Asset and equity beta

CFA Level I Corporate Finance
#1

If βdebt = 0, then

(B)asset = (B) equity [1 / 1 + ((1-t) * d/e))

market risk of equity is affected by the asset’s market risk and a factor representing the nondiversifiable portion of the company’s financial risk

(B)equity = (B)asset [1 + ((1-t) * d/e)

Company A has equity beta of 1.5, D/E = 0.4, marginal tax = 30%. Asset beta:

(B)asset = (B) equity [1 / 1 + ((1-t) * d/e))

(B)asset = 1.5

beta = 1.5 [1 / 1 + (1-30%) * 40%] = 1.1719

If the company did not have debt financing, (B)asset = (B)equity = 1.1719. Debt financing increases its (B)equity from 1.1719 to 1.5. What woul equity beta be if the D/E ratio were 0.5 and not 0.4? So my two questions are as follows: a.) when the book says that the debt financing increases (B)equity from 1.1719 to 1.5, how is that? It appears that (B)equity is 1.5 and therefore, the (B) of the asset is 1.1719. Maybe I’m jsut misunderstanding the wording… b.) when the book asks you to find the (B)equity if the D/E ratio is 0.5, not 0.4, why does the book use:

(B)equity = 1.1719 [1 + ((1-30%)*(50%)) = 1.5821

As opposed to using the original formula and plugging in the new D/E ratio?

Thanks!

[1+−t

DE

#2

a)

Take the fomula for ßE = ßA x [1 + (1 - t) x D/E] and you’ll see that ßE is just a linear function of the levarage ratio (D/E).

For a leverage ratio of zero ßE is just equal to ßA and increases on a linear path with an increasing D/E ratio. Note that the asset beta is a “fix” number. The asset beta is only depended on the market risk of the company. Hence, it is only a variable of the business nature of the company. As such, the asset beta is 1.1719 and is not depended on the leverage of the company whatsoever. With increasing leverage the equity beta increases, the asset beta however stays constant.

b)

If you understood the explanation in a) this should become clear now to you. The asset beta is still 1.1719 (it will not change until the company does not enter into new businesses with a different risk characteristic). You just apply the higher D/E ratio to the asset beta of 1.1719.

Best, Oscar