**Firm-wide
versus divisional cost of capital**

This issue concerns any firm with
two or more divisions that differ in risk from each other. As each division
considers investment opportunities, it must use an interest rate (cost of
capital) to evaluate the effects of expected cash flows in differing time
periods. This interest rate is also called a "cutoff" rate. It is the
minimum rate of return acceptable for projects in that division. The decision
as to the appropriate cutoff rate is critical and is typically made at the
highest levels of the firm. A firm-wide rate would be determined from the
average risk of the whole firm. If a multidivisional firm uses a firm-wide
cutoff rate, this rate will be too high for low-risk divisions and too low for
high-risk divisions. The firm will accept bad high-risk projects and reject
good low-risk projects. It is therefore necessary to estimate divisional cutoff
rates that will reflect the risk of each division. In addition, because this
process involves political rivalries within the firm, the approach used to
justify these rates must be as comprehensible as possible.

The cost of equity capital for a
firm is estimated from its beta using the security market line. Individual
divisions typically don't have separate stocks and therefore beta can't be
calculated for them directly. In order to estimate the beta of each division we
first find stand-alone companies comparable to our division. The betas of these
companies are then adjusted to remove the effects of financial leverage. The
reason for this is to remove the variation between these comparable companies
that is caused by variations in financial leverage. The average
"unlevered" beta for each division is then calculated. This unlevered
beta may then be used in the security market line, to estimate a
"pure-equity" cutoff rate. (Theoretically, the unlevered beta should
really be relevered at a rate appropriate for each division and averaged in
with the cost of debt to obtain a weighted average cost of capital. We will not
carry it any further than the "pure-equity" rate on the final
however.)

Example:
Comparable Company has a beta of .1.5 and a debt to assets of 46%. Assume a tax
rate of 40%. Also assume that the risk free rate is 5% and the expected return
on the market is 11%. Find its pure equity cost of capital.

First,
compute the Debt to Equity= Debt to Assets/Equity to Assets. .85=.46/(1-.46)

Then,
Unlevered Beta = Beta/[1+(1-Tax Rate)(Debt to Equity)] .99 = 1.5/[1+(1-.4)*(.85)]

The
pure equity cost of capital is .109 =
.05+ (.06*.99)