Question

Two types of power converters are being considered for a specific application. You want to make a comparison using a 15 percent interest rate and you have the following information:

Alternative	Alpha	Omega
Purchase Price	10,000	20,000
Estimate useful life	5 years	9 years
Salvage Value	1,000	5,000
Anual operation cost	2,600	1,300

a. Determine the annual equivalent cost of both alternatives.

b. Using a useful life of 6 years, determine the present value of both alternatives if the residual value of alpha after one year of use is $ 8,000 and the residual value of Omega after 6 years of use is $ 8,500.

Answer 1

A.

For Alpha alternative:

Present value of total cost = 10000 + 2600*(1-1/1.15^5)/.15   - 1000/1.15^5

Present value of total cost = $18218.43

Let, uniform annual cost = EUAC1

Then,

18218.43 = EUAC1*(1-1/1.15^5)/.15  

EUAC1 = 18218.43/3.3522

EUAC1 = $5434.77

For Omega alternative:

Present value of total cost = 20000 + 1300*(1-1/1.15^9)/.15   - 5000/1.15^9

Present value of total cost = $24781.75

Let, uniform annual cost = EUAC2

Then,

24781.75 = EUAC2*(1-1/1.15^9)/.15  

EUAC2 = 24781.75/4.7716

EUAC2 = $5193.59

B.

Present value of Alpha = 10000 + 2600/1.15 – 8000/1.15

Present value of Alpha = $5304.35 (-ve)

Present value of Omega = 20000 + 1300*(1-1/1.15^6)/.15   - 8500/1.15^6

Present value of Omega = $21245.04 (-ve)