10. Beginning with the fact that the NPV of a merger is the value of the target minus the cost, we get:
NPV =
*
B
V
– Cost
11. a. The synergy will be the present value of the incremental cash flows of the proposed purchase.
Since the cash flows are perpetual, the synergy value is:
b. The value of Flash-in-the-Pan to Fly-by-Night is the synergy plus the current market value of
Flash-in-the-Pan, which is:
c. The value of the cash option is the amount of cash paid, or $20.4 million. The value of the stock
acquisition is the percentage of ownership in the merged company, times the value of the merged
company, so:
d. The NPV is the value of the acquisition minus the cost, so the NPV of each alternative is:
NPV of cash offer = $21,825,000 – 20,400,000
NPV of cash offer = $1,425,000
NPV of stock offer = $2,216,250
e. The acquirer should make the stock offer since its NPV is greater.
12. a. The number of shares after the acquisition will be the current number of shares outstanding for
the acquiring firm, plus the number of new shares created for the acquisition, which is:
And the share price will be the value of the combined company divided by the shares outstanding,
which will be:
b. Let equal the fraction of ownership for the target shareholders in the new firm. We can set the
percentage of ownership in the new firm equal to the value of the cash offer, so:
CHAPTER 21 B-2
So, the shareholders of the target firm would be equally as well off if they received 25.96 percent
of the stock in the new company as if they received the cash offer. The ownership percentage of
the target firm shareholders in the new firm can be expressed as:
New shares issued = 1,753,131
To find the exchange ratio, we divide the new shares issued to the shareholders of the target firm
by the existing number of shares in the target firm, so:
13. a. The value of each company is the sum of the probability of each state of the economy times the
value of the company in that state of the economy, so:
b. The value of each company’s equity is sum of the probability of each state of the economy times
the value of the equity in that state of the economy. The value of equity in each state of the
economy is the maximum of total company value minus the value of debt, or zero. Since Rolls
is an all equity company, the value of its equity is the total value of the firm, or $280,000. The
value), and the value of Bentley’s equity in a recession is zero since the value of its debt is greater
than the value of the company in that state of the economy. So, the value of Bentley’s equity is:
The value of Bentley’s debt in a boom is the full face value of $150,000. In a recession, the value
of the company’s debt is $140,000 since the value of the debt cannot exceed the value of the
company. So, the value of Bentley’s debt today is:
Note, this is also the value of the company minus the value of the equity, or:
CHAPTER 21 B-3
c. The combined value of the companies, the combined equity value, and combined debt value is:
Combined value = $280,000 + 243,000
d. To find the value of the merged company, we need to find the value of the merged company in
each state of the economy, which is:
Boom merged value = $340,000 + 300,000
Boom merged value = $640,000
Recession merged value = $140,000 + 110,000
So, the value of the merged company today is:
Merged company value = .70($640,000) + .30($250,000)
Since the merged company will still have $150,000 in debt, the value of the equity in a boom is
The merged company will have a value greater than the face value of debt in both states of the
e. There is a wealth transfer in this case. The combined equity value before the merger was
$376,000, but the value of the equity in the merged company is only $373,000, a loss of $3,000
for stockholders. The value of the debt in the combined companies was only $147,000, but the
f. If the value of Bentley’s debt before the merger is less than the lowest firm value, there is no
coinsurance effect. Since there is no possibility of default before the merger, bondholders do not
Challenge
14. a. To find the value of the target to the acquirer, we need to find the share price with the new growth
rate. We begin by finding the required return for shareholders of the target firm. The earnings per
share of the target are:
EPSP = $960,000/750,000
EPSP = $1.28 per share
The price per share is:
And the dividends per share are:
The current required return for Palmer shareholders, which incorporates the risk of the company,
is:
The price per share of Palmer with the new growth rate is:
The value of the target firm to the acquiring firm is the number of shares outstanding times the
price per share under the new growth rate assumptions, so:
*
*
b. The gain to the acquiring firm will be the value of the target firm to the acquiring firm minus the
market value of the target, so:
c. The NPV of the acquisition is the value of the target firm to the acquiring firm minus the cost of
the acquisition, so:
d. The most the acquiring firm should be willing to pay per share is the offer price per share plus
the NPV per share, so:
CHAPTER 21 B-5
e. The price of the stock in the merged firm would be the market value of the acquiring firm plus
the value of the target to the acquirer, divided by the number of shares in the merged firm, so:
PFP = ($60,900,000 + 16,114,285.71)/(1,300,000 + 225,000)
PFP = $50.50
The NPV of the stock offer is the value of the target to the acquirer minus the value offered to
the target shareholders. The value offered to the target shareholders is the stock price of the
merged firm times the number of shares offered, so:
f. Yes, the acquisition should go forward, and Plant should offer shares since the NPV is higher.
g. Using the new growth rate in the dividend growth model, along with the dividend and required
return we calculated earlier, the price of the target under these assumptions is:
And the value of the target firm to the acquiring firm is:
The gain to the acquiring firm will be:
And the new price per share of the merged firm will be:
And the NPV of the stock offer under the new assumption will be:
CHAPTER 21 B-6
Even with the lower projected growth rate, the stock offer still has a positive NPV. The NPV of
the stock offer is still higher. Plant should purchase Palmer with a stock offer of 225,000 shares.
15. 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 probability
Rain-Rain
.1(.1) = .01
Rain-Warm
.1(.4) = .04
Rain-Hot
.1(.5) = .05
Warm-Rain
.4(.1) = .04
Warm-Warm
.4(.4) = .16
Warm-Hot
.4(.5) = .20
Hot-Rain
.5(.1) = .05
Hot-Warm
.5(.4) = .20
Hot-Hot
.5(.5) = .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 probability
Rain-Rain
.01
Rain-Warm
.08
Rain-Hot
.10
Warm-Warm
.16
Warm-Hot
.40
Hot-Hot
.25
Finally, the joint values are the sums of the values of the two companies for the particular state.
Joint value
$250,000 + 250,000 =
$500,000
$250,000 + 425,000 =
675,000
$250,000 + 875,000 =
1,125,000
$425,000 + 425,000 =
850,000
$425,000 + 875,000 =
1,300,000
$875,000 + 875,000 =
1,750,000
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 reduced to the value of the company if the face value of the debt is greater
Possible states
Joint Prob.
Joint Value
Debt Value
Stock Value
Rain-Rain
.01
$500,000
$500,000
$0
Rain-Warm
.08
675,000
675,000
0
Rain-Hot
.10
1,125,000
850,000
275,000
Warm-Warm
.16
850,000
850,000
0
Warm-Hot
.40
1,300,000
850,000
450,000
Hot-Hot
.25
1,750,000
850,000
900,000
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:
Possible states
Probability
Debt Value
Rain
.10
$250,000
Warm
.40
425,000
Hot
.50
425,000
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: