Question

Boeing has purchased composite wing fixtures for the assembly of its new Dreamliner Commercial airliner Assume this system costs 4 million to install and an estimated 400,000 per year for all materials, operating, personnel, and maintenance costs The expected life is 10 years An engineer wants to estimate the total revenue requirement for each 6 month period that is necessary to recover the investment, interest, and annual costs Find this semiannual A value if capital funds are evaluated at 8% per year compounded semiannually

Answer 1

i = 8% / 2 = 4% per semiannual period

t = 10*2 = 20 semiannual periods

Effective interest rate = (1+0.04)^2 -1

= (1.04)^2 -1

= 0.0816 ~ 8.16%

PW of cost = 4000000 + 400000*(P/A,8.16%,10)

= 4000000 + 400000*((1 + 0.0816)^10-1)/(0.0816*(1 + 0.0816)^10)

= 4000000 + 400000*((1.0816)^10-1)/(0.0816*(1.0816)^10)

= 4000000 + 400000*6.661924679

= 6664769.87

Semi annual revenue required = 6664769.87*(A/P,4%,20)

= 6664769.87* 0.04*((1 + 0.04)^20)/((1 + 0.04)^20-1)

= 6664769.87* 0.04*((1.04)^20)/((1.04)^20-1)

= 6664769.87* 0.07358175

= 490405.43 ~ 490405