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 $870,000 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

Answer:

Rate of return 9.1864%

Explanation:

Scenario description:

using the new alloy, will extend the life of a telecommunication satellite thus, more years for the porject life.

We need to calcualte the rate at which the extra revenues in years 11  through 15 equalize the extra cost of 870,000 at F0

each extra revenue will be considered a lump sum, we will add them and check the present value.

$\frac{Maturity}{(1 + rate)^{time} } = PV$

Maturity   450,000 500,000 550,000 600,000 650,000

time              11.00   12.00   13.00   14.00   15.00

rate :  ??

As this is a complex equation the human way to solve this is with trial an error.

Also, we could solve this with a financial calcualtor or excel.

We are going to use the latter.

you will do as follow:

from A1 to A5 write the maturity values

from B1 to B5 write the time

on c1 write 0.1 this will be the first rate we will build the formulas and then, excel will solve for the answer:

on D1 you will write:

=A1/power(1+$C$1,B1)

Thisformula calculates the presnet value of the additional revenues

then drag this up to D5

on D6 =sum(D1:D5) this add them

Then select d6 goo to goal seek and define it as 870,000 changing the cell C1

This will give you: 0.091863796 = 9.1864% this is the rate ofr eturn for impelenting the alloy