1. Alpha Natural Resources (ANR), a coal producer, buys a large but privately held coal producer in China. As a result of the cross-border acquisition of a private company, ANR’s standard deviation of returns is reduced from 50 percent to 30 percent and its correlation with the market falls from 0.95 to 0.75. Assume that the standard deviation and return of the market remain unchanged at 25 percent and 10 percent, respectively, and that the risk-free rate is 3 percent.

A. Calculate the beta of ANR stock and its expected return before the acquisition.

B. Calculate the expected return after the acquisition.

2. Mr. Miles observes the strong demand for iPods and iPhones and wants to invest in Apple stock. Unfortunately, Mr. Miles doesn’t know the return he should expect from his investment. He has been given a risk-free rate of 3 percent, a market return of 10 percent, and Apple’s beta of 1.5.
A. Calculate Apple’s expected return.
B. An analyst looking at the same information decides that the past performance of Apple is not representative of its future performance. He decides that, given the increase in Apple’s market capitalization, Apple acts much more like the market than before and thinks Apple’s beta should be closer to 1.1. What is the analyst’s expected return for Apple stock?