Independent solution

How to solve this Net Present Value Equivalence question

Setup

Setup

Choose time 0 as the comparison date and write v = 1/1.10. Record each project’s signed cash flows, including the unknown terminal amount X.

−4000+2000v+4000v2=2000+4000v−Xv2-4000+2000v+4000v^2=2000+4000v-Xv^2

Model

Model

Equal net present values require the two discounted cash-flow polynomials to be equal. Collecting the Xv² term on one side gives a single linear equation.

i=0.10,v=1/1.10i=0.10,\quad v=1/1.10

Compute

Compute

Substituting v and solving yields X = 5,460 exactly, so choice D is selected.

X=5460X=5460

Answer

Answer

The calculation gives 5460 for net present value equivalence, matching published choice D.

X=5460(D)\boxed{X=5460\quad\text{(D)}}