 12000(.1483) AW2(15)
7997.30/year -8426.20 7997.30 428.90/year,
so it is recommended that the new filter press be
purchased and the old press be sold Note that
the 30,000 first cost for the Old press was not
considered because it occurred in the past and
the 12,600 book value was not considered. Using
the 9,000 which the old press can be sold
for Sunk cost 12600 9000 3600 To add
this cost to the new press in cash flow analysis
gives the old press an unfair advantage.
52
Example 5.32
53
Example 5.33
If we use a 10 year planning horizon, we
recommend that the old press be replaced in 5
years. In 5 years, we anticipate that a filter
press will be available for 31,000.
54
Example 5.33
Annual worth using a MARR 15 AW1(15)
-7000(PA, 15, 5) 1000(AG, 15, 5) -
29000(PF, 15, 5) 1000(PG, 15, 5)(PF, 15, 5,)
15000(PF, 15, 10)(AP, 15, 10) AW1(15)
-7000(3.3522) 1000(5.7751) - 29000(.4872)
1000(5.7751)(.4972) 15000(.2472)(.1993) AW1(15
) 8534.56/year AW2(15) -27000(PA, 15,
5) 1000(AG, 15, 5) 3000(AF, 15,
10) AW2(15) -27000(.1993) 1000(3.3832)
3000(.0493) AW2(15) -8616.40/year
8534.56/year (-8616.40/year) 81.84/year thus
choose Alternative 1
55
Example 5.33
What are the risks associated with a 10 year
planning horizon? The degree of uncertainty in
our forecast of the cash flows
56
Example 5.35
Consider Example 5.32 with the Outsider Approach.
The present filter press has a market value of
9,000, a life of 5 years and a salvage value of
2,000 at that time. The challenger has a cost of
36,000, a life of 10 years and an estimated
salvage values at any point in time as given in
the table. Use a 5 year planning horizon and MARR
15.
57
Example 5.32
58
Example 5.35
Annual worth using a MARR 15 AW1(15)
-9000(AP, 15, 5) 7,000 1000(AG, 15, 5)
2000(AF, 15, 5) AW1(15) -9000(.2983) 7,000
1000(1.7228) 2000(.1483) AW1(15)
11,110.90/year AW2(15) -36,000(AP, 15, 5)
1000(AG, 15, 5) 12000(AF, 15, 5) AW2(15)
-36,000(.2983) 1000(1.7228)
12000(.1483) AW2(15) -10,682.00/year
11,110.90/year (-10,682.00/year) 428.90/year
thus buy the new press, which is the same
conclusion we had in Example 5.32
59
Replacement Analysis
First, for the cash flow of alternative 2 in
Table 5.20, the cash flow in year 1 should be
-1000. The minus sign was omitted in my edition
of the book. Second, in the calculation of
annual worth for alternative 1 (below Table 5.20
on page 217), there should be an open parentheses
in front of the P/A, 15, 5) and the sign
following the P/A, 15, 5) should be minus not
plus. Three lines down there is a missing open
bracket it should look like this
(-7,000(3.3522) (1,000)(5.7751) . . . You
should read and understand examples 5.33 and 5.34
on pages 216 218. The next section covers the
Outsider Viewpoint approach for replacement
analysis problems. This approach assumes you own
neither the current asset (Defender) nor the
possible replacement asset (Challenger). If this
were the case then you would need to pay the
current market value for the asset that in
reality you already own.
60
Replacement Analysis
Table 5.22 on page 219 shows that the different
in cash flows between the two alternatives is the
same whether you use the cash flow approach (See
Table 5.19) or the outsider viewpoint
approach. You should read and understand example
5.35 and 5.36 on pages 219 and 220, respectively
61
Replacement Analysis

• Problem 5.24. p. 233
• The ABC Company is considering three investment
  proposals, A, B and C. Proposals A and B are
  mutually exclusive, and proposal C is contingent
  on Proposal B. The cash flow data for the
  investments over a 10-year planning horizon are
  given below. The ABC Company has a budget limit
  of 1 million for investments of the type being
  considered currently. MARR 15
• a) Clearly specify the alternatives available and
  their net cash flow profiles.
•  
• b) Determine which alternative ABC's decision
  maker should select. Use a ranking approach and
  the present worth method.
•  
• c) Determine which alternative ABC's decision
  maker should select. Use a incremental approach
  and the present worth method.

62
Example Section 5.5.1
Consider the following capital structure
63
Example Section 5.5.1
  The tax rate is 20. Determine the firm's
overall average after-tax cost of capital.   kl
(1 r/m) m - 1(1-T) (1 .12/2) 2 -
1(1-.20) 0.09888   kb (1 r/m) m -
1(1-T) (1 .16/4) 4 - 1(1-.20)
0.13589   ks D/Ps 8.00/40 0.20 or 20   ka
kl pl kb pb ks ps kr pr 0.09888(3/17)
0.13589(2/17) 0.20(12/17) ka .01744
.015987 .14117 .1746 17.46