The salvage value on a piece of equipment for excavators, inc. is expected to be $10,000 in 12 years. if the discount rate is 8%, what is the present value of the equipment's salvage value?

In 12 years the salvage value will be $10,000.

The discount rate is 8% per year, which means that if the present value is X, in year from now the value will be X-8%*X, in two years: X--8%*X-8%*X=X-2*8%*X ...

In n years the value will be: X-n*8%*X = X-0.08*nX = (1-0.08*n) * X=0.02*n*X

We know that in n=12 years the value will be $10,000. So, we can solve the equation:

$10,000=0.02*12*X

$10,000=0.24*X

X=$10,000/0.24

X=$41,666