how to get this 0.9563Keu & 1.9563Keu?? please help

Exam standard example (extract)
Mlima Co is a private company involved in aluminium mining.

Mlima Co is an unlisted company and wants to be listed on a stock exchange and be financed entirely by equity.

Mlima Co’s closest competitor is Ziwa Co, a listed company which mines metals worldwide.

Mlima Co’s directors are of the opinion that after listing Mlima Co’s cost of capital should be based on Ziwa Co’s ungeared cost of equity.

Ziwa Co’s geared cost of equity is estimated at 16•83% and its pre-tax cost of debt is estimated at 4•76%.

These costs are based on a capital structure comprising of 200 million shares, trading at $7 each, and $1,700 million 5% irredeemable bonds, trading at $105 per $100.

Both Ziwa Co and Mlima Co pay tax at an annual rate of 25% on their taxable profits.

Required

Calculate Mlima Co’s WACC.

Solution
Ziwa Co

MV debt = $1,700m x 1•05 = $1,785m
MV equity = 200m x $7 = $1,400m

Ziwa Co, ungeared Ke

Keg = Keu + (1 – t) (Keu – Kd) D/E

16.83% = Keu + 0.75 x (Keu – 4.76%) x 1,785/1,400
16.83% = Keu + 0.9563Keu – 4.55%
16.83% + 4.55% = Keu + 0.9563Keu
21.38% = 1.9563Keu
Keu = 10.93% (say 11%)