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

Per Unit Cost of Robots = $ 155000, Number of Units Purchased in year 1 = 4000 and Units Purchased in year 2 = 7500

Cost in Year 1 = 155000 x 4000 = $ 620000000 or $ 620 million and Cost in Year 2 = 155000 x 7500 = $ 1162500000 or $ 1162.5 million

Interest Rate = 8 %

Total Present Value of Costs at current time (t=0) = 620 / (1.08) + 1162.5 / (1.08)^(2) = $ 1570.73 million

Let the equivalent annual cost over 8 years be $ K million

Therefore, 1570.73 = K x (1/0.08) x [1-{1/(1.08)^(8)}]

K = $ 273.3302837 million or $ 273330283.7