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- This topic has 1 reply, 2 voices, and was last updated 1 year ago by John Moffat.

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- May 16, 2023 at 7:10 pm #684474
ke = kei + (1 – T)(kei – kd )(Vd / Ve)

Moondog Co is a company with a 20:80 debt: equity ratio. Using CAPM,

its cost of equity has been calculated as 12%.It is considering raising some debt finance to change its gearing ratio to

25:75 debt to equity. The expected return to debt holders is 4% per year,

and the rate of corporate tax is 30%.Required:

Calculate the theoretical cost of equity in Moondog Co after the

refinancing.ANSWER:

Using M+M’s Proposition 2 equation, we can degear the existing ke and

then regear it to the new gearing level:

Degearing:

ke = kei + (1 – T)(kei – kd)(Vd/Ve)

12% = kei + (1 – 0.30)(kei – 4% )(20/80)

Now we need to rearrange this formula:

0.12 = kei + (1-0.30)( kei – 0.04)(20/80)

0.12 = kei + (0.7)( kei – 0.04)(0.25)

0.12 = kei + (0.175)( kei – 0.04)

0.12 = kei + 0.175 kei – 0.007

0.12 = 1.175 kei – 0.007

0.127 = 1.175 kei

(0.127/1.175) = keiSo rearranging carefully gives kei = 0.108 (10.8%)

Now regearing:

ke = 10.8% + (1 – 0.30)(10.8% – 4%)(25/75)

ke = 12.4%QUERY:

Please can you take me through this formula step by step. I cannot get my head around this.

How is the ‘0.007’ calculated?Where does the 1.175 come from? I can work out how to get the 0.175 (0.7*0.25).

Please clarify the above.

Many thanks in advance

RoryMay 17, 2023 at 7:58 am #684491I assume that you are happy with the first five lines of this

ke = kei + (1 – T)(kei – kd)(Vd/Ve)

12% = kei + (1 – 0.30)(kei – 4% )(20/80)

Now we need to rearrange this formula:

0.12 = kei + (1-0.30)( kei – 0.04)(20/80)

0.12 = kei + (0.7)( kei – 0.04)(0.25)So…0.12 = kei + (0.7 x 0.25) (kei – 0.04)

which gives:

0.12 = kei + (0.175)( kei – 0.04)0.12 = kei + 0.175kei – (0.175 x 0.04)

0.12 = kei + 0.175 kei – 0.007

1kei + 0.175kei = 1.175Kei, so…..

0.12 = 1.175 kei – 0.007

The rest should now be clear.

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