Average book rate of return method

Input(s)

$C$ : Initial Investment/Capital ($)

E: Total Net Undiscounted Cash Flow during the whole project ($)

$n$ : Life of the Project (years)

$N$ : Total Recoverable Oil Amount (bbl)

$N_{k}$ : Total Recoverable Oil Amount in $\mathrm{k}^{\text {th }}$ year (bbl)

$N_{p}$ : Total Recoverable Oil Amount in $\mathrm{n}^{\text {th }}$ year (bbl)

$Q_{k}$ : Oil Production in $\mathrm{k}^{\text {th }}$ year (bbl)

$D$ : Present worth Factor (dimensionless)

$W_{p}$ : Working Profit per barrel of Oil $(\$ / b b l)$

P: Profit $(\$)$

$\sum$ B: Total End of Year Balance not Amortized ($)

$\sum \mathrm{B}_{\mathrm{md}}$ : Total Mid-Year Balance not Amortized ($)

$\mathrm{r}$ : Annual Average Rate of Return ($)

$\mathrm{r}_{\mathrm{md}}$ : Average Mid Year Rate of Return ($)

\begin{gathered} \sum B=\frac{C}{N} \sum_{k=1}^{n} k \cdot Q_{k} \\ \sum B_{m d}=C\left(n+\frac{1}{2}\right)-\frac{C}{N_{p}} \sum_{k=1}^{n} N_{k} \\ r=\frac{\left(E \cdot W_{p}\right)-C}{\sum B} \\ r_{m d}=\frac{\left(E \cdot W_{p}\right)-C}{\sum B_{m d}} \end{gathered}

Serpen, U., Petroleum Economics, Course Notes, ITU Petroleum and Natural Gas Engineering, Istanbul, Turkey, (2008) Page: 45.