MM proposition 2

When you are not given information about the Betas.

Hi john, I’m not sure if I’ve overloaded my brain too much in the past 2 days but I’m not understanding how to calculate the ungeared cost of equity by rearranging the M&M formula Are you able to help on rearranging the below: 0.12 = keu + 0.75 x (keu-0.05) x 500/200 I understand that I times 0.75 and 500/200 together, but then I get lost.. perhaps my algebraic knowledge is very bad. Thanks in advance

0.12 = Keu + 0.75 x (Keu - 0.05) x 500/200 Multiply 0.75 by 500/200: 0.12 = Keu + 1.875 x (Keu - 0.05) Multiply each item in the brackets by 1.875: 0.12 = Keu + 1.875 Keu - 0.09375 Add 0.09375 to both sides: 0.21375 = Keu + 1.875 Keu So 0.21375 = 2.875 Keu Keu = 0.21375 / 2.875 = 0.07435

When u add 0.09375+1.875=1.96875 So where is that 2.875 comes from? Little confused

Good heavens!! Nobody is adding 0.09375 + 1.875 !! If you add 0.09375 to both sides then you get: 0.12 + 0.09375 = Keu + 1.875Keu - 0.09375 + 0.09375 Which gives: 0.21375 = Keu + 1.875Keu ( Keu + 1.875Keu is equal to 2.875Keu )

Oh great thanks so much highly appreciated

You are welcome :-)