Question

6.15 The Bureau of Indian Affairs provides v services to American Indians and Alaskan N The Director of Indian Health Services is with chief nationwide to select the better of two X-ray system alternatives to be locat secondary-level clinics. At 5% per year, select the more economical system physicians at some of the 230 clin Del Medical 250,000 Siemens -224,000 First cost, $ Annual operating cost, $ per year Overhaul in year 3, $ Overhaul in year 4, $ Salvage value, $ Expected life, years 231,000 -235,000 -26,000 - 140,000 50,000 10,000

Answer 1

The present value of the cost of Del medical = $ 250,000 + $ 231,000 $\div$ (1+0.05)¹ + $ 231,000 $\div$ (1+0.05)² + $ 231,000 $\div$ (1+0.05)³ + $ 371,000 $\div$ (1+0.05)⁴ + $ 231,000 $\div$ (1+0.05)⁵ + $ 231,000 $\div$ (1+0.05)⁶ - $ 50,000 $\div$ (1+0.05)⁶   

The present value of the cost of Del medical = $ 1,500,352.44

Equivalent uniform annual cost = $ 1,500,352.44 $\div$ PVIFA_{r=5%, n = 6 years}

Equivalent uniform annual cost = $ 1,500,352.44 $\div$5.075692

Equivalent uniform annual cost = $ 295,595.64

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The present value of the cost of Siemens = $ 224,000 + $ 235,000 $\div$ (1+0.05)¹ + $ 235,000 $\div$ (1+0.05)² + $ 261,000 $\div$ (1+0.05)³ + $ 235,000 $\div$ (1+0.05)⁴ + $ 235,000 $\div$ (1+0.05)⁵ + $ 235,000 $\div$ (1+0.05)⁶ - $ 10,000 $\div$ (1+0.05)⁶  

The present value of the cost of Siemens = $ 1,431,785.26

Equivalent uniform annual cost = $ 1,431,785.26 $\div$ PVIFA_{r=5%, n = 6 years}  

Equivalent uniform annual cost = $ 1,431,785.26 $\div$ 5.075692

Equivalent uniform annual cost = $ 282,086.71

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The present worth and equivalent annual cost of Siemens is low compared to Del medical, hence the most economical system is Siemens.