The following information is for five mutually exclusive alternatives that have 20-year useful lives. The decision maker may choose any one of the options or reject them all. Prepare a choice table.

Alternatives

E D C B A

$9000 $1000 $6000 $2000 $4000 Cost

785 117 761 410 639 Uniform annual benefit

Question

The following information is for five mutually exclusive alternatives that have 20-year useful lives. The decision maker may choose any one of the options or reject them all. Prepare a choice table.

Alternatives
E	D	C	B	A
$9000	$1000	$6000	$2000	$4000	Cost
785	117	761	410	639	Uniform annual benefit

Accepted Answer

Figure 8–6 is an NPW graph of the alternatives constructed by means of a spreadsheet.

The graph clearly shows that Alternatives D and E are never part of the solution. They are dominated by the other three. The crossover points can either be read from the graph (if you have plotted it at a large enough scale) or found by calculating the ΔIRR of the intersecting curves.

Entering the data for the five alternatives also makes it easy to solve for the IRR of each. However, only [latex]IRR_{B}[/latex] is useful. As the highest rate, it is the rate above which doing nothing is the best choice. This can be seen from the right-hand side of Figure 8–6. Fortunately, the graph shows us that the rate is about 20%. Some spreadsheet packages fail to find rates that high, unless an initial guess is supplied. It turns out that the guess is almost exactly the [latex]IRR_{B}[/latex] of 19.96%.

The figure also identifies the two incremental calculations that are needed—for C − A and for A − B. The first value appears to be about 2% and the second a bit less than 10%. The rate on the incremental investment is also the rate at which the two alternatives have the same NPW. The three “useful” IRRs are left-indented for emphasis.

H	G	F	E	D	C	B	A
Answer	Solve for	FV	PV	PMT	n	i	Alternative	1
15.00%	i	0	-4000	639	20		A	2
20.0%	i	0	-2000	410	20		B	3
11.2%	i	0	-6000	761	20		C	4
9.9%	i	0	-1000	117	20		D	5
6.0%	i	0	-9000	785	20		E	6
2.0%	i	0	-2000	122	20		C - A	7
9.6%	i	0	-2000	229	20		A - B	8

Placing these numbers in a choice table:

If MARR ≥ 20% do nothing
If 20% ≥ MARR ≥ 9.6% select B

If 9.6% ≥ MARR ≥ 2% select A

If 2% ≥ MARR ≥ 0% select C

Examining Figure 8–6 also makes it clear that C is only slightly better than A for MARRs below 2%.

Question 8.6: The following information is for five mutually exclusive alt...

Related Answered Questions

The following information refers to three mutually exclusive alternatives. The decision maker wishes to choose the right machine but is uncertain what MARR to use. Create a choice table that will help the decision maker to make the correct economic decision. ...

Verified Answer:

Solve Example 7–14 by means of an NPW graph. Two machines are being considered for purchase. If the minimum attractive rate of return (MARR) is 10%, which machine should be bought? ...

Verified Answer:

In Example 8–2 Machine X was assumed to be “replaced with an identical machine” for a 12-year analysis period. In Chapter 6 this was shown to be equivalent to using EUAW as the comparison measure. Construct a choice table using EUAW. ...

Verified Answer:

For the alternatives in Example 8–6, conduct a pairwise incremental comparison. Which alternative is the best at an interest rate of 10%? Each of the five alternatives has no salvage value at the end of a 20-year useful life. ...

Verified Answer:

Verified Answer:

The student engineering society is building a snack cart to raise money. Members must decide what capacity the cart should be able to serve. To serve 100 customers per hour costs $10,310, and to serve 150 customers per hour costs $13,400. The 50% increase in capacity is less than 50% of $10,310 ...

Verified Answer: