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I am studying using my text and came across this formula and I believe that something is wrong in the explanation of the terms which is preventing me from understanding and example>
ke = kei + (1–T)(kei – kd )(Vd / Ve)
Ve and Vd are the market values of equity and debt respectively.
kd i is the (pre tax) return required by the debt holders.
T is the corporation tax rate
ke is the cost of equity in an equivalent ungeared firm
ke is the cost of equity in the geared firm
I copied and paste the information above exactly but it appears that the last 2 values are the same thing.
This example was in the book, can you assist me in finding the answer
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 annum, and the rate of corporate tax is 30%.
Required:
Calculate the theoretical cost of equity in Moondog Co after the refinancing.
ke is the cost of equity in the geared firm; kei is the cost of equity if ungeared.
Since the cost of equity is currently 12%, using the formula ‘backwards’ gives kei = 10.81%.
If you use the formula again with the new gearing, then the new ke = 12.4%
(Incidentally, I think I am right in saying that the formula has only ever been relevant in one exam question. Even then you can in fact always get the same answer by ungearing and then regearing the Beta (which is often needed both in F9 and in P4). The only problem here is that in order to calculate the current equity beta you need to know the market return. But ‘invent’ any market return you want and you will still end up with the same answer as above. It is because the asset beta formula in fact comes from M&M.
Just try it (because you have to be able to ungear and regear betas for the exam) and ‘invent’ a market return of 10%. If you do, then you will get a current equity beta of 1.333. When you use the asset beta formula you will get an asset beta of 1.135. Then using the asset beta formula again with the new gearing you will get a new equity beta of 1.4. Applying this to a market return of 10% and a risk free rate of 4% then you will get a new cost of equity of 12.4% again 🙂 )
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