Question

Movie Inc., an entertainment conglomerate, has a beta of 1.60. Part of the reason for the high beta is the debt left over from the leveraged buyout of Pic Inc. in 2009, which amounted to $10 billion in 2014. The market value of equity at Movie Inc in 2014 was also $ 10 billion (and the book value of equity was also $10 billion). The marginal tax rate was 40%.

1. Estimate the unlevered beta for Movie Inc.

2. Estimate the effect of reducing the debt ratio (Total Debt/Total Assets) by 10% each year for the year (for example if the debt ratio was 40% it will be reduced to 30%) on the beta of the stock. Assume that Movie Inc has no short-term debt (i.e. TD=TL).

Answer 1

Unlevered beta of Movie Inc. = 1.6

MV of debt = $10 billion

MV of equity = $10 billion

So, D/E ratio = 1

a). We know that unlevered beta = levered beta/(1 + (1-t)*D/E)

So, unlevered beta of firm = 1.6/(1 + (1-.4)*1) = 1

b). Debt/asset ratio = Debt/(debt + equity) = 10/(10+10) = 50%

After 10% reduction, new Debt/asset ratio = 40%

So, Debt/Equity = Debt/(asset-debt) = 0.4/(1-0.4) = 2/3

So, new levered beta = unlevered beta*(1 + (1-t)*D/E) = 1*(1 + (1-.4)*2/3) = 1.4

When debt/asset ratio = 30%

Debt/equity = (0.3/(1-0.3)) = 3/7

So, levered beta = 1*(1+0.6*3/7) = 1.26

When debt/asset ratio = 20%

Debt/equity = (0.2/(1-0.)) = 1/4

So, levered beta = 1*(1+0.6*1/4) = 1.15

When debt/asset ratio = 10%

Debt/equity = (0.1/(1-0.1)) = 1/9

So, levered beta = 1*(1+0.6*1/9) = 1.07

When debt/asset ratio = 0%

Debt/equity = (0.0/(1-0.0)) = 0

So, levered beta = 1*(1+0.6*0) = 1

So, company's beta at different Debt/asset ratio is

Debt/Asset ratio	Debt/equity	Company's beta
50%	1	1.6
40%	2/3	1.4
30%	3/7	1.26
20%	1/4	1.15
10%	1/9	1.07
0	0	1