Question

Given the following two potential locations to construct an urgent care, use incremental B/C ratio to determine which location, if any, is better at an interest rate of 8% per year.
Location 1 2
Initial Cost, $1,000,000 $2,000,000
Annual M&O cost, $/year 80,000 75,000
Annual Benefits, $/year 520,000 580,000
Annual Disbenefits, $/year 90,000 140,000
Site Availability, years 10 20

a. DN Alternative
b. Site 1
c. Site 2
d. Both Sites 1 and 2

Answer 1

Answer:

The incremental benefit cost ratio is less than 1 therefore we must select site 1.

Explanation:

The incremental BCR can be determined using the following formula

$\Delta BC_R = \frac{AW_B-AW_D-AW_M}{AW_i}$

$AW_C=1,000,000(A/P,$ 8% , 10)

⇒ $AW_C= 1,000,000 \times \frac{0.08}{1-1.08^-^1^0}$

⇒ $AW_2=2,000,000(A/P,$ 8%, 20)

⇒ $AW_2= 2,000,000 \times \frac{0.08}{1-1.08^-^2^0}$

⇒$AW_C_2$ = $203,704.42

Incremental initial investment = 203,704.42 - 149,029.49

= $ 54,674.93

Incremental benefits = 580,000 - 520,000 = 60,000

Incremental O&M = 75,000 - 80,000 = - $ 5000

Incremental Disbenefits = 140,000 - 90,000 =$ 50,000

$\Delta BC_R = \frac{60,000-50,000-(-5000)}{54,674.93} \\\\\Delta BC_R=0.2743$

All solving using the present worth method also incremental benefit cost ratio comes out to be 0.2743.

The incremental benefit cost ratio is less than 1 therefore we must select site 1.