Question

a company has assets $336.11 million, and it has debt with total face value of $204.5 million. If the standard deviation of monthly returns on the company stock is 0.158, what is the likelihood the company will be unable to repay the debt in three years when it is due?

Answer 1

3 year standard deviation= 0.158*sqrt(36)=0.948

Lets find out the distance to default (DD):

(Market Value Assets- Default Point)/ (Market Value of Assets *Assets Volatility)

Default Point= Short Term Debt +0.5 Long Term Debt

                       = 0+0.5*204.5

                      =102.25

Therefore,

DD= (336.11-102.25)/(0.948*336.11)

      =0.7339

So the Probability of default in 3 years is (using help of z table):

N(-0.7339)= 0.2206=22.06%