Derivation of Formula Re = Ro + (Ro - Rd(1-t)) D/E from Equation of WACC

Ro = WACC, Re = Cost of Equity, Rd = Cost of Debt

Ro = (D/V)xRd(1-t) + (E/V)xRe

Ro - (DxRd(1-t)) / V = (E/V)xRe

Taking LCM and cutting both denominators (V)

VRo - DRd(1-t) = ERe

(VxRo)/E - (DxRd(1-t))/E= Re

We know V = D+E, Substituting V with D+E

((D+E)Ro)/E - (DxRd(1-t))/E = Re

Rewriting it & Opening the bracket

(D/E x Ro) + ERo/E - (D/E x Rd(1-t)) = Re

(D/E x Ro) + ERo/E - (D/E x Rd(1-t)) = Re

(D/E)Ro + Ro - (D/E)Rd(1-t) = Re

Ro + (D/E)Ro - (D/E)Rd(1-t) = Re

Taking D/E as common

Ro + (D/E) (Ro - Rd(1-t)) = Re

Rewrite it

Re = Ro + (Ro - Rd(1-t))D/E