Question

Steinberg Corporation and Dietrich Corporation are identical firms except that Dietrich is more levered. Both companies will remain in business for one more year. The companies' economists agree that the probability of the continuation of the current expansion is 70 percent for the next year and the probability of a recession is 30 percent. If the expansion continues, each firm will generate earnings before interest and taxes (EBIT) of $2.8 million. If a recession occurs, each firm will generate earnings before interest and taxes (EBIT) of $1.2 million. Steinberg's debt obligation requires the firm to pay $910,000 at the end of the year. Dietrich's debt obligation requires the firm to pay $1.3 million at the end of the year. Neither firm pays taxes. Assume a discount rate of 12 percent. a-1. What is the value today of Steinberg's debt and equity? (Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.) a-2. What is the value today of Dietrich's debt and equity? (Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.) b. Steinberg’s CEO recently stated that Steinberg’s value should be higher than Dietrich’s because the firm has less debt and therefore less bankruptcy risk. Do you agree or disagree with this statement?

Answer 1

a1.

Value of equity for firm is the discounted value of the expected cashflows for the shareholders

Cash flow at the end of year 1 for Steinberg is expansion continues = $2,800,000 - debt obligation =$2,800,000 - $910,000 = $1,890,000

Cash flow at the end of year 1 for Steinberg if recession occurs = $1,200,000 - debt obligation =$1,200,000 - $910,000 = $290,000

Value of equity for Steinberg = (0.7*$1,890,000 + 0.3*$290,000)/1.12 = $1,258,928.57

Debt amount is indpendent of recession or expansion and will remain same. Hence

Value of debt for Steinberg = $910,000/1.12 = $812500.00

a2.

Value of equity for firm is the discounted value of the expected cashflows.

Cash flow at the end of year 1 for Dietrich is expansion continues = $2,800,000 - debt obligation =$2,800,000 - $1,300,000 = $1,500,000

Cash flow at the end of year 1 for Dietrich if recession occurs = $1,200,000 - debt obligation

Since the EBIT of $1,200,000 - is lower than the debt obligation of $1,300,000 and since bondholders have senior claim for cashflows over shareholders, cash flow for sharedholders of Dietrich in case of recession would be 0

Value of equity for Dietrich = (0.7*$1,50,000 + 0.3*0)/1.12 = $937,500

Bondholders will receive $1,300,000 if expansion continues but will only receive $ 1,200,000 if recession occurs. Hence

Value of debt for Dietrich = (0.7*1,300,000 + 0.3*1,200,00)/1.12 = $1,133,928.57

b. Disagree with CEO's statement.

Steinberg’s CEO is incorrect in mentioning that "Steinberg’s value should be higher than Dietrich’s because the firm has less debt and therefore less bankruptcy risk". Risk of bankruptcy does not per se effect the firm's value. It is the cost of brankruptcy that decreases the firm value. Since discount rate is 12% and EBIT is same for the firms with taxes as 0, the value of both firms will in fact be same in the given case. This can be proved by computing the value of the two firms as below:

The firm's value is given by value of debt + value of equity

Value of Steinberg = $812500.00 + $1,258,928.57 = $2,071,428.57

Value of Dietrich = $1,133,928.57 + $937,500 = $2,071,428.57