# 5.1.2. FCFE for multiple periods and a residual value

The goal of this approach is to estimate the FCFE for a medium-term extent through the forecast of the financial statements, while adding a perpetuity to FCFE of the last year, which should be also updated.

- \(Operations\ equity\ value=NPV\ FCFE\ +Residual\ value\)

While using the FCFE, the NPV accounts for the accumulation of the discounted FCFE.

- \(FCFE\ NPV=\frac{{FCFE}_t}{{(1+r_e)}^t}+\frac{{FCFE}_{t+1}}{{(1+r_e)}^{t+1}}+\ldots+\frac{{FCFE}_n}{{(1+r_e)}^n}\)

The residual value results from a perpetuity in the first year after the forecasts.

- \(Residual\ value=\frac{{FCFE}_{n+1}}{(r_e-g_{FCFE})}\frac{1}{{(1+r_e)}^n}\)

Since the FCFE_{n+1} cannot be obtained through the financial statements, you can use the g_{FCFE} growth rate to estimate it.

- \({FCFE}_{n+1}={FCFE}_n\ast(1+g_{FCFE})\)