Question

An indium-gallium-arsenide-nitrogen alloy developed at Sandia National Laboratory is said to have potential uses in electricity-generating solar cells. The new material is expected to have a longer life, and it is believed to have a 40% efficiency rate, which is nearly twice that of standard silicon solar cells. The useful life of a telecommunications satellite could be extended from 10 to 15 years by using the new solar cells. What rate of return could be realized if an extra investment now of $880,000 would result in extra revenues of $450,000 in year 11, $500,000 in year 12, and amounts increasing by $50,000 per year through year 15?

Answer 1

Let ROR be i%, then

450000*(P/A,i%,5)*(P/F,i%,10) + 50000*(P/G,i%,5)*(P/F,i%,10) = 880000

Dividing by 10000

45*(P/A,i%,5)*(P/F,i%,10) + 5*(P/G,i%,5)*(P/F,i%,10) = 88

using trail and error method

When i = 9%, value of 45*(P/A,i%,5)*(P/F,i%,10) + 5*(P/G,i%,5)*(P/F,i%,10) = 45*3.889651*0.422411 + 5*7.111048*0.422411 = 88.9553

When i = 10%, value of 45*(P/A,i%,5)*(P/F,i%,10) + 5*(P/G,i%,5)*(P/F,i%,10) = 45*3.790787*0.385543 + 5*6.861802*0.385543 = 78.9957

using interpolation

i = 9% + (88.9553-88)/(88.9553-78.9957)*(10%-9%)

i = 9% + 0.09% = 9.09%