Question

Can you solve for the following? Thanks!

You are analyzing the beta for IBM and have broken down the company into four broad business groups S 20 billion $ 2.0 billion 1.0 billion S 3.0 billion 1.00 Estimate the beta for IBM as a company. Is this beta going to be equal to the beta estimated by regressing past retums on IBM stock against a market index. Why or Why b In he treasury bond rate ts75% estimate the cost of equity for IBM. Estimate the cost of equity for each divisaon. Which cost of equity would you use to value the pnnter division? oc.Assume that IBM divests itself of the mainframe business and pays the cash out as a dividend. Estimate the beta for IBM after the divestiture. (IBM had S 1 billion in debt outstanding,)

Answer 1

a) Beta as a whole=sum of product of individual beta*market weight of each
Wt of mainframes= equity of main frames/total market value of firm
=2/(2+2+1+3)=25%
wt of personal computers=2/(2+2+1+3)=25%
Wt of software=1/(2+2+1+3)=12.5%
wt of printers=3/(2+2+1+3)=37.5%
unlevered Beta of IBM=(1.1*25%)+(1.5*25%)+(2*12.5%)+(1*37.5%)=1.275
We can find levered beta as well assuming tax rate as 40% and market return as 13%
levered beta=unlevered beta*(1+(D/E)*(1-tax))
D/E=1/8 and tax=40%
levered beta=1.275*(1+(1/8)*(1-40%))
=1.371

The beta estimated by regressing past returns will not be same as above since many factors would have been chnaged now and past

b)Risk free=7.5% , here we use levered beta
cost of equity using capm
=risk free+(beta*(market return-risk free))
=7.5%+(1.371*(13%-7.5%))
=15.04%
Levered Beta = Unlevered x (1 + (1 –Tax Rate) (D/E))
Mainframes=1.10 x (1+ (1 – 0.4) (1/8))=1.1825
PCs = 1.50 x (1+ (1 – 0.4) (1/8))=1.6125
Software = 2.00 x (1+ (1 – 0.4) (1/8))=2.15
Printers = 1.00 x (1+ (1 – 0.4) (1/8))=1.075

cost of equity of each division:
Main frames=7.5%+(1.1825*(13%-7.5%))=14%
PC=7.5%+(1.6125*(13%-7.5%))=16.37%
Software=7.5%+(2.15*(13%-7.5%))=19.33%
printers=7.5%+(1.075*(13%-7.5%))=13.41%
cost of equity for printer divison is 13.41%

c)Since mainframe division is sold at market value of 2bn and we are assuming out of 1bn of debt 0.25bn of debt is for mainframes so the amount we genertae out of sale is 2.25bn and this is paid as dividend .
current value of firm=(2+1+3)+0,75=6.75bn
debt to equiy=0.75/6
Unlevered beta=(2.0/6.0) (1.50) + (1.0/6.0)(2.00) + (3.0/6.0)(1.0) = 1.33
Levered Beta = Unlevered x (1 + (1 –Tax Rate) (D/E))
=1.33*(1+(1-40%)*(0.75/6))
=1.43