# 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.

## Related

### Average annual rate of return method

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