Rate of Return Analysis: Multiple Alternatives

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Rate of Return Analysis Multiple Alternatives

• Chapter 8

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Learning Objectives
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WHY INCREMENTAL ANALYSIS IS NECESSARY

• This chapter presents methods where 2 or more
  alternatives can be evaluated using a rate of
  return (ROR) comparison based on methods of the
  previous chapter.
• The ROR evaluation correctly performed will
  result in the same selection as the PW, AW and FW
  analyses, but the computational procedure is
  considerably different for ROR evaluations.

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• Assume that a company uses a MARR of 16 per
  year, has 90,000 available for investment, and
  that two alternatives (A and B) are being
  evaluated.
• Alternative A requires an investment of 50,000
  and has an internal rate of return iA of 35 per
  year.
• Alternative B requires 85,000 and has an iB of
  29 per year. Intuitively we may conclude that
  the better alternative is the one that has the
  larger return, A in this case.
• However, this is not necessarily so. While A has
  the higher projected return, it requires an
  initial investment that is much less than the
  total money available (90,000).
• What happens to the investment capital that is
  left over? It is generally assumed that excess
  funds will be invested at the companys MARR.
  Using this assumption, it is possible to
  determine the consequences of the alternative
  investments.
• If alternative A is selected, 50,000 will return
  35 per year. The remaining 40,000 will be
  invested at the MARR of 16 per year. The rate of
  return on the total capital available, then, will
  be the weighted average.

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• A tool and die company in Pittsburgh is
  considering the purchase of a drill press with
  fuzzy-logic software to improve accuracy and
  reduce tool wear. The company has the opportunity
  to buy a slightly used machine for 15,000 or a
  new one for 21,000.
• Because the new machine is a more sophisticated
  model, its operating cost is expected to be 7000
  per year, while the used machine is expected to
  require 8200 per year.
• Each machine is expected to have a 25-year life
  with a 5 salvage value.
• Tabulate the incremental cash flow.

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Solution

• Incremental cash flow is tabulated in Table 82.
  Using Equation 8.1, the subtraction performed
  is (new - used) since the new machine has a
  larger initial cost.
• The salvage values in year 25 are separated from
  ordinary cash flow for clarity. When
  disbursements are the same for a number of
  consecutive years, it saves time to make a single
  cash flow listing, as is done for years 1 to 25.
  This approach cannot be used for spreadsheets
  (Excel).

Incremental cash flow cash flowB - cash flowA
8.1
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• Sandersen Meat Processors has asked its lead
  process engineer to evaluate two different types
  of conveyors for the bacon curing line.
• Type A has an initial cost of 70,000 and a life
  of 8 years.
• Type B has an initial cost of 95,000 and a life
  expectancy of 12 years.
• The annual operating cost (AOC) for type A is
  expected to be 9000, while the AOC for type B is
  expected to be 7000.
• If the salvage values are 5000 and 10,000 for
  type A and type B, respectively, tabulate the
  incremental cash flow using their LCM.

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Solution The LCM of 8 and 12 is 24 years. In the
incremental cash flow tabulation for 24 years
(Table 83) note that the reinvestment and
salvage values are shown in years 8 and 16 for
type A and in year 12 for type B.
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INTERPRETATION OF RATE OF RETURNON THE EXTRA
INVESTMENT

• The incremental cash flows in year 0 of Tables
  82 and 83 reflect the extra investment or cost
  required if the alternative with the larger first
  cost is selected. This is important in an
  incremental ROR analysis to determine the ROR
  earned on the extra funds expended for the
  larger-investment alternative.
• If the incremental cash flows of the larger
  investment dont justify it, we must select the
  cheaper one. In Example 8.1 the new drill press
  requires an extra investment of 6000 (Table
  82). If the new machine is purchased, there will
  be a savings of 1200 per year for 25 years,
  plus an extra 300 in year 25. The decision to
  buy the used or new machine can be made on the
  basis of the profitability of investing the extra
  6000 in the new machine.
• If the equivalent worth of the savings is greater
  than the equivalent worth of the extra investment
  at the MARR, the extra investment should be made
  (i.e., the larger first-cost proposal should be
  accepted).
• On the other hand, if the extra investment is not
  justified by the savings, select the
  lower-investment proposal.
• It is important to recognize that the rationale
  for making the selection decision is the same as
  if only one alternative were under consideration,
  that alternative being the one represented by the
  incremental cash flow series. When viewed in this
  manner, it is obvious that unless this investment
  yields a rate of return equal to or greater than
  the MARR, the extra investment should not be
  made.
• As further clarification of this extra-investment
  rationale, consider the following The rate of
  return attainable through the incremental cash
  flow is an alternative to investing at the MARR.
  Section 8.1 states that any excess funds not
  invested in the alternative are assumed to be
  invested at the MARR.
• The conclusion If the rate of return available
  through the incremental cash flow equals or
  exceeds the MARR, the alternative associated with
  the extra investment should be selected.

