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# Beta and Required Rate of Return of a Holding Company

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Bill Gates Corporation is a holding company with four main subsidiaries. The percentage of its business coming from each of the subsidiaries, and their respective betas, are as follows:

Software 45% 1.50
Hardware 25 1.20
Outerwear 10 0.90
Underwear 20 0.60

a. What is the holding company's beta?

b. Assume that the risk-free rate is 4 percent and the market risk premium is 9.0 percent. What is the holding company's required rate of return?

c. An analyst predicts that this stock is expected to provide a return of 16.0%. Is the analyst optimistic or pessimistic given your answer in part a? (Circle 0ne)

optimistic pessimistic

d. Gates Corp. is considering a change in its strategic focus: it will reduce its reliance on the software subsidiary, so the percentage of its business from this subsidiary will be 30 percent. At the same time, the company will increase its reliance on the outerwear division, so the percentage of its business from that subsidiary will rise to 25 percent. What will be the new beta coefficient and shareholder required rate of return if the company adopts these changes?

Software 30% 1.50
Hardware 25 1.20
Outerwear 25 0.90
Underwear 20 0.60

#### Solution Summary

This solution illustrates how to compute the beta and required rate of return of a holding company.

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## Beta, and rate of return

ABC Company is a holding company with three subsidiaries. The following data pertains to these subsidiaries:

A 50 .8
B 30 1.1
C 20 1.2

1. What is the holding company's beta?

2. Assume that the RFR is 5% and MRP is 4%, what is the holding company required rate of return?

3. Assume that ABC is planning to acquire M, the following are data pertains to this option:

The business percentage of M will be 40%

The beta of M is estimated to be 1.1

The other subsidiaries business percentages will remain in the same proportions as before.

What is the shareholders required rate of return if the company acquires M?

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