Question

A firm's assets have a beta of 1.0. Assuming that the debt beta equals 0.0 and that there are no taxes, calculate the firm's equity beta under the following assumptions:

a. The firm's capital structure is 100% equity.

b. The capital structure is 20% debt and 80% equity.

c. The capital structure is 40% debt and 60% equity.

d. The capital structure is 60% debt and 40% equity.

e. The capital structure is 80% debt and 20% equity.

Do you believe that the assumption of a zero debt beta is equally valid for each of these capital structures? Why or why not?

Answer 1

Solution:-

We know that

Beta assets = Beta _equity*Equity/[Equity+Debt(1-tax) + Beta _debt* Debt(1-tax)/[Equity+Debt(1-tax)

Since the beta debt = 0 and tax rate is = 0 hence the above formula can be simplified as

Beta assets = Beta _equity*Equity/[Equity+Debt]

we will substitute value for each capital structure

a)The firm's capital structure is 100% equity.

1= Beta _equity*1/(1+0)

Hence Beta _equity = 1

b) The capital structure is 20% debt and 80% equity.

1= Beta _equity*0.80/(0.80+0.20)

Beta _equity=1/0.80 = 1.25

Hence beta equity = 1.25

c) The capital structure is 40% debt and 60% equity.

1= Beta _equity*0.60/(0.60+0.40)

Beta _equity=1/0.60 = 1.67

Hence beta equity = 1.67

d) The capital structure is 60% debt and 40% equity

1= Beta _equity*0.40/(0.40+0.60)

Beta _equity=1/0.40 = 2.5

Hence beta equity = 2.5

e) The capital structure is 80% debt and 20% equity.

1= Beta _equity*0.20/(0.20+0.80)

Beta _equity=1/0.20 = 5

Hence beta equity = 5

No the assumption of zero debt beta may not be equally valid for all capital structure. When the proportion of the debt increases substantially like 60% or 80%, the company may make default in the payment to the debt holder due to the increased pressure of fixed payment. Hence in those case the risk to debt holder is not zero. Hence in those case the debt beta might not be zero.

Note:- Beta of debt represent risk to that debt holder.

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