a) International Business Machine (IBM) stock currently (2015) pays $1.30 per sh
ID: 2760211 • Letter: A
Question
a) International Business Machine (IBM) stock currently (2015) pays $1.30 per share quarterly dividend (the dividend was $0.50 per share in 2008). Assuming constant growth, what is the growth rate on the IBM stock dividend? b) Find the beta for IBM stock, and the current interest rate on 6-month T-bill. c) For the past 5 years, the Dow Jones Industrial Average went from 12,380.05 to 17,576.96. Assume it represents the expected return for the market portfolio, calculated the expected return for IBM stock based on CAPM? d) Based the closing price of IBM stock on 4/08/16, what is the yield of IBM stock? Is this stock over-priced or underpriced?
Explanation / Answer
a) The total number of quarters=(2015-2008)*4=7*4=28
Let the the growth rate on the IBM stock dividend be r therefore,
0.50*(1+r/4)28=1.30 =>(1+r/4)28=1.30/0.50=2.60 =>1+r/4=2.601/28 =>1+r/4=1.034714361
=>r=4*(1.034714361-1)=0.138857444=0.1389=13.89%
Therefore the growth rate on the IBM stock dividend is 13.89% per annum or 3.47% per quarter.
b)The beta for IBM stock is 0.79 and the current interest rate on 6-month T-bill is 0.35%.
c)expected return for the market portfolio=(17,576.96/12,380.05)^(1/5)-1=0.072616=7.26%
expected return for IBM stock based on CAPM=0.35%+0.79*(7.26%-0.35%)
expected return for IBM stock based on CAPM=0.35%+0.79*(6.91%)
expected return for IBM stock based on CAPM=0.35%+5.4589%
expected return for IBM stock based on CAPM=5.81%
d)The closing price of IBM stock on 4/08/16=$139.35
quarterly yield of IBM stock=(1.30*(1+.0.347)^8)/139.35=1.23%
The return for IBM stock =4*1.23%+13.89%=18.81%>5.81% expected return for IBM stock based on CAPM therefore the Price of IBM should decrease so that the expected return for IBM stock comes down to the CAPM level therefore the stock is over-priced.
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