Question

The Chocolate Ice Cream Company and the Vanilla Ice Cream Company have agreed to merge and form Fudge Swirl Consolidated. Both companies are exactly alike except that they are located in different towns. The end-of-period value of each firm is determined by the weather, as shown below. There will be no synergy to the merger.

State	Probability			Value
Rainy	.2			$	290,000
Warm	.3				470,000
Hot	.5				935,000

  

The weather conditions in each town are independent of those in the other. Furthermore, each company has an outstanding debt claim of $470,000. Assume that no premiums are paid in the merger.

a. What are the possible values of the combined company? (Do not round intermediate calculations.)
  

Possible states	Joint Value
Rain-Rain	$
Rain-Warm
Rain-Hot
Warm-Warm
Warm-Hot
Hot-Hot

  

b. What are the possible values of end-of-period debt and stock after the merger? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations.)
  

	Debt Value		Stock Value
Rain-Rain	$		$
Rain-Warm
Rain-Hot
Warm-Warm
Warm-Hot
Hot-Hot

c. How much do stockholders and bondholders each gain or lose if the merger is undertaken? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations.)
  

Bondholder gain/loss	$
Stockholder gain/loss	$

Answer 1

a. To find the distribution of joint values, we first must find the joint probabilities. To do this, we need to find the joint probabilities for each possible combination of weather in the two towns. The weather conditions are independent; therefore, the joint probabilities are the products of the individual probabilities.

Possible states		Joint Prob.
Rain-Rain	.2 x .2	0.04
Rain-Warm	.2 x .3	0.06
Rain-Hot	.2 x .5	0.1
Warm-Rain	.3 x .2	0.06
Warm-Warm	.3 x .3	0.09
Warm-Hot	.3 x .5	0.15
Hot-Rain	.5 x .2	0.1
Hot-Warm	.5 x .3	0.15
Hot-Hot	.5 x .5	0.25

Next, note that the revenue when rainy is the same regardless of which town. So, since the state "Rain-Warm" has the same outcome (revenue) as "Warm-Rain", their probabilities can be added. The same is true of "Rain-Hot" / "Hot-Rain" and "Warm-Hot" / "Hot-Warm". Thus the joint probabilities are:

Possible states	Joint Prob
Rain-Rain	0.04
Rain-Warm	0.12
Rain-Hot	0.2
Warm-Warm	0.09
Warm-Hot	0.3
Hot-Hot	0.25

Finally, the joint values are the sums of the values of the two companies for the particular state.

Possible states	Joint Value
Rain-Rain	580,000
Rain-Warm	760,000
Rain-Hot	1,225,000
Warm-Warm	940,000
Warm-Hot	1,405,000
Hot-Hot	1,870,000

b. Recall that if a firm cannot service its debt, the bondholders receive the value of the assets. Thus, the value of the debt is the value of the company if the face value of the debt is greater than the value of the company. If the value of the company is greater than the value of the debt, the value of the debt is its face value. Here, the value of the common stock is always the residual value of the firm over the value of the debt. So, the value of the debt and the value of the stock in each state is:

Possible states	Joint Prob	Joint Value	Debt Value	Stock Value
Rain-Rain	0.04	580000	580000	0
Rain-Warm	0.12	760000	760000	0
Rain-Hot	0.2	1225000	940000	285000
Warm-Warm	0.09	940000	940000	0
Warm-Hot	0.3	1405000	940000	465000
Hot-Hot	0.25	1870000	940000	930000

c. The bondholders are better off if the value of the debt after the merger is greater than the value of the debt before the merger. The value of the debt is the smaller of the debt value or the company value. So, the value of the debt of each individual company before the merger in each state is:

State	Probability	Debt Value
Rainy	0.2	290,000
Warm	0.3	470,000
Hot	0.5	470,000

Individual debt value = .2($290,000) + .4($470,000) + .5($470,000)
Individual debt value = $434,000

This means the total value of the debt for both companies pre-merger must be:
Total debt value pre-merger = 2($434,000)
Total debt value pre-merger = $868,000

To get the expected debt value, post-merger, we can use the joint probabilities for each possible state and the debt values corresponding to each state we found in part c. Using this information to find the value of the debt in the post-merger firm, we get:

Total debt value post-merger = 904,000

The bondholders are better off by $36,000. Since we have already shown that the total value of the combined company is the same as the sum of the value of the individual companies, the implication is that the stockholders are worse off by $36,000.