A pressure vessel can be made out of brass, stainless steel, or titanium. The first cost and expected life for each material are: The pressure vessel will be in the nonradioactive portion of a nuclear power plant that is expected to have a life of 50 to 75 years. The public utility commission and

Question

A pressure vessel can be made out of brass, stainless steel, or titanium. The first cost and expected life for each material are:

Titanium	Stainless Steel	Brass
$300,000	$175,000	$100,000	Cost
25	10	4	Life, in years

The pressure vessel will be in the nonradioactive portion of a nuclear power plant that is expected to have a life of 50 to 75 years. The public utility commission and the power company have not yet agreed on the interest rate to be used for decision making and rate setting. Build a choice table for the interest rates to show where each material is the best.

Accepted Answer

The pressure vessel will be replaced repeatedly during the life of the facility, and each material has a different life. Thus, the best way to compare the materials is using EUAC (see Chapter 6). This assumes identical replacements.

Figure 8–4 graphs the EUAC for each alternative. In this case the best alternative at each interest rate is the material with the lowest EUAC. (We maximize worths, but minimize costs.) The Excel function is

=PMT (interest rate,life,-first cost)

The factor equation is

EUAC=first cost (A/P,interest rate,life)

H	G	F	E	D	C	B	A
Answer	Solve for	FV	PV	PMT	n	i	Alternative	1
$35,206	PMT	0	-100,000		4	15.3%	Brass	2
35,206	PMT	0	-175,000		10	15.3%	Stainless Steel	3
47,114	PMT	0	-300,000		25	15.3%	Titanium	4
0	Difference in EUAW for brass & stainless					15.3%		5
11,908	Difference in EUAW for stainless & titanium					15.3%		6
								7
Answer	Solve for	FV	PV	PMT	n	i	Alternative	8
29,043	PMT	0	-100,000		4	6.3%	Brass	9
24,091	PMT	0	-175,000		10	6.3%	Stainless Steel	10
24,091	PMT	0	-300,000		25	6.3%	Titanium	11
-4,952	Difference in EUAW for brass & stainless					6.3%		12
0	Difference in EUAW for stainless & titanium					6.3%		13

Because these alternatives have different-length lives, calculating the incremental IRRs is best done using the spreadsheet function GOAL SEEK. This spreadsheet is structured somewhat differently. In the top block of rows, each interest rate is set equal to the highlighted interest rate in cell B5. Copying the formula =$B$5 is easiest. In the lower block of rows, each interest rate is set equal to the highlighted interest rate in cell B13. Then two GOAL SEEKS are used to find the highlighted interest rates that make their respective differences in EUAW equal to zero.The choice table for each material is:

Best Choice	Interest Rate
Titanium	0% ≤ i ≤ 6.3%
Stainless steel	6.3% ≤ i ≤ 15.3%
Brass	15.3%≤ i

Question 8.4: A pressure vessel can be made out of brass, stainless steel,...

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