610 An electronics firm invested S60000 in a precision inspe

6-10: An electronics firm invested S60,000 in a precision inspection device. It cost $4000 to operate and maintain in the first year and S3000 in each of the subsequent years. At the end of4 years, the firm changed their inspection procedure, eliminating the need for the device. The purchasing agent was very fortunate in being able to sell the inspection device for $60,000, the original price. The plant manager asks you to compute the equivalent uniform annual cost of the device during the 4 years it was used. Assume interest at 10% per year.

Solution

Initial investment = $60000

Number of years of work = 4 years

O&M cost in year 1 = $4000

O&M cost for the remaining 3 years = $3000/ year

Resale value after 4 years = $60000

R = 10%

Net present value of the investment = 60000 + 4000/(1+10%) + 3000/(1+10%)^2 + 3000/(1+10%)^3 + 3000/(1+10%)^4 - 60000/(1+10%)^4

Net present value of the investment = $29437.88

Let equivalent uniform annual cost of the investment = EUAC

Then,

29437.88 = EUAC*(1-1/(1+10%)^4)/.1 = EUAC*3.1698

EUAC = 29437.88/3.1698

EUAC = $9286.98

So, the equivalent uniform annual cost is $9286.98 for the given investment.