I attached the question and the answer and I highlight the part need to explain

Question

I attached the question and the answer and I highlight the part need to explain

You work for a firm that is trying to decide whether they want to expand their operations by buying another company that caters to a different industry. The company thinks that with the resulting synergies between the two firms, there will be enough cost savings and economies of scale to make the new venture extremely profitable. The company’s current revenue stream is $50MM with negligible costs. For the purposes of this exercise only, let us assume that the costs are zero. If they bought the company, it would initially cost them $4MM with annual ongoing costs of $1MM.

The president of the firm asked you to conduct an analysis. The time period that you are looking at is one year with six month increments. The current risk-free rate is 4.00%. Your current research has shown that the standard deviation of the revenues is 55%. Does it makes sense for your firm to buy the company?

Explanation / Answer

The explanation part is

When you have calculated the up move as 1.475 and the down move= 0.678

Then if the bus of company's revenue is 50$ million today after 1 year it will be either 50*1.475= 73.75$ M

And if there is a Down move the value will be= 50*0.678= 33.90$ M

At t2 the value at upper node = 73.75* 1.475= 108.78$

The middle Node = 73.75* 0.678= 50 or 33.9* 1.475= 50$

The lower node= 33.9* 0.678= 22.98$ M

When calculating the present values of the expected outcomes at t2, By using the formulae we get the values of outcomes at t1= 72.78 and 33.89 $ million.

Then we will use the incremental cost of 4$ million i.e. if there is a upward trend then only the company will continue operations so we get 72.78$ M - 4$M= 68.78$

But if there is a downward trend I.e. the value of revenue goes down to 33.89$ M then the company will abandon this option and hence no payout.

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