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.