Modigliani and Miller Proposition 2 (with tax) formula

I would also like to know how the formula is rearranged to derive Kei.

I would like to know how to rearrange it as well.

It is easier to rearrange when you actually have numbers in it!!! But here goes :-) Ke = Kei + (1 - T)(Kei - Kd) Vd/Ve Multiply everything by Ve: Ke Ve = Kei Ve + Vd (1 - T) (Kei - Kd) Multiply both terms in the last bracket by Vd(1-T) Ke Ve = Kei Ve + Vd(1-T)Kei - Vd(1-T)Kd Add Vd(1-T)Kd to both sides KeVe + KdVd(1-T) = KeiVe + Kei Vd(1-T) = Kei ( Ve + Vd (1-T)) Divide both sides by (Ve + Vd (1-T)) (and write the equation the other way round) Kei = (KeVe + KdVd(1-T)) / (Ve + Vd(1-T)) :-)

I'm confused with the part 'Add Vd(1-T)Kd to both sides KeVe + KdVd(1-T) = KeiVe + Kei Vd(1-T) = Kei ( Ve + Vd (1-T))' Please rearrange with these values: 12% = kei + (1 - 0.30) (kei - 4%) (20/80)

0.12 = Kei + 0.7 (Kei - 0.04) 0.25 0.12 = Kei + 0.175 (Kei - 0.04) 0.12 = Kei + 0.175Kei - 0.007 0.127 = 1.175Kei Kei = 0.127/1.175 = 0.1081 or 10.81%

Thank you :D was a big deal for me now a piece of cake

You are welcome :-)

Hi Sir, Would appreciate if you could show how to rearrange below value 35.8% = Kei + (1-0.24)(Kei-4.6) (65/35) Thanks in advance sir.

First, it is best to express the % as a decimal. So..... 0.358 = Kei + (1-0.24)(Kei - 4.6)(65/35) 0.348 = Kei + 0.76 (Kei - 4.6) 1.9429 0.348 = Kei + 1.463 (Kei - 4.6) (1.463 = 0.76 x 1.9429) 0.348 = Kei + 1.463 Kei - 6.730 (6.730 = 1.463 x 4.6) 0.348 = 2.463 Kei - 6.730 add 6.730 to both sides: 7.079 = 2.463 Kei Divide both sides by 2.463 Kei = 7.079/2.463 = 2.874 This would be a ridiculous answer - it is 287.4% !!! Check my workings, but I don't think I made a mistake. I think that maybe you have copied the figures in the question wrongly :-)

1. What cost of debt should be used here. Is it risk free rate or actual cost of debt. 2. Should the Vd be subjected to tax as well i.e. Ve/Vd(1-t)?

But I explain all of this (with an example) in my free lectures !!! 1. The cost of debt is the actual pre-tax cost of debt. 2. There is no Ve/Vd in the formula, it is Vd/Ve. These market values themselves are not subject to tax, but the effect of tax is dealt with in the second term of the formula (where there is (1-t).