Question

2 You are analyzing the beta for IBM and have broken down the company into four broad business 3 Business Group 4 Mainframes 5 Personal Computers 6 Software 7 Printers groups, with market values and betas for each group Market Value of Equity $ 2.0 billion $ 2.0 billiorn Beta 1.10 1.50 2.00 1.00 $1.0 billion S 3.0 billiorn 8 a. Estimate the beta for IBM as a company. Is this beta going to be equal to the beta estimated by regressing past returns on IBM stock against a market index. Why or Why not? b. If the treasury bond rate is 7.5%, estimate the cost of equity for IBM. Estimate the cost of equity for each division. Which cost of equity would you use to value the printer division? 10 C. 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 $ 1 billion in debt outstanding.) 12 13 14 15 16 17 18 19 20

Answer 1

a) Beta of Company = Weighted average of Beta of different business groups with market value of equity as weight

= (2*1.1 + 2*1.5 + 1*2 + 3*1)/(2+2+1+3) = 1.28

Beta from regression of IBM stock over a correctly chosen time horizon should ideally be the same as the above calculated Beta. Any difference in beta would be due to difference in choice of model used to calculate business groups' beta. The difference in beta symbolises difference in pricing of risk.

b)

Here, we have been given treasury bond which gives us the risk free rate. Hence, Risk Free Rate = 7.5%.

We also need the market risk premium to get cost of equity. Let's assume market risk premium to be 2.5%. Also, a market risk premium of 2.5% means total market risk is 10% (ie 7.5% + 2.5%).

Cost of Equity of IBM = Risk Free Rate + Beta * (Market Risk Premium) = 7.5% + 1.28*2.5% = 10.69%

Similarly, we can get cost of equity for each division by same formula.

Hence, the Cost of Equity are:

	MV($Bn)	Beta	Cost of Equity
Mainframe	2	1.1	10.25%
Personal Computers	2	1.5	11.25%
Software	1	2	12.50%
Printers	3	1	10.00%

For the printer division's valuation, we'll take it's own beta & cost of equity. Hence, it's cost of Equity = 10%.

c)

On divestment of mainframe business, IBM will receive $ 2 Bn in cash. Considering it has $1 Bn in debt. Hence, it can payoff/netoff debt against cash that IBM would receive as debt holders have first right to cash flow to firm.

So, the total equity value of IBM = Market Value of Personal Computers + Market Value of Software + Market Value of Printers + Cash - Debt = 2 + 1 +3 + 2 - 1 = $ 7 Bn

To calculate the beta of IBM now, we'll need to tale the weighted average again like in the above case. Only the beta for cash will be 0 due to no risk in it.

Beta of Company after divestiture = Weighted average of Beta of different business groups with market value of equity as weight

= (2*1.5 + 1*2 + 3*1+1*0)/(2+1+3+1) = 1.14