Chicago Savings Corp. is planning to make an offer for Ernie’s Bank & Trust. The stock of Ernie’s Bank & Trust is currently selling for \(44 a share.

a.If the tender offer is planned at a premium of 50 percent over market price, what will be the value offered per share for Ernie’s Bank & Trust?

b.Suppose before the offer is actually announced, the stock price of Ernie’s Bank & Trust goes to \)60 because of strong merger rumors. If you buy the stock at that price and the merger goes through (at the price computed in part a), what will be your percentage gain?

c.Because there is always the possibility that the merger could be called off after it is announced, you also want to consider your percentage loss if that happens. Assume you buy the stock at \(60 and it falls back to its original value after the merger cancellation, what will be your percentage loss?

d. If there is an 80 percent probability that the merger will go through when you buy the stock at \)60, and only a 20 percent chance that it will be called off, does this appear to be a good investment? Compute the expected value of the return on the investment.

Step by step solution

01

Definition of expected value of return on investment

The expected value of the return on investment is the estimated value of the return earned from investment.

02

Calculation of offered per share value

$\begin{array}{rcl}\mathbf{Offered}\mathbf{}\mathbf{Per}\mathbf{}\mathbf{Share}\mathbf{}\mathbf{Value}& \mathbf{=}& \mathbf{Current}\mathbf{}\mathbf{Price}\mathbf{+}\mathbf{50}\mathbf{\%}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Current}\mathbf{}\mathbf{Price}\\ & \mathbf{=}& \mathbf{\$}\mathbf{44}\mathbf{+}\mathbf{\$}\mathbf{22}\\ & \mathbf{=}& \mathbf{\$}\mathbf{66}\end{array}$

Hence, the offered per share price is $66.

03

Calculation of profit percentage

$\begin{array}{rcl}\mathbf{Profit}\mathbf{}\mathbf{Percentage}& \mathbf{=}& \frac{\mathbf{Price}}{\mathbf{Purchase}\mathbf{}\mathbf{Price}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{6}}{\mathbf{\$}\mathbf{60}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \mathbf{10}\mathbf{\%}\end{array}$

Hence, the profit percentage is 10%.

04

Calculation of loss percentage

$\begin{array}{rcl}\mathbf{Loss}\mathbf{}\mathbf{Percentage}& \mathbf{=}& \frac{\mathbf{Loss}}{\mathbf{Purchase}\mathbf{}\mathbf{Price}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{16}}{\mathbf{\$}\mathbf{60}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \mathbf{26}\mathbf{.}\mathbf{67}\mathbf{\%}\end{array}$

Hence, the loss percentage is 26.67%.

05

Calculation of excepted value of return on investment

Let us assume,

P₁is the probability of a merger

P₂ is the probability of the merger not being placed

R₁is the price of purchase when the merger is taken place.

R₂ is the price of purchase if the merger is not taking place.

$\begin{array}{rcl}\mathbf{Expected}\mathbf{}\mathbf{Value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Return}\mathbf{}\mathbf{on}\mathbf{}\mathbf{Investment}& \mathbf{=}& \left(P_1\times R_1\right)\mathbf{+}\left(P_2\times R_2\right)\\ & \mathbf{=}& \left(80\%\times \$60\right)\mathbf{+}\left(20\%\times \$44\right)\\ & \mathbf{=}& \mathbf{\$}\mathbf{48}\mathbf{+}\mathbf{\$}\mathbf{8}\mathbf{.}\mathbf{8}\\ & \mathbf{=}& \mathbf{\$}\mathbf{56}\mathbf{.}\mathbf{8}\end{array}$

Yes, this appears a good investment.

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