Box 3–3: Formulas for Current Rent Method I
total mineral reserve value_t_ = V_t_ =
[
p_t_ - a_t_]
R_t_ - rR_t_ K_t_/q_t_ - R_t_ D_t_/q_t_=
[
p_t_ - a_t_ - rK_t_/q_t_ - D_t_/q_t_]
* R_t_
additions_t_ =
[ p_t_ - a_t_ - rK_t_/q_t_ - D_t_/q_t_
] * A_t_
depletions_t_ =
[ p_t_ - a_t_ - rK_t_/q_t_ - D_t/q_t_
] * q_t_
revaluations_t_ = V_t_ - V_t-1_ + depletions_t_ - additions_t_
where
V_t_ = value of mineral reserves
p_t_ = price of commodity
a_t_ = average cost of current production
R_t_ = total quantity of reserves
r =
average rate of return on capital
K_t_ = value of associated capital, valued at current replacement cost
q_t_ = total quantity extracted
D_t_ = depreciation of associated capital
A_t_ =
quantity of discoveries of new reserves
additions_t_ =
value of discoveries of new reserves
depletions_t_ =
value of depletions
revaluations_t_ = change in value of reserves corrected
for depletions and additions
The revaluation term is not directly calculated; it will
include any errors in calculating additions, depletions, and opening and closing
stock values.