Nationwide Children\'s Hospital is evaluating different proposals to improve chi

Question

Nationwide Children's Hospital is evaluating different proposals to improve children's comfort during MRIs. The Hospital's engineering committee selected two finalists. Both proposals call for the installation of new scanners that have better programming. The CEO of the hospital needs a recommendation. Perform B/C analysis at 6% per year. Vendor A proposes Vendor B proposes: First cost to build the system is $700,000. First cost to build the system is $1,350,000 M&O; cost per year is $120,000 Annual benefits is $530,000 Annual disbenefits is $200,000 Life is 14 years M&O; cost per year is $200,000 Annual benefits is $750,000 Annual disbenefits is $300,000 Life is 20 years · . · ·

Explanation / Answer

For vendor-A proposal:

First cost = 700000

Time n = 14 years

R = 6%

Let, uniform annual cost = UAC1

Then,

700000 = UAC1*(1-1/1.06^14)/.06 = UAC1*9.295

UAC1 = 700000/9.295= $75309.31

B/C ratio (Conventional) = (benefits per year – disbenefits per year)/(UAC1 + M&O cost per year)

B/C ratio (Conventional) = (530000-200000)/(75309.31+120000) = 1.69

B/C ratio (modified) = (benefits per year – disbenefits per year - M&O cost per year)/UAC1

B/C ratio (modified) = (530000-200000-120000)/ 75309.31 = 2.79

For vendor-B proposal:

First cost = 1350000

Time n = 20 years

R = 6%

Let, uniform annual cost = UAC2

Then,

1350000= UAC2*(1-1/1.06^20)/.06 = UAC2*11.47

UAC2 =1350000/11.47 = $117698.34

B/C ratio (Conventional) = (benefits per year – disbenefits per year)/(UAC2 + M&O cost per year)

B/C ratio (Conventional) = (750000-300000)/( 117698.34+200000) =1.42

B/C ratio (modified) = (benefits per year – disbenefits per year - M&O cost per year)/UAC2

B/C ratio (modified) = (750000-300000-200000)/ 117698.34 =2.12

Since the B/C ratio of vendor A proposal is higher than the B/C ratio of vendor B, then the Vendor A proposal should be accepted.

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