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RATE OF RETURN EVALUATION USING PRESENT
WORTHINCREMENTAL AND BREAKEVEN

• In 2000, Bell Atlantic and GTE merged to form a
  giant telecommunications corporation named
  Verizon Communications. As expected, some
  equipment incompatibilities had to be rectified,
  especially for long distance and international
  wireless and video services. One item had two
  suppliers - a U.S. firm (A) and an Asian firm
  (B). Approximately 3000 units of this equipment
  were needed. Estimates for vendors A and B are
  given for each unit.

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• Determine which vendor should be selected if the
  MARR is 15 per year.
• These are service alternatives, since all cash
  flows are costs.
• Alternatives A and B are correctly ordered with
  the higher first-cost alternative in column (2).
• The cash flows for the LCM of 10 years are shown
  in Table 84.
• The incremental cash flow diagram is shown in
  Figure 81 (next page).
• There are 3 sign changes in the incremental cash
  flow series, indicating as many as three roots.
  There are also three sign changes in the
  cumulative incremental series that starts
  negatively at S0 - 5000 and continues to S10
  5000, indicating that more than one positive
  root may exist.
• The rate of return equation based on the PW of
  incremental cash flows is
• 0 - 5000 1900(P/A, i,10) - 11,000(P/F, i, 5)
  2000 (P/F, i, 10) 8.2

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0 - 5000 1900(P/A, i,10) - 11,000(P/F, i, 5)
2000 (P/F, i, 10) 8.2

• Assume that the reinvestment rate is equal to the
  resulting iBA (or i for a shortened symbol).
• Solution of Equation 8.2 for the first root
  finds results for i between 12 and 15.
• By interpolation i 12.65.
• Since the rate of return of 12.65 on the extra
  investment is less than the 15 MARR, the
  lower-cost vendor A is selected.
• The extra investment of 5000 is not economically
  justified by the lower annual cost and higher
  salvage estimates.

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IRR(D4D14)
NPV(B1,D5D14)D4
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• Bank of America uses a MARR of 30 on
  alternatives for its own business that are
  considered risky, that is, the response of the
  public to the service has not been well
  established by test marketing. Two alternative
  software systems and the marketing/delivery plans
  have been jointly developed by software engineers
  and the marketing department. They are for new
  online banking and loan services to passenger
  cruise ships and military vessels at sea
  internationally.
• For each system, start-up, annual net income, and
  salvage value (i.e., sell-out value to another
  financial corporation) estimates are summarized
  below.
• (a) Perform the incremental ROR analysis by
  computer.
• (b) Develop the PW vs. i graphs for each
  alternative and the increment. Which alternative,
  if either, should be selected.?

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Present Worth vs. Interest Rate, MARR 30
Interest rate, i
NPV(C3,B4B11)B3
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• Figure 84b (previous slide) provides the
  opportunity to see why the ROR method can result
  in selecting the wrong alternative when only i
  values are used to select between two
  alternatives.
• This is sometimes called the ranking
  inconsistency problem of the ROR method. The
  inconsistency occurs when the MARR is set less
  than the breakeven rate between two revenue
  alternatives.
• Since the MARR is established based on conditions
  of the economy and market, MARR is established
  external to any particular alternative
  evaluation. In the previous graph, the breakeven
  rate is 29.41 and the MARR is 30.
• If the MARR were established lower than
  breakeven, say at 26, the incremental ROR
  analysis results in correctly selecting B,
  because i 29.41, which exceeds 26. When only
  the i values were used, system A would be
  wrongly chosen, because its i 39.31.
• This error occurs because the rate of return
  method assumes reinvestment at the alternatives
  ROR value (39.31), while PW and AW analyses use
  the MARR as the reinvestment rate.
• The conclusion If the ROR method is used to
  evaluate two or more alternatives, use the
  incremental cash flows and i to make the
  decision between alternatives.