The following estimates (in $1000 units) have been developed for a security system upgrade at Chicago’s O’Hare Airport. (a) Calculate the con­ventional B/C ratio at a discount rate of 10% per year. Is the project justified? (b) Determine the minimum first cost that is possible to render the project just economically unjustified.

Question

Answer 1

(a) In $1000 units
AW of C = 13,000(A/P,10%,20) + 400
= 13,000(0.11746) + 400
= $1927

AW of B – D = 3800 – 6750(A/F,10%,20)
= 3800 – 6750(0.01746)
= $3682

B/C = 3682/1927
= 1.91 Well justified, since 1.91 > 1.0
(b) Let P = minimum first cost allowed

AW of C = P(A/P,10%,20) + 400
AW of B – D = 3682 from part (a)

1.00 = 3682/[P(A/P,10%,20) + 400]
0.11746P = 3682 - 400
P = $27,941 ($27,941,000)

The first cost must > $27,941,000 to force B/C < 1.0