2. Problem Statement: Quantum Logistics, Inc., a wholesale distributor, is considering the construction of a new warehouse to serve the southeastern geographic region near the Alabama-Georgia border. There are three cities being considered. After site visits and a budget analysis, the expected income and costs associated with locating in each of the cities has been determined. The life of the warehouse is expected to be 12 years, and MARR is 15%/year.

City Initial Cost Net Annual Income
Lagrange $990,000 $50,000
Auburn $710,000 $155,000
Anniston $850,000 $270,000

What is the annual worth of each site? (Round answers to the nearest dollar; tolerance is +2.00)

City                     Annual worth($)

Lagrange            (132,635.97)  

Auburn                 24,018.65

Anniston              113,191.34

Explanation:

Annual worth of each site is the equivalent annual cost . It is determined by dividing the net present value of cost by the annuity factor of the investment period.

Net Present Value of cost = Initial cost - Present Value(PV) of annual income

PV of annual income = Annual income × Annuity factor

Annuity factor = (1 - (1+r)^(-n))/ r

r 15%, n -12

Annuity factor = (1 - 1.15^(-12))/0.15= 5.4206

PV of annual income = 50,000 × 5.4206= 271,030.9499

Net Present Value of cost = 990,000 - 271,030.94 =  $(718,969.05 )

Annual worth= $(718,969.05 )/ 5.4206=   (132,635.97)  

Auburn

PV of annual income = 155,000× 5.4206= 840,195.94

NPV = 710,000 - 840,195.94 = 130,195.94

Annual worth = 130,195.9448/ 5.4206=  24,018.65  

Anniston

PV of annual income = 270,000× 5.4206= 1,463,567.13

NPV = 850,000 - 1,463,567.13 = 613,567.12

Annual cost =  613,567.12 /5.4206= 113,191.34

City                     Annual worth

Lagrange            (132,635.97)  

Auburn                 24,018.65

Anniston              113,191.34

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