Engineering Economy - Lecture - MultipleAlternatives, Lecture notes of Economics

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Rate of Return Analysis:

Multiple Alternatives

Learning Objectives

4

• (^) 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 company’s 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.

• (^) 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.

• (^) 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

• (^) If the salvage values are $5000 and $10,000 for type A and

type B, respectively, tabulate the incremental cash flow

using their LCM.

Solution The LCM of 8 and 12 is 24 years. In the incremental cash flow tabulation for 24 years (Table 8–3) note that the reinvestment and salvage values are shown in years 8 and 16 for type A and in year 12 for type B.

• (^) 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.

RATE OF RETURN EVALUATION USING PRESENT WORTH: INCREMENTAL AND BREAKEVEN

 (^) 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 8–4.  (^) The incremental cash flow diagram is shown in Figure 8–1 (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 S 0 = - $5000 and continues to S 10 = +$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]

=IRR(D4:D14) =NPV($B$1,D5:D14)+D

• (^) 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.?

• (^) Figure 8–4b (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 alternative’s 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.