Independent solution

How to solve this Interest Rate Valuation question

Setup

Setup

Discount all three project cash flows to time zero with signs for receipts and payment.

Xv2−Yv4+Xv6=0Xv^2-Yv^4+Xv^6=0

Model

Model

After removing a positive common discount factor, substitute z for the two-year discount factor.

z=v2:Xz2−Yz+X=0z=v^2:\quad Xz^2-Yz+X=0

Compute

Compute

The quadratic formula gives the possible values of z.

z=Y±Y2−4X22Xz=\frac{Y\pm\sqrt{Y^2-4X^2}}{2X}

Answer

Answer

Because one plus i is the reciprocal square root of z, the resulting expression is choice E.

i=2XY±Y2−4X2−1(E)\boxed{i=\sqrt{\frac{2X}{Y\pm\sqrt{Y^2-4X^2}}}-1\quad\text{(E)}}