# 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 FCFEn+1 cannot be obtained through the financial statements, you can use the gFCFE growth rate to estimate it.

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