Question

Good Time Co. is a regional chain department store. It will remain in business for one more year. The estimated probability of a boom year for next year is .60 and the estimated probability of a recession year for next year is .40. It is projected that Good Time will have a total cash flow of $250 million in a boom year and $100 million in a recession. Good Time’s required debt payment next year is $150 million. The firm has few fixed assets, so assume that after next year is over the firm is liquidated for $0. Assume the appropriate annual discount rate for cash flows to both equity holders and debtholders is 12%. There are no corporate or personal taxes.

1. What is the total value of equity today assuming no bankruptcy costs
2. If equity has the value you calculated in part (a) and the debt on Good Time is currently selling for $108.93 million, what is the expected bankruptcy cost for Good Time?

Answer 1

Answer a)

Essentially, we would take out combined probability of both the events i.e. Boom period and Recession Period for cash flows and there by debt payment. Hence we would multiple Boom period probability (0.60) with expected cash flow of $250 and multiple recession period probability (0.40) with expected cash flow of $100.

This would result in equation as (0.60*250) + (0.40*100) = $190 at period ending after 1 year.

Likewise we would calculate the debt payment which is (0.60*150) + (0.40*100) = $130. Since we only have $100 as cash flow for recession period, we can only pay Debt for $100 and not $150; this means also the value for equity shareholder is 0.

Equity value thus becomes residual value after payment of debt which is (190 - 130) = $60 at end of period of 1 year.

To know the value today we discount the value of equity to today at 12% which becomes 60/(1.12) = $53.57

Answer b)

For knowing the value of bankruptcy, value of debt today is $108.93 and equity value is $53.57, hence the total value of company is 108.93+53.57 = $162.50. Total available cash flow is $169.64, hence after payment to debt and equity holder of $162.50 the remainder would be the cost incurred for bankruptcy, i.e. 169.64 - 162.50 = $7.14.

See calculation below:

Formula used: