strikethree

RI = NI - (BV of equity * Re)
EVA = EBIT(1-t) - $WACC
(EBIT)(1-t) - Interest(1-t) = NI
$WACC = (cost of debt * total debt)(1-t) + (Re * BV of equity)
Therefore, if (Cost of debt * Total Debt)(1-t) = Interest Expense(1-t) then
RI = (EBIT(1-t) - Interest Expense(1-t)) - (Re * BV of equity) and
EVA = EBIT(1-t) - (Interest Expense(1-t) + (Re * BV of equity))
And
(EBIT(1-t) - Interest Expense(1-t)) - (Re * BV of equity) = EBIT(1-t) - (Interest Expense(1-t) + (Re * BV of equity))
For example if EBIT(1-t)=5, Interest Expense(1-t)=2, and (Re * BV of equity)=1
(5 - 2) - 1 = 2 and
5 - (2 + 1) = 2
Therefore, if (Cost of debt * Total Debt)(1-t) = Interest Expense(1-t) then
EVA = RI