Question

Good Time Company is a regional chain department store. It will remain in business for one more year. The probability of a boom year is 80 percent and the probability of a recession is 20 percent. It is projected that the company will generate a total cash flow of $204 million in a boom year and $95 million in a recession. The company's required debt payment at the end of the year is $129 million. The market value of the company’s outstanding debt is $102 million. The company pays no taxes.
a. What payoff do bondholders expect to receive in the event of a recession?

b. What is the promised return on the company's debt?

c. What is the expected return on the company's debt?

Answer 1

Answer:

a. $95 million

b. 26.5%

c. 78.6%

Explanation:

a. It is projected that the company will generate a total cash flow of $95 million in a recession.  The bondholders expect to receive a payoff of $95 million.

b. The promised return is the company's required debt payment at the end of the year ($129 million) and the $(\frac{expected debt value}{market value of the company’s outstanding deb}) - 1$t ($102 million).

Promised return = $(\frac{company's required debt payment at the end of the year}{market value of the company’s outstanding debt}) - 1$

Promised return = $(\frac{129 million}{102 million}) - 1$

Promised return = 0.2647 ≈ 0.265

The promised return on the company's debt is 0.265 or 26.5%

c. The expected return is the company's expected debt value and the current market value of the company’s outstanding debt ($102 million). We will need to find the company's expected value of debt since it is unknown.

expected debt value = $(Probability of a boom year* cash flow of boom year) + (probability of a recession year * cash flow of recession year)$expected debt value = (80% ×$204 million ) + ( 20% × $95 million)

expected debt value = (0.8 ×$204 million ) + ( 0.2 × $95 million)

expected debt value = ($163.2 million ) + ($19 million)

expected debt value = $182.2 million

We can now determine the expected return.

The expected return =  $(\frac{expected debt value}{market value of the company’s outstanding debt}) - 1$

expected return = $(\frac{182.2 million}{102 million}) - 1$

Expected return = 0.7863 ≈ 78.6%

The expected return on the company's debt is 78.6%