Question

Improvised explosive devices (IEDs) are responsible for many deaths in times of strife and war. Unmanned ground vehicles (robots) can be used to disarm the IEDs and perform other tasks as well. If the robots cost $155,000 each and the military arms unit signs a contract to purchase 4,000 of them now and another 7,500 one year from now, what is the equivalent annual cost of the contract over a 8-year period at 8% per year interest? The equivalent cost of the contract is determined to be $

Answer 1

Purchase for current year = 155000*4000 = 620000000 (Purchase 1 )

Purchase after 1 year  = 155000*7500 =1162500000 (Purchase 2 )

Equivalent annual cost can be arrived at by calculating future value of Purchase 1 and Purchase 2 at the end of year 8.

Future value of purchase 1 after 8 years = 620000000*(1.08^8) = 1147576730

Future value of purchase 1 after 8 years = 620000000*(1.08^7) = 1992320712

Total Cost of purchase after 8 years = 1147576730 + 1992320712 = 3139897443

Equivalent Annual Cost of project = 3139897443/8 = $1396616819