Formula 7.7
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 $(\$ / b b l)$
Output(s)
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 (\$)
Formula(s)
$$ \begin{gathered} \sum B=\frac{C}{N} \sum_{k=1}^{n} k \cdot Q_{k} \\ \sum B_{m d}=C\left(n+\frac{1}{2}\right)-\frac{C}{N_{p}} \sum_{k=1}^{n} N_{k} \\ r=\frac{\left(E \cdot W_{p}\right)-C}{\sum B} \\ r_{m d}=\frac{\left(E \cdot W_{p}\right)-C}{\sum B_{m d}} \end{gathered} $$
Reference(s)
Serpen, U., Petroleum Economics, Course Notes, ITU Petroleum and Natural Gas Engineering, Istanbul, Turkey, (2008) Page: 45.