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 $930,000 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?

The rate of return that could be realized was  %____

I got 9%, but my answer is wrong. Please help:(

Answer 1

Let ROR realized be i%, then as per given condition

450000*(P/A,i%,5)*(P/F,i%,10) + 50000*(P/G,i%,5)*(P/F,i%,10) = 930000

Dividing by 10000

45*(P/A,i%,5)*(P/F,i%,10) + 5*(P/G,i%,5)*(P/F,i%,10) = 93

Using trail and error method

When i = 8%, value of 45*(P/A,i%,5)*(P/F,i%,10) + 5*(P/G,i%,5)*(P/F,i%,10) = 45*3.992710*0.463193 + 5*7.372426*0.463193 = 100.297175

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 = 88.955300

using interpolation

i = 8% + (100.297175-93)/(100.297175-88.955300)*(9%-8%)

i = 8% + 0.64% = 8.64